WEBVTT Kind: captions Language: en 00:00:00.080 --> 00:00:01.790 align:start position:0% our<00:00:00.280> next<00:00:00.480> speaker<00:00:00.799> will<00:00:01.040> talk<00:00:01.199> about<00:00:01.480> Beyond 00:00:01.790 --> 00:00:01.800 align:start position:0% our next speaker will talk about Beyond 00:00:01.800 --> 00:00:04.190 align:start position:0% our next speaker will talk about Beyond recours<00:00:02.159> of<00:00:02.480> approving<00:00:02.879> for<00:00:03.199> starnet<00:00:03.919> please 00:00:04.190 --> 00:00:04.200 align:start position:0% recours of approving for starnet please 00:00:04.200 --> 00:00:12.350 align:start position:0% recours of approving for starnet please welcome<00:00:05.000> gon 00:00:12.350 --> 00:00:12.360 align:start position:0% 00:00:12.360 --> 00:00:16.349 align:start position:0% CER<00:00:13.360> hi 00:00:16.349 --> 00:00:16.359 align:start position:0% 00:00:16.359 --> 00:00:19.109 align:start position:0% everyone<00:00:17.359> let's<00:00:17.520> see<00:00:17.680> if<00:00:17.800> you<00:00:17.880> can<00:00:18.039> hear 00:00:19.109 --> 00:00:19.119 align:start position:0% everyone let's see if you can hear 00:00:19.119 --> 00:00:23.070 align:start position:0% everyone let's see if you can hear me<00:00:20.119> okay<00:00:20.439> so<00:00:21.519> uh<00:00:22.519> the<00:00:22.640> goal<00:00:22.840> of<00:00:22.920> this 00:00:23.070 --> 00:00:23.080 align:start position:0% me okay so uh the goal of this 00:00:23.080 --> 00:00:24.750 align:start position:0% me okay so uh the goal of this presentation<00:00:23.480> is<00:00:23.640> to<00:00:23.760> talk<00:00:24.039> about<00:00:24.359> everything 00:00:24.750 --> 00:00:24.760 align:start position:0% presentation is to talk about everything 00:00:24.760 --> 00:00:26.470 align:start position:0% presentation is to talk about everything Beyond<00:00:25.080> recursive<00:00:25.599> proving<00:00:26.039> but<00:00:26.199> I'm<00:00:26.320> not 00:00:26.470 --> 00:00:26.480 align:start position:0% Beyond recursive proving but I'm not 00:00:26.480 --> 00:00:28.470 align:start position:0% Beyond recursive proving but I'm not going<00:00:26.679> to<00:00:26.920> assume<00:00:27.760> you<00:00:27.920> know<00:00:28.160> everything 00:00:28.470 --> 00:00:28.480 align:start position:0% going to assume you know everything 00:00:28.480 --> 00:00:31.589 align:start position:0% going to assume you know everything about<00:00:28.760> proving<00:00:29.199> or<00:00:29.400> recursive<00:00:30.160> proving<00:00:31.160> uh<00:00:31.279> so 00:00:31.589 --> 00:00:31.599 align:start position:0% about proving or recursive proving uh so 00:00:31.599 --> 00:00:34.830 align:start position:0% about proving or recursive proving uh so I'll<00:00:31.800> just<00:00:31.960> begin<00:00:32.239> with<00:00:32.399> the<00:00:32.599> basics<00:00:33.120> and<00:00:33.840> uh 00:00:34.830 --> 00:00:34.840 align:start position:0% I'll just begin with the basics and uh 00:00:34.840 --> 00:00:37.229 align:start position:0% I'll just begin with the basics and uh you'll<00:00:35.440> uh<00:00:35.840> follow<00:00:36.160> me<00:00:36.440> I 00:00:37.229 --> 00:00:37.239 align:start position:0% you'll uh follow me I 00:00:37.239 --> 00:00:40.110 align:start position:0% you'll uh follow me I assume<00:00:38.239> so<00:00:38.719> uh<00:00:38.840> let's<00:00:39.079> talk<00:00:39.280> about<00:00:39.480> the<00:00:39.680> basics 00:00:40.110 --> 00:00:40.120 align:start position:0% assume so uh let's talk about the basics 00:00:40.120 --> 00:00:42.470 align:start position:0% assume so uh let's talk about the basics of<00:00:40.280> a<00:00:40.440> validity<00:00:40.879> rollup<00:00:41.440> what<00:00:41.760> uh<00:00:41.879> composes<00:00:42.320> a 00:00:42.470 --> 00:00:42.480 align:start position:0% of a validity rollup what uh composes a 00:00:42.480 --> 00:00:44.670 align:start position:0% of a validity rollup what uh composes a validity<00:00:42.879> rollup<00:00:43.440> you<00:00:43.559> have 00:00:44.670 --> 00:00:44.680 align:start position:0% validity rollup you have 00:00:44.680 --> 00:00:47.270 align:start position:0% validity rollup you have transactions<00:00:45.680> uh<00:00:45.960> sequencers<00:00:46.680> select<00:00:47.079> these 00:00:47.270 --> 00:00:47.280 align:start position:0% transactions uh sequencers select these 00:00:47.280 --> 00:00:49.830 align:start position:0% transactions uh sequencers select these transactions<00:00:48.039> Define<00:00:48.399> their<00:00:48.600> order<00:00:49.480> and<00:00:49.640> I'll 00:00:49.830 --> 00:00:49.840 align:start position:0% transactions Define their order and I'll 00:00:49.840 --> 00:00:51.470 align:start position:0% transactions Define their order and I'll use<00:00:50.000> the<00:00:50.120> term<00:00:50.360> sequencer<00:00:51.000> also<00:00:51.199> for 00:00:51.470 --> 00:00:51.480 align:start position:0% use the term sequencer also for 00:00:51.480 --> 00:00:53.389 align:start position:0% use the term sequencer also for execution<00:00:52.039> of<00:00:52.199> these<00:00:52.399> transactions<00:00:53.000> so<00:00:53.280> if 00:00:53.389 --> 00:00:53.399 align:start position:0% execution of these transactions so if 00:00:53.399 --> 00:00:55.549 align:start position:0% execution of these transactions so if you're<00:00:53.680> confused<00:00:54.280> by<00:00:54.480> base<00:00:54.800> rollups<00:00:55.359> where 00:00:55.549 --> 00:00:55.559 align:start position:0% you're confused by base rollups where 00:00:55.559 --> 00:00:57.150 align:start position:0% you're confused by base rollups where they<00:00:55.800> separate<00:00:56.199> the<00:00:56.320> sequencing<00:00:56.920> from 00:00:57.150 --> 00:00:57.160 align:start position:0% they separate the sequencing from 00:00:57.160 --> 00:01:00.389 align:start position:0% they separate the sequencing from execution<00:00:58.160> here<00:00:58.320> I'm<00:00:58.480> going<00:00:58.600> to<00:00:58.760> combine<00:00:59.160> them 00:01:00.389 --> 00:01:00.399 align:start position:0% execution here I'm going to combine them 00:01:00.399 --> 00:01:03.830 align:start position:0% execution here I'm going to combine them um<00:01:01.199> and<00:01:01.359> they<00:01:01.519> build<00:01:01.800> the<00:01:02.320> blocks<00:01:03.320> uh<00:01:03.480> once<00:01:03.680> we 00:01:03.830 --> 00:01:03.840 align:start position:0% um and they build the blocks uh once we 00:01:03.840 --> 00:01:06.550 align:start position:0% um and they build the blocks uh once we have<00:01:03.960> a<00:01:04.119> block<00:01:05.119> uh<00:01:05.640> the<00:01:05.760> way<00:01:06.000> a<00:01:06.159> validity 00:01:06.550 --> 00:01:06.560 align:start position:0% have a block uh the way a validity 00:01:06.560 --> 00:01:09.030 align:start position:0% have a block uh the way a validity rollup<00:01:07.000> works<00:01:07.439> is<00:01:07.640> that<00:01:07.960> it<00:01:08.159> proves<00:01:08.880> the 00:01:09.030 --> 00:01:09.040 align:start position:0% rollup works is that it proves the 00:01:09.040 --> 00:01:10.870 align:start position:0% rollup works is that it proves the validity<00:01:09.439> of<00:01:09.600> the<00:01:09.759> execution<00:01:10.320> of<00:01:10.520> these 00:01:10.870 --> 00:01:10.880 align:start position:0% validity of the execution of these 00:01:10.880 --> 00:01:13.789 align:start position:0% validity of the execution of these blocks<00:01:11.880> using<00:01:12.159> a<00:01:12.320> prover<00:01:12.720> instance<00:01:13.200> and<00:01:13.439> send 00:01:13.789 --> 00:01:13.799 align:start position:0% blocks using a prover instance and send 00:01:13.799 --> 00:01:16.990 align:start position:0% blocks using a prover instance and send this<00:01:14.080> sends<00:01:14.520> this<00:01:14.720> proof<00:01:15.680> per<00:01:15.960> block<00:01:16.680> to 00:01:16.990 --> 00:01:17.000 align:start position:0% this sends this proof per block to 00:01:17.000 --> 00:01:18.789 align:start position:0% this sends this proof per block to verify<00:01:17.360> our<00:01:17.600> contract<00:01:18.000> on<00:01:18.159> ethereum<00:01:18.560> on<00:01:18.680> the 00:01:18.789 --> 00:01:18.799 align:start position:0% verify our contract on ethereum on the 00:01:18.799 --> 00:01:21.429 align:start position:0% verify our contract on ethereum on the layer<00:01:19.040> underlying<00:01:19.479> layer<00:01:19.799> one<00:01:20.799> and<00:01:21.000> once<00:01:21.240> that 00:01:21.429 --> 00:01:21.439 align:start position:0% layer underlying layer one and once that 00:01:21.439 --> 00:01:22.789 align:start position:0% layer underlying layer one and once that proof<00:01:21.680> has<00:01:21.799> been 00:01:22.789 --> 00:01:22.799 align:start position:0% proof has been 00:01:22.799 --> 00:01:26.310 align:start position:0% proof has been accepted<00:01:23.799> uh<00:01:24.640> a<00:01:24.880> state<00:01:25.320> contract<00:01:25.840> tracking 00:01:26.310 --> 00:01:26.320 align:start position:0% accepted uh a state contract tracking 00:01:26.320 --> 00:01:28.830 align:start position:0% accepted uh a state contract tracking the<00:01:26.520> state<00:01:26.880> of<00:01:27.040> the<00:01:27.159> rollup<00:01:28.040> is<00:01:28.240> updated<00:01:28.720> with 00:01:28.830 --> 00:01:28.840 align:start position:0% the state of the rollup is updated with 00:01:28.840 --> 00:01:31.350 align:start position:0% the state of the rollup is updated with a<00:01:29.000> new<00:01:29.240> state<00:01:30.240> uh<00:01:30.520> together<00:01:30.759> with<00:01:30.880> the<00:01:31.079> state 00:01:31.350 --> 00:01:31.360 align:start position:0% a new state uh together with the state 00:01:31.360 --> 00:01:34.270 align:start position:0% a new state uh together with the state update<00:01:31.960> we<00:01:32.159> also<00:01:32.720> uh<00:01:32.920> add<00:01:33.399> what<00:01:33.479> we<00:01:33.640> call<00:01:33.880> State 00:01:34.270 --> 00:01:34.280 align:start position:0% update we also uh add what we call State 00:01:34.280 --> 00:01:37.230 align:start position:0% update we also uh add what we call State diff<00:01:35.280> and<00:01:35.960> uh<00:01:36.119> we<00:01:36.240> may<00:01:36.520> include<00:01:36.960> also 00:01:37.230 --> 00:01:37.240 align:start position:0% diff and uh we may include also 00:01:37.240 --> 00:01:39.710 align:start position:0% diff and uh we may include also messaging<00:01:37.799> between<00:01:38.200> the<00:01:38.320> layer<00:01:38.600> two<00:01:39.119> and<00:01:39.320> the 00:01:39.710 --> 00:01:39.720 align:start position:0% messaging between the layer two and the 00:01:39.720 --> 00:01:43.149 align:start position:0% messaging between the layer two and the validity<00:01:40.159> rollup<00:01:40.680> and<00:01:41.079> the<00:01:41.159> underlying 00:01:43.149 --> 00:01:43.159 align:start position:0% validity rollup and the underlying 00:01:43.159 --> 00:01:46.789 align:start position:0% validity rollup and the underlying Network<00:01:44.159> State<00:01:44.520> diff<00:01:45.200> just<00:01:45.360> to<00:01:45.600> make<00:01:45.880> sure<00:01:46.280> you 00:01:46.789 --> 00:01:46.799 align:start position:0% Network State diff just to make sure you 00:01:46.799 --> 00:01:48.069 align:start position:0% Network State diff just to make sure you understand<00:01:47.000> what<00:01:47.119> I<00:01:47.240> mean<00:01:47.439> when<00:01:47.560> I<00:01:47.719> talk<00:01:47.880> about 00:01:48.069 --> 00:01:48.079 align:start position:0% understand what I mean when I talk about 00:01:48.079 --> 00:01:51.149 align:start position:0% understand what I mean when I talk about State<00:01:48.399> diff<00:01:49.240> is<00:01:49.479> basically<00:01:50.200> the<00:01:50.600> update<00:01:51.000> to 00:01:51.149 --> 00:01:51.159 align:start position:0% State diff is basically the update to 00:01:51.159 --> 00:01:53.389 align:start position:0% State diff is basically the update to the<00:01:51.360> state<00:01:51.640> of<00:01:51.799> the<00:01:51.920> rollup<00:01:52.600> uh<00:01:52.759> resulting 00:01:53.389 --> 00:01:53.399 align:start position:0% the state of the rollup uh resulting 00:01:53.399 --> 00:01:56.830 align:start position:0% the state of the rollup uh resulting from<00:01:53.680> the<00:01:54.079> executed<00:01:55.159> block<00:01:56.159> uh<00:01:56.360> validity 00:01:56.830 --> 00:01:56.840 align:start position:0% from the executed block uh validity 00:01:56.840 --> 00:01:58.990 align:start position:0% from the executed block uh validity rollups<00:01:57.439> do<00:01:57.600> not<00:01:57.799> need<00:01:58.000> to<00:01:58.200> transmit<00:01:58.759> the 00:01:58.990 --> 00:01:59.000 align:start position:0% rollups do not need to transmit the 00:01:59.000 --> 00:02:02.029 align:start position:0% rollups do not need to transmit the actual<00:01:59.360> transaction<00:02:00.280> that<00:02:00.520> they<00:02:01.039> sequenced 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send much less much less data to the underlying<00:02:18.879> Network<00:02:19.400> in<00:02:19.519> order<00:02:19.760> to<00:02:19.879> be<00:02:20.000> able 00:02:20.190 --> 00:02:20.200 align:start position:0% underlying Network in order to be able 00:02:20.200 --> 00:02:21.710 align:start position:0% underlying Network in order to be able to<00:02:20.319> reconstruct<00:02:20.959> the<00:02:21.040> full<00:02:21.280> state<00:02:21.519> of<00:02:21.640> the 00:02:21.710 --> 00:02:21.720 align:start position:0% to reconstruct the full state of the 00:02:21.720 --> 00:02:24.309 align:start position:0% to reconstruct the full state of the layer<00:02:22.000> two<00:02:22.879> so<00:02:23.040> a<00:02:23.160> state<00:02:23.400> diff<00:02:23.640> is<00:02:23.760> basically 00:02:24.309 --> 00:02:24.319 align:start position:0% layer two so a state diff is basically 00:02:24.319 --> 00:02:26.190 align:start position:0% layer two so a state diff is basically just<00:02:24.840> the<00:02:25.040> locations<00:02:25.519> in<00:02:25.680> the<00:02:25.800> state<00:02:26.040> that 00:02:26.190 --> 00:02:26.200 align:start position:0% just the locations in the state that 00:02:26.200 --> 00:02:28.710 align:start position:0% just the locations in the state that have<00:02:26.360> changed<00:02:27.280> and<00:02:27.480> their<00:02:27.760> values<00:02:28.120> so<00:02:28.280> in<00:02:28.440> this 00:02:28.710 --> 00:02:28.720 align:start position:0% have changed and their values so in this 00:02:28.720 --> 00:02:31.150 align:start position:0% have changed and their values so in this simple<00:02:29.080> example<00:02:29.599> the<00:02:30.000> has<00:02:30.280> been<00:02:30.480> changed<00:02:30.840> into 00:02:31.150 --> 00:02:31.160 align:start position:0% simple example the has been changed into 00:02:31.160 --> 00:02:33.589 align:start position:0% simple example the has been changed into X<00:02:31.920> so<00:02:32.120> the<00:02:32.239> state<00:02:32.599> diff<00:02:32.800> of<00:02:32.920> the<00:02:33.080> transition 00:02:33.589 --> 00:02:33.599 align:start position:0% X so the state diff of the transition 00:02:33.599 --> 00:02:36.070 align:start position:0% X so the state diff of the transition from<00:02:33.840> State<00:02:34.080> one<00:02:34.280> to<00:02:34.440> state<00:02:34.680> two<00:02:34.920> is<00:02:35.120> just<00:02:35.319> a 00:02:36.070 --> 00:02:36.080 align:start position:0% from State one to state two is just a 00:02:36.080 --> 00:02:38.790 align:start position:0% from State one to state two is just a single<00:02:36.440> element<00:02:37.160> change<00:02:37.680> location<00:02:38.120> 3<00:02:38.519> to 00:02:38.790 --> 00:02:38.800 align:start position:0% single element change location 3 to 00:02:38.800 --> 00:02:40.630 align:start position:0% single element change location 3 to Value 00:02:40.630 --> 00:02:40.640 align:start position:0% Value 00:02:40.640 --> 00:02:44.309 align:start position:0% Value x<00:02:41.640> what<00:02:41.760> does<00:02:41.920> it<00:02:42.120> mean<00:02:42.560> to<00:02:42.879> prove<00:02:43.200> a<00:02:43.400> block<00:02:44.080> so 00:02:44.309 --> 00:02:44.319 align:start position:0% x what does it mean to prove a block so 00:02:44.319 --> 00:02:45.869 align:start position:0% x what does it mean to prove a block so basically<00:02:44.959> what<00:02:45.080> we're<00:02:45.239> doing<00:02:45.519> is<00:02:45.680> we're 00:02:45.869 --> 00:02:45.879 align:start position:0% basically what we're doing is we're 00:02:45.879 --> 00:02:49.990 align:start position:0% basically what we're doing is we're using<00:02:46.280> the<00:02:46.519> context<00:02:47.080> of<00:02:47.599> uh<00:02:48.599> of<00:02:48.959> uh<00:02:49.400> proof<00:02:49.879> in 00:02:49.990 --> 00:02:50.000 align:start position:0% using the context of uh of uh proof in 00:02:50.000 --> 00:02:51.509 align:start position:0% using the context of uh of uh proof in order<00:02:50.319> to 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new state B and 00:03:03.080 --> 00:03:05.110 align:start position:0% State a resulting in a new state B and the<00:03:03.239> resulting<00:03:03.680> stative<00:03:04.280> between<00:03:04.640> State<00:03:04.920> a 00:03:05.110 --> 00:03:05.120 align:start position:0% the resulting stative between State a 00:03:05.120 --> 00:03:08.190 align:start position:0% the resulting stative between State a and<00:03:05.319> state<00:03:05.680> B<00:03:06.400> is<00:03:06.760> such<00:03:06.959> and<00:03:07.200> such<00:03:07.920> so<00:03:08.080> the 00:03:08.190 --> 00:03:08.200 align:start position:0% and state B is such and such so the 00:03:08.200 --> 00:03:10.149 align:start position:0% and state B is such and such so the statement<00:03:08.680> is<00:03:08.959> the<00:03:09.159> transactions<00:03:09.720> were 00:03:10.149 --> 00:03:10.159 align:start position:0% statement is the transactions were 00:03:10.159 --> 00:03:12.390 align:start position:0% statement is the transactions were correctly<00:03:10.640> sequenced<00:03:11.239> and<00:03:11.480> the<00:03:11.799> input<00:03:12.120> State 00:03:12.390 --> 00:03:12.400 align:start position:0% correctly sequenced and the input State 00:03:12.400 --> 00:03:14.030 align:start position:0% correctly sequenced and the input State results<00:03:12.760> in<00:03:12.879> the<00:03:13.000> output 00:03:14.030 --> 00:03:14.040 align:start position:0% results in the output 00:03:14.040 --> 00:03:16.670 align:start position:0% results in the output State<00:03:15.040> what<00:03:15.159> are<00:03:15.280> we<00:03:15.400> doing<00:03:15.640> on<00:03:15.879> layer<00:03:16.159> one<00:03:16.440> for 00:03:16.670 --> 00:03:16.680 align:start position:0% State what are we doing on layer one for 00:03:16.680 --> 00:03:19.630 align:start position:0% State what are we doing on layer one for the<00:03:16.799> validity<00:03:17.239> rollup<00:03:18.239> in<00:03:18.440> this<00:03:18.720> simple<00:03:19.480> uh 00:03:19.630 --> 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costly in some cases we need to publish 00:03:28.840 --> 00:03:31.789 align:start position:0% costly in some cases we need to publish the<00:03:29.000> state<00:03:29.360> diff<00:03:29.920> typically<00:03:30.360> using<00:03:30.799> blobs<00:03:31.280> on 00:03:31.789 --> 00:03:31.799 align:start position:0% the state diff typically using blobs on 00:03:31.799 --> 00:03:34.390 align:start position:0% the state diff typically using blobs on ethereum<00:03:32.799> and<00:03:32.920> we<00:03:33.040> need<00:03:33.200> to<00:03:33.400> update<00:03:33.799> the<00:03:33.959> state 00:03:34.390 --> 00:03:34.400 align:start position:0% ethereum and we need to update the state 00:03:34.400 --> 00:03:37.070 align:start position:0% ethereum and we need to update the state which<00:03:34.519> is<00:03:34.720> typically<00:03:35.239> some<00:03:35.599> contract<00:03:36.040> call<00:03:36.840> of 00:03:37.070 --> 00:03:37.080 align:start position:0% which is typically some contract call of 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large<00:03:46.480> this<00:03:46.599> is<00:03:46.799> all<00:03:47.040> this<00:03:47.159> is<00:03:47.400> fine<00:03:48.080> but<00:03:48.200> if<00:03:48.319> we 00:03:48.429 --> 00:03:48.439 align:start position:0% large this is all this is fine but if we 00:03:48.439 --> 00:03:50.429 align:start position:0% large this is all this is fine but if we want<00:03:48.879> just<00:03:49.000> to<00:03:49.200> have<00:03:49.319> a<00:03:49.439> few<00:03:49.720> transactions<00:03:50.280> per 00:03:50.429 --> 00:03:50.439 align:start position:0% want just to have a few transactions per 00:03:50.439 --> 00:03:53.830 align:start position:0% want just to have a few transactions per block<00:03:50.680> on<00:03:50.799> Layer<00:03:51.080> Two<00:03:51.400> or<00:03:52.120> quick<00:03:52.840> finality 00:03:53.830 --> 00:03:53.840 align:start position:0% block on Layer Two or quick finality 00:03:53.840 --> 00:03:55.830 align:start position:0% block on Layer Two or quick finality this<00:03:54.000> can<00:03:54.200> become<00:03:54.599> quite<00:03:54.920> costly<00:03:55.480> so<00:03:55.680> the 00:03:55.830 --> 00:03:55.840 align:start position:0% this can become quite costly so the 00:03:55.840 --> 00:03:58.309 align:start position:0% this can become quite costly so the basic<00:03:56.159> validity<00:03:56.599> rollup<00:03:57.079> is<00:03:57.280> good<00:03:58.000> if<00:03:58.120> you 00:03:58.309 --> 00:03:58.319 align:start position:0% basic validity rollup is good if you 00:03:58.319 --> 00:04:00.750 align:start position:0% basic validity rollup is good if you have<00:03:58.599> either<00:03:58.840> a<00:03:58.959> very<00:03:59.159> large<00:03:59.439> block 00:04:00.750 --> 00:04:00.760 align:start position:0% have either a very large block 00:04:00.760 --> 00:04:02.630 align:start position:0% have either a very large block or<00:04:01.000> you<00:04:01.159> have<00:04:01.319> a<00:04:01.439> lot<00:04:01.560> of<00:04:01.799> traffic<00:04:02.400> and<00:04:02.519> then 00:04:02.630 --> 00:04:02.640 align:start position:0% or you have a lot of traffic and then 00:04:02.640 --> 00:04:04.630 align:start position:0% or you have a lot of traffic and then you<00:04:02.760> can<00:04:02.959> still<00:04:03.280> have<00:04:03.560> a<00:04:03.720> short<00:04:04.040> finality<00:04:04.480> on 00:04:04.630 --> 00:04:04.640 align:start position:0% you can still have a short finality on 00:04:04.640 --> 00:04:05.390 align:start position:0% you can still have a short finality on Layer 00:04:05.390 --> 00:04:05.400 align:start position:0% Layer 00:04:05.400 --> 00:04:09.030 align:start position:0% Layer Two<00:04:06.400> or<00:04:07.040> you<00:04:07.200> have<00:04:07.400> long<00:04:07.799> finality<00:04:08.720> then<00:04:08.879> it 00:04:09.030 --> 00:04:09.040 align:start position:0% Two or you have long finality then it 00:04:09.040 --> 00:04:11.670 align:start position:0% Two or you have long finality then it becomes<00:04:09.480> less<00:04:10.000> costly<00:04:11.000> but<00:04:11.159> it's<00:04:11.400> less 00:04:11.670 --> 00:04:11.680 align:start position:0% becomes less costly but it's less 00:04:11.680 --> 00:04:14.110 align:start position:0% becomes less costly but it's less effective<00:04:12.519> because<00:04:12.760> you<00:04:12.879> have<00:04:13.040> long 00:04:14.110 --> 00:04:14.120 align:start position:0% effective because you have long 00:04:14.120 --> 00:04:17.710 align:start position:0% effective because you have long finality<00:04:15.120> enter<00:04:15.840> recursive 00:04:17.710 --> 00:04:17.720 align:start position:0% finality enter recursive 00:04:17.720 --> 00:04:20.469 align:start position:0% finality enter recursive proving<00:04:18.720> recursive<00:04:19.280> proving<00:04:19.799> intends<00:04:20.280> to 00:04:20.469 --> 00:04:20.479 align:start position:0% proving recursive proving intends to 00:04:20.479 --> 00:04:23.110 align:start position:0% proving recursive proving intends to reduce<00:04:20.840> the<00:04:21.000> overhead<00:04:21.680> of<00:04:22.479> verifying<00:04:23.000> the 00:04:23.110 --> 00:04:23.120 align:start position:0% reduce the overhead of verifying the 00:04:23.120 --> 00:04:25.070 align:start position:0% reduce the overhead of verifying the proofs<00:04:23.479> per 00:04:25.070 --> 00:04:25.080 align:start position:0% proofs per 00:04:25.080 --> 00:04:27.790 align:start position:0% proofs per block<00:04:26.080> so<00:04:26.320> let's<00:04:26.520> begin<00:04:26.840> with<00:04:27.040> what<00:04:27.240> recursive 00:04:27.790 --> 00:04:27.800 align:start position:0% block so let's begin with what recursive 00:04:27.800 --> 00:04:29.870 align:start position:0% block so let's begin with what recursive proving<00:04:28.240> really<00:04:28.479> is<00:04:28.880> so<00:04:29.039> on<00:04:29.160> the<00:04:29.280> left<00:04:29.479> hand 00:04:29.870 --> 00:04:29.880 align:start position:0% proving really is so on the left hand 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and you want to prove that given<00:04:38.360> a<00:04:38.680> a<00:04:38.840> current<00:04:39.560> uh<00:04:40.039> given<00:04:40.280> an<00:04:40.479> input<00:04:41.160> or<00:04:41.400> a 00:04:41.590 --> 00:04:41.600 align:start position:0% given a a current uh given an input or a 00:04:41.600 --> 00:04:44.870 align:start position:0% given a a current uh given an input or a witness<00:04:42.120> if<00:04:42.199> you<00:04:42.600> like<00:04:43.600> uh<00:04:44.160> there<00:04:44.400> is<00:04:44.720> a 00:04:44.870 --> 00:04:44.880 align:start position:0% witness if you like uh there is a 00:04:44.880 --> 00:04:46.790 align:start position:0% witness if you like uh there is a correct<00:04:45.280> execution<00:04:45.880> of<00:04:46.000> the<00:04:46.199> statement 00:04:46.790 --> 00:04:46.800 align:start position:0% correct execution of the statement 00:04:46.800 --> 00:04:49.230 align:start position:0% correct execution of the statement resulting<00:04:47.280> in<00:04:47.400> a<00:04:47.560> given<00:04:47.880> output<00:04:48.880> and<00:04:49.039> what<00:04:49.120> the 00:04:49.230 --> 00:04:49.240 align:start position:0% resulting in a given output and what the 00:04:49.240 --> 00:04:51.870 align:start position:0% resulting in a given output and what the prover<00:04:49.639> does<00:04:49.960> it<00:04:50.199> basically<00:04:50.680> proves<00:04:51.560> that<00:04:51.720> the 00:04:51.870 --> 00:04:51.880 align:start position:0% prover does it basically proves that the 00:04:51.880 --> 00:04:53.710 align:start position:0% prover does it basically proves that the statement<00:04:52.240> was<00:04:52.400> run<00:04:52.680> correctly<00:04:53.039> on<00:04:53.160> the<00:04:53.280> input 00:04:53.710 --> 00:04:53.720 align:start position:0% statement was run correctly on the input 00:04:53.720 --> 00:04:56.749 align:start position:0% statement was run correctly on the input and<00:04:53.919> that<00:04:54.120> the<00:04:54.520> actual<00:04:54.880> output<00:04:55.400> is<00:04:55.919> the<00:04:56.080> given 00:04:56.749 --> 00:04:56.759 align:start position:0% and that the actual output is the given 00:04:56.759 --> 00:04:59.430 align:start position:0% and that the actual output is the given output<00:04:57.759> uh<00:04:58.080> the<00:04:58.240> proof<00:04:58.560> does<00:04:58.759> not<00:04:58.960> necessarily 00:04:59.430 --> 00:04:59.440 align:start position:0% output uh the proof does not necessarily 00:04:59.440 --> 00:05:02.070 align:start position:0% output uh the proof does not necessarily need<00:04:59.800> to<00:04:59.919> divulge<00:05:00.400> the<00:05:00.560> input<00:05:01.199> as<00:05:01.320> we<00:05:01.479> call<00:05:01.680> it 00:05:02.070 --> 00:05:02.080 align:start position:0% need to divulge the input as we call it 00:05:02.080 --> 00:05:04.629 align:start position:0% need to divulge the input as we call it zero<00:05:02.400> knowledge<00:05:02.840> proofs<00:05:03.800> but<00:05:03.919> if<00:05:04.039> you<00:05:04.240> like<00:05:04.440> to 00:05:04.629 --> 00:05:04.639 align:start position:0% zero knowledge proofs but if you like to 00:05:04.639 --> 00:05:06.110 align:start position:0% zero knowledge proofs but if you like to include<00:05:04.960> some<00:05:05.080> of<00:05:05.199> the<00:05:05.280> input<00:05:05.560> in<00:05:05.680> the<00:05:05.759> output 00:05:06.110 --> 00:05:06.120 align:start position:0% include some of the input in the output 00:05:06.120 --> 00:05:08.350 align:start position:0% include some of the input in the output you<00:05:06.199> can<00:05:06.360> just<00:05:06.600> copy<00:05:06.880> that<00:05:07.039> within<00:05:07.280> the 00:05:08.350 --> 00:05:08.360 align:start position:0% you can just copy that within the 00:05:08.360 --> 00:05:11.590 align:start position:0% you can just copy that within the statement<00:05:09.360> so<00:05:09.560> how<00:05:09.680> do<00:05:09.800> we<00:05:09.919> use<00:05:10.160> this<00:05:10.600> context 00:05:11.590 --> 00:05:11.600 align:start position:0% statement so how do we use this context 00:05:11.600 --> 00:05:13.790 align:start position:0% statement so how do we use this context uh<00:05:11.759> this<00:05:12.000> concept<00:05:12.639> to<00:05:12.880> create<00:05:13.199> recursive 00:05:13.790 --> 00:05:13.800 align:start position:0% uh this concept to create recursive 00:05:13.800 --> 00:05:16.270 align:start position:0% uh this concept to create recursive proving<00:05:14.680> basically<00:05:15.080> we<00:05:15.680> replace<00:05:16.120> the 00:05:16.270 --> 00:05:16.280 align:start position:0% proving basically we replace the 00:05:16.280 --> 00:05:18.070 align:start position:0% proving basically we replace the statement<00:05:16.720> with<00:05:16.840> a<00:05:16.960> new<00:05:17.199> statement<00:05:17.600> that<00:05:17.759> just 00:05:18.070 --> 00:05:18.080 align:start position:0% statement with a new statement that just 00:05:18.080 --> 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position:0% output one and proof two with output two you<00:05:27.960> use<00:05:28.160> a<00:05:28.400> statement<00:05:28.919> that<00:05:29.080> performs 00:05:29.749 --> 00:05:29.759 align:start position:0% you use a statement that performs 00:05:29.759 --> 00:05:32.230 align:start position:0% you use a statement that performs verification<00:05:30.720> which<00:05:30.840> is<00:05:31.039> just<00:05:31.280> an<00:05:31.520> algorithm 00:05:32.230 --> 00:05:32.240 align:start position:0% verification which is just an algorithm 00:05:32.240 --> 00:05:33.950 align:start position:0% verification which is just an algorithm right<00:05:32.440> so<00:05:32.880> there's<00:05:33.080> no<00:05:33.280> reason<00:05:33.680> that<00:05:33.800> you 00:05:33.950 --> 00:05:33.960 align:start position:0% right so there's no reason that you 00:05:33.960 --> 00:05:37.150 align:start position:0% right so there's no reason that you can't<00:05:34.600> uh<00:05:35.080> build<00:05:35.400> such<00:05:35.560> a<00:05:35.880> statement<00:05:36.880> and<00:05:37.000> the 00:05:37.150 --> 00:05:37.160 align:start position:0% can't uh build such a statement and the 00:05:37.160 --> 00:05:39.870 align:start position:0% can't uh build such a statement and the result<00:05:37.560> is<00:05:38.280> the<00:05:38.400> two<00:05:38.639> outputs<00:05:39.360> the<00:05:39.520> original 00:05:39.870 --> 00:05:39.880 align:start position:0% result is the two outputs the original 00:05:39.880 --> 00:05:41.430 align:start position:0% result is the two outputs the original outputs<00:05:40.319> you<00:05:40.520> just<00:05:40.680> copy<00:05:41.000> them<00:05:41.160> from<00:05:41.319> the 00:05:41.430 --> 00:05:41.440 align:start position:0% outputs you just copy them from the 00:05:41.440 --> 00:05:43.990 align:start position:0% outputs you just copy them from the input<00:05:41.680> to<00:05:41.840> the<00:05:41.919> output<00:05:42.919> so<00:05:43.280> when<00:05:43.440> we<00:05:43.639> prove 00:05:43.990 --> 00:05:44.000 align:start position:0% input to the output so when we prove 00:05:44.000 --> 00:05:46.350 align:start position:0% input to the output so when we prove this<00:05:44.240> statement<00:05:45.240> exactly<00:05:45.720> like<00:05:45.880> on<00:05:46.000> the<00:05:46.120> left 00:05:46.350 --> 00:05:46.360 align:start position:0% this statement exactly like on the left 00:05:46.360 --> 00:05:49.270 align:start position:0% this statement exactly like on the left hand<00:05:46.600> side<00:05:47.199> the<00:05:47.360> result<00:05:47.680> is<00:05:47.800> a<00:05:48.039> proof<00:05:49.039> and<00:05:49.160> the 00:05:49.270 --> 00:05:49.280 align:start position:0% hand side the result is a proof and the 00:05:49.280 --> 00:05:50.790 align:start position:0% hand side the result is a proof and the outputs<00:05:49.720> that<00:05:49.840> we<00:05:49.919> want<00:05:50.080> to<00:05:50.199> generate<00:05:50.680> which 00:05:50.790 --> 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outputs 00:05:57.759 --> 00:06:01.189 align:start position:0% combined two proofs with two outputs into<00:05:58.120> one<00:05:58.440> proof<00:05:59.120> with<00:05:59.280> two<00:05:59.440> out 00:06:01.189 --> 00:06:01.199 align:start position:0% into one proof with two out 00:06:01.199 --> 00:06:04.029 align:start position:0% into one proof with two out outputs<00:06:02.199> now<00:06:02.360> we<00:06:02.479> can<00:06:02.639> use<00:06:02.880> this<00:06:03.160> construct<00:06:03.880> in 00:06:04.029 --> 00:06:04.039 align:start position:0% outputs now we can use this construct in 00:06:04.039 --> 00:06:07.350 align:start position:0% outputs now we can use this construct in order<00:06:04.319> to<00:06:04.880> combine<00:06:05.880> various<00:06:06.360> statements 00:06:07.350 --> 00:06:07.360 align:start position:0% order to combine various statements 00:06:07.360 --> 00:06:09.390 align:start position:0% order to combine various statements possibly<00:06:07.919> totally<00:06:08.440> different<00:06:08.800> statements 00:06:09.390 --> 00:06:09.400 align:start position:0% possibly totally different statements 00:06:09.400 --> 00:06:11.790 align:start position:0% possibly totally different statements from<00:06:09.680> different<00:06:10.160> sources<00:06:11.160> if<00:06:11.280> you<00:06:11.440> like<00:06:11.720> we 00:06:11.790 --> 00:06:11.800 align:start position:0% from different sources if you like we 00:06:11.800 --> 00:06:13.909 align:start position:0% from different sources if you like we can<00:06:12.080> prove<00:06:12.599> uh<00:06:12.800> statements<00:06:13.280> from<00:06:13.520> multiple 00:06:13.909 --> 00:06:13.919 align:start position:0% can prove uh statements from multiple 00:06:13.919 --> 00:06:18.510 align:start position:0% can prove uh statements from multiple rollups<00:06:15.120> even<00:06:16.120> uh<00:06:16.360> into<00:06:16.639> a<00:06:16.800> single<00:06:17.280> proof<00:06:18.280> and 00:06:18.510 --> 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in this 00:06:25.560 --> 00:06:27.670 align:start position:0% statements I I should say so in this diagram<00:06:25.960> you<00:06:26.080> can<00:06:26.240> see<00:06:27.000> four<00:06:27.319> different 00:06:27.670 --> 00:06:27.680 align:start position:0% diagram you can see four different 00:06:27.680 --> 00:06:29.189 align:start position:0% diagram you can see four different statements<00:06:28.319> there's<00:06:28.520> no<00:06:28.720> relationship 00:06:29.189 --> 00:06:29.199 align:start position:0% statements there's no relationship 00:06:29.199 --> 00:06:30.710 align:start position:0% statements there's no relationship between<00:06:29.639> them<00:06:29.800> each<00:06:29.919> of<00:06:30.039> them<00:06:30.199> has<00:06:30.319> their<00:06:30.479> own 00:06:30.710 --> 00:06:30.720 align:start position:0% between them each of them has their own 00:06:30.720 --> 00:06:33.510 align:start position:0% between them each of them has their own input<00:06:31.560> creates<00:06:32.039> the<00:06:32.160> own<00:06:32.440> their<00:06:32.599> own<00:06:32.840> output 00:06:33.510 --> 00:06:33.520 align:start position:0% input creates the own their own output 00:06:33.520 --> 00:06:36.110 align:start position:0% input creates the own their own output and<00:06:33.960> uh<00:06:34.120> using<00:06:34.520> recursive<00:06:35.000> proving<00:06:35.479> twice<00:06:35.960> in 00:06:36.110 --> 00:06:36.120 align:start position:0% and uh using recursive proving twice in 00:06:36.120 --> 00:06:38.909 align:start position:0% and uh using recursive proving twice in this<00:06:36.360> example<00:06:37.240> we<00:06:37.560> result<00:06:38.080> with<00:06:38.240> one<00:06:38.520> proof 00:06:38.909 --> 00:06:38.919 align:start position:0% this example we result with one proof 00:06:38.919 --> 00:06:40.990 align:start position:0% this example we result with one proof and<00:06:39.080> four 00:06:40.990 --> 00:06:41.000 align:start position:0% and four 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you<00:06:48.199> have<00:06:48.360> the<00:06:48.520> transactions<00:06:49.280> the 00:06:50.790 --> 00:06:50.800 align:start position:0% you have the transactions the 00:06:50.800 --> 00:06:52.909 align:start position:0% you have the transactions the sequencers<00:06:51.800> Define<00:06:52.120> the 00:06:52.909 --> 00:06:52.919 align:start position:0% sequencers Define the 00:06:52.919 --> 00:06:55.830 align:start position:0% sequencers Define the sequence<00:06:53.919> uh<00:06:54.280> execute<00:06:54.720> the<00:06:54.919> transactions<00:06:55.639> and 00:06:55.830 --> 00:06:55.840 align:start position:0% sequence uh execute the transactions and 00:06:55.840 --> 00:06:57.909 align:start position:0% sequence uh execute the transactions and create<00:06:56.160> blocks<00:06:56.680> just<00:06:56.879> like<00:06:57.080> before<00:06:57.520> in<00:06:57.720> this 00:06:57.909 --> 00:06:57.919 align:start position:0% create blocks just like before in this 00:06:57.919 --> 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with one<00:07:06.720> proof<00:07:07.720> as<00:07:07.840> opposed<00:07:08.160> to<00:07:08.319> four<00:07:08.639> proofs<00:07:08.960> in 00:07:09.110 --> 00:07:09.120 align:start position:0% one proof as opposed to four proofs in 00:07:09.120 --> 00:07:10.830 align:start position:0% one proof as opposed to four proofs in the<00:07:09.280> previous<00:07:09.680> example<00:07:10.039> in<00:07:10.199> the<00:07:10.479> basic 00:07:10.830 --> 00:07:10.840 align:start position:0% the previous example in the basic 00:07:10.840 --> 00:07:13.110 align:start position:0% the previous example in the basic validity<00:07:11.240> roll<00:07:11.520> up<00:07:12.199> and<00:07:12.360> this<00:07:12.520> proof<00:07:12.759> is<00:07:12.879> sent 00:07:13.110 --> 00:07:13.120 align:start position:0% validity roll up and this proof is sent 00:07:13.120 --> 00:07:15.710 align:start position:0% validity roll up and this proof is sent to<00:07:13.240> the<00:07:13.360> same<00:07:13.599> verifier<00:07:14.120> contract<00:07:14.479> on<00:07:14.639> layer 00:07:15.710 --> 00:07:15.720 align:start position:0% to the same verifier contract on layer 00:07:15.720 --> 00:07:19.950 align:start position:0% to the same verifier contract on layer one<00:07:16.720> then<00:07:17.560> for<00:07:17.879> every<00:07:18.199> block<00:07:19.000> a<00:07:19.160> state<00:07:19.479> update 00:07:19.950 --> 00:07:19.960 align:start position:0% one then for every block a state update 00:07:19.960 --> 00:07:21.990 align:start position:0% one then for every block a state update takes<00:07:20.280> place<00:07:20.520> on<00:07:20.680> layer<00:07:21.000> one<00:07:21.319> on<00:07:21.479> the<00:07:21.639> smart 00:07:21.990 --> 00:07:22.000 align:start position:0% takes place on layer one on the smart 00:07:22.000 --> 00:07:23.869 align:start position:0% takes place on layer one on the smart contract<00:07:22.360> that<00:07:22.520> tracks<00:07:22.879> the<00:07:23.039> state<00:07:23.360> of<00:07:23.560> the 00:07:23.869 --> 00:07:23.879 align:start position:0% contract that tracks the state of the 00:07:23.879 --> 00:07:27.230 align:start position:0% contract that tracks the state of the rollup<00:07:24.879> and<00:07:25.520> the<00:07:25.680> statives<00:07:26.520> per<00:07:26.720> block<00:07:27.080> are 00:07:27.230 --> 00:07:27.240 align:start position:0% rollup and the statives per block are 00:07:27.240 --> 00:07:30.309 align:start position:0% rollup and the statives per block are sent<00:07:27.560> to<00:07:27.759> layer<00:07:28.039> one<00:07:28.919> so<00:07:29.560> using<00:07:29.840> recursive 00:07:30.309 --> 00:07:30.319 align:start position:0% sent to layer one so using recursive 00:07:30.319 --> 00:07:32.830 align:start position:0% sent to layer one so using recursive proving<00:07:30.879> we've<00:07:31.120> basically<00:07:31.520> reduced<00:07:31.960> the<00:07:32.160> cost 00:07:32.830 --> 00:07:32.840 align:start position:0% proving we've basically reduced the cost 00:07:32.840 --> 00:07:36.710 align:start position:0% proving we've basically reduced the cost of<00:07:33.840> verifying<00:07:34.639> proofs<00:07:35.039> on<00:07:35.240> layer<00:07:35.520> one<00:07:36.400> but<00:07:36.560> we 00:07:36.710 --> 00:07:36.720 align:start position:0% of verifying proofs on layer one but we 00:07:36.720 --> 00:07:39.270 align:start position:0% of verifying proofs on layer one but we still<00:07:37.039> keep<00:07:37.879> uh<00:07:38.000> the<00:07:38.160> concept<00:07:38.520> of<00:07:38.759> publishing 00:07:39.270 --> 00:07:39.280 align:start position:0% still keep uh the concept of publishing 00:07:39.280 --> 00:07:43.230 align:start position:0% still keep uh the concept of publishing State<00:07:39.639> diffs<00:07:40.039> per<00:07:40.280> block<00:07:41.280> and<00:07:42.039> State<00:07:42.360> updates 00:07:43.230 --> 00:07:43.240 align:start position:0% State diffs per block and State updates 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because<00:07:52.639> sometimes<00:07:52.919> a<00:07:53.159> significant<00:07:53.800> cost<00:07:54.039> is 00:07:54.149 --> 00:07:54.159 align:start position:0% because sometimes a significant cost is 00:07:54.159 --> 00:07:56.629 align:start position:0% because sometimes a significant cost is on<00:07:54.280> the<00:07:54.440> verification<00:07:55.000> of<00:07:55.159> the<00:07:55.520> proof<00:07:56.520> uh 00:07:56.629 --> 00:07:56.639 align:start position:0% on the verification of the proof uh 00:07:56.639 --> 00:08:00.589 align:start position:0% on the verification of the proof uh State<00:07:56.960> updates<00:07:57.319> are<00:07:57.560> less<00:07:58.159> costly<00:07:59.159> but 00:08:00.589 --> 00:08:00.599 align:start position:0% State updates are less costly but 00:08:00.599 --> 00:08:03.469 align:start position:0% State updates are less costly but the<00:08:00.800> smaller<00:08:01.319> the<00:08:01.479> blocks<00:08:01.919> get<00:08:02.919> the<00:08:03.159> more 00:08:03.469 --> 00:08:03.479 align:start position:0% the smaller the blocks get the more 00:08:03.479 --> 00:08:05.029 align:start position:0% the smaller the blocks get the more significant<00:08:04.080> the<00:08:04.240> cost<00:08:04.479> of<00:08:04.599> these<00:08:04.759> State 00:08:05.029 --> 00:08:05.039 align:start position:0% significant the cost of these State 00:08:05.039 --> 00:08:08.469 align:start position:0% significant the cost of these State updates<00:08:05.520> become<00:08:06.199> so<00:08:07.199> this<00:08:07.560> allows<00:08:07.919> us<00:08:08.159> to 00:08:08.469 --> 00:08:08.479 align:start position:0% updates become so this allows us to 00:08:08.479 --> 00:08:11.869 align:start position:0% updates become so this allows us to improve<00:08:09.400> uh<00:08:09.639> to<00:08:09.919> reduce<00:08:10.919> uh<00:08:11.120> block<00:08:11.440> times<00:08:11.720> on 00:08:11.869 --> 00:08:11.879 align:start position:0% improve uh to reduce uh block times on 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00:08:27.350 align:start position:0% batching on the blocks on layer to but still<00:08:23.919> I<00:08:24.080> would<00:08:24.240> like<00:08:24.400> to<00:08:24.599> optimize<00:08:25.080> this 00:08:27.350 --> 00:08:27.360 align:start position:0% 00:08:27.360 --> 00:08:30.189 align:start position:0% further<00:08:28.360> which<00:08:28.560> brings<00:08:28.919> me<00:08:29.520> to<00:08:29.720> Beyond 00:08:30.189 --> 00:08:30.199 align:start position:0% further which brings me to Beyond 00:08:30.199 --> 00:08:32.029 align:start position:0% further which brings me to Beyond recursive<00:08:30.720> proving<00:08:31.120> which<00:08:31.240> is<00:08:31.360> the<00:08:31.560> topic<00:08:31.840> of 00:08:32.029 --> 00:08:32.039 align:start position:0% recursive proving which is the topic of 00:08:32.039 --> 00:08:33.029 align:start position:0% recursive proving which is the topic of my 00:08:33.029 --> 00:08:33.039 align:start position:0% my 00:08:33.039 --> 00:08:36.029 align:start position:0% my discussion<00:08:34.039> uh<00:08:34.599> we<00:08:34.719> want<00:08:34.880> to<00:08:35.080> build<00:08:35.640> something 00:08:36.029 --> 00:08:36.039 align:start position:0% discussion uh we want to build something 00:08:36.039 --> 00:08:38.509 align:start position:0% discussion uh we want to build something which<00:08:36.200> we<00:08:36.399> call<00:08:36.959> applicative 00:08:38.509 --> 00:08:38.519 align:start position:0% which we call applicative 00:08:38.519 --> 00:08:40.909 align:start position:0% which we call applicative recursion<00:08:39.519> so<00:08:39.680> let's<00:08:39.959> define<00:08:40.440> applicative 00:08:40.909 --> 00:08:40.919 align:start position:0% recursion so let's define applicative 00:08:40.919 --> 00:08:43.670 align:start position:0% recursion so let's define applicative recursion<00:08:41.440> roughly<00:08:41.800> in<00:08:41.919> the<00:08:42.039> following<00:08:42.680> way 00:08:43.670 --> 00:08:43.680 align:start position:0% recursion roughly in the following way 00:08:43.680 --> 00:08:46.110 align:start position:0% recursion roughly in the following way here<00:08:43.839> you<00:08:43.959> see<00:08:44.360> again<00:08:44.800> the<00:08:44.920> same<00:08:45.160> recursive 00:08:46.110 --> 00:08:46.120 align:start position:0% here you see again the same recursive 00:08:46.120 --> 00:08:47.870 align:start position:0% here you see again the same recursive proving<00:08:46.480> tree<00:08:46.800> that<00:08:46.959> we<00:08:47.120> had 00:08:47.870 --> 00:08:47.880 align:start position:0% proving tree that we had 00:08:47.880 --> 00:08:51.870 align:start position:0% proving tree that we had before<00:08:48.880> uh<00:08:49.040> we<00:08:49.200> have<00:08:49.640> four<00:08:50.000> input<00:08:50.880> statements 00:08:51.870 --> 00:08:51.880 align:start position:0% before uh we have four input statements 00:08:51.880 --> 00:08:53.509 align:start position:0% before uh we have four input statements uh<00:08:52.040> we<00:08:52.240> combine<00:08:52.600> them<00:08:52.880> together<00:08:53.120> into<00:08:53.360> a 00:08:53.509 --> 00:08:53.519 align:start position:0% uh we combine them together into a 00:08:53.519 --> 00:08:55.269 align:start position:0% uh we combine them together into a single<00:08:53.839> proof<00:08:54.200> with<00:08:54.399> four 00:08:55.269 --> 00:08:55.279 align:start position:0% single proof with four 00:08:55.279 --> 00:08:58.350 align:start position:0% single proof with four outputs<00:08:56.279> with<00:08:56.560> applicative<00:08:57.160> recursion<00:08:58.160> uh 00:08:58.350 --> 00:08:58.360 align:start position:0% outputs with applicative recursion uh 00:08:58.360 --> 00:09:00.750 align:start position:0% outputs with applicative recursion uh the<00:08:58.519> difference<00:08:59.519> uh<00:08:59.640> from<00:09:00.000> regular<00:09:00.680> uh 00:09:00.750 --> 00:09:00.760 align:start position:0% the difference uh from regular uh 00:09:00.760 --> 00:09:03.230 align:start position:0% the difference uh from regular uh recursive<00:09:01.279> proving<00:09:01.760> is<00:09:02.560> that<00:09:02.760> here<00:09:02.959> we're 00:09:03.230 --> 00:09:03.240 align:start position:0% recursive proving is that here we're 00:09:03.240 --> 00:09:05.310 align:start position:0% recursive proving is that here we're going<00:09:03.440> to<00:09:03.720> assume<00:09:04.160> that<00:09:04.360> all<00:09:04.560> the<00:09:04.760> statements 00:09:05.310 --> 00:09:05.320 align:start position:0% going to assume that all the statements 00:09:05.320 --> 00:09:07.269 align:start position:0% going to assume that all the statements come<00:09:05.640> from<00:09:05.839> a<00:09:06.000> single<00:09:06.440> application<00:09:06.959> so<00:09:07.120> they 00:09:07.269 --> 00:09:07.279 align:start position:0% come from a single application so they 00:09:07.279 --> 00:09:09.550 align:start position:0% come from a single application so they have<00:09:07.560> some<00:09:07.839> kind<00:09:08.000> of<00:09:08.279> common 00:09:09.550 --> 00:09:09.560 align:start position:0% have some kind of common 00:09:09.560 --> 00:09:12.470 align:start position:0% have some kind of common semantics<00:09:10.560> uh<00:09:10.720> for<00:09:10.920> instance<00:09:11.800> these<00:09:11.920> are<00:09:12.120> four 00:09:12.470 --> 00:09:12.480 align:start position:0% semantics uh for instance these are four 00:09:12.480 --> 00:09:15.870 align:start position:0% semantics uh for instance these are four proofs<00:09:12.839> of<00:09:13.040> blocks<00:09:13.519> coming<00:09:13.839> from<00:09:14.040> the<00:09:14.200> same 00:09:15.870 --> 00:09:15.880 align:start position:0% proofs of blocks coming from the same 00:09:15.880 --> 00:09:18.910 align:start position:0% proofs of blocks coming from the same rollup<00:09:16.880> then<00:09:17.120> what<00:09:17.240> we<00:09:17.399> do<00:09:18.240> is<00:09:18.399> we<00:09:18.519> use<00:09:18.760> the 00:09:18.910 --> 00:09:18.920 align:start position:0% rollup then what we do is we use the 00:09:18.920 --> 00:09:22.110 align:start position:0% rollup then what we do is we use the same<00:09:19.240> context<00:09:19.959> the<00:09:20.160> concept<00:09:20.640> of<00:09:20.920> proving<00:09:21.880> but 00:09:22.110 --> 00:09:22.120 align:start position:0% same context the concept of proving but 00:09:22.120 --> 00:09:25.190 align:start position:0% same context the concept of proving but now<00:09:22.480> for<00:09:22.880> basically<00:09:23.519> squashing<00:09:24.360> the<00:09:24.519> outputs 00:09:25.190 --> 00:09:25.200 align:start position:0% now for basically squashing the outputs 00:09:25.200 --> 00:09:26.910 align:start position:0% now for basically squashing the outputs together<00:09:25.600> into<00:09:25.839> a<00:09:26.000> single 00:09:26.910 --> 00:09:26.920 align:start position:0% together into a single 00:09:26.920 --> 00:09:29.509 align:start position:0% together into a single output<00:09:27.920> uh<00:09:28.040> so<00:09:28.200> in<00:09:28.360> this<00:09:28.600> case<00:09:28.920> we'll<00:09:29.160> have<00:09:29.440> a 00:09:29.509 --> 00:09:29.519 align:start position:0% output uh so in this case we'll have a 00:09:29.519 --> 00:09:31.350 align:start position:0% output uh so in this case we'll have a new<00:09:29.720> statement<00:09:30.240> which<00:09:30.440> basically<00:09:30.880> says<00:09:31.279> this 00:09:31.350 --> 00:09:31.360 align:start position:0% new statement which basically says this 00:09:31.360 --> 00:09:34.630 align:start position:0% new statement which basically says this is<00:09:31.519> in<00:09:31.760> the<00:09:32.760> red<00:09:33.040> rectangle<00:09:33.519> on<00:09:33.680> the<00:09:33.800> bottom 00:09:34.630 --> 00:09:34.640 align:start position:0% is in the red rectangle on the bottom 00:09:34.640 --> 00:09:37.069 align:start position:0% is in the red rectangle on the bottom basically<00:09:35.200> we<00:09:35.440> verify<00:09:36.000> the<00:09:36.160> last<00:09:36.480> proof<00:09:36.839> so<00:09:36.959> we 00:09:37.069 --> 00:09:37.079 align:start position:0% basically we verify the last proof so we 00:09:37.079 --> 00:09:39.069 align:start position:0% basically we verify the last proof so we make<00:09:37.360> sure<00:09:37.680> that<00:09:37.800> the<00:09:37.920> outputs<00:09:38.320> are<00:09:38.519> valid<00:09:38.920> by 00:09:39.069 --> 00:09:39.079 align:start position:0% make sure that the outputs are valid by 00:09:39.079 --> 00:09:43.190 align:start position:0% make sure that the outputs are valid by using<00:09:39.600> verification<00:09:40.240> of<00:09:40.440> this<00:09:40.959> proof<00:09:41.959> and<00:09:42.959> we 00:09:43.190 --> 00:09:43.200 align:start position:0% using verification of this proof and we 00:09:43.200 --> 00:09:45.750 align:start position:0% using verification of this proof and we perform<00:09:43.720> a<00:09:43.920> statement<00:09:44.800> that<00:09:44.920> is<00:09:45.079> a<00:09:45.360> valid 00:09:45.750 --> 00:09:45.760 align:start position:0% perform a statement that is a valid 00:09:45.760 --> 00:09:48.150 align:start position:0% perform a statement that is a valid combination<00:09:46.480> of<00:09:46.640> the<00:09:46.760> four<00:09:47.040> outputs<00:09:47.640> into<00:09:48.000> a 00:09:48.150 --> 00:09:48.160 align:start position:0% combination of the four outputs into a 00:09:48.160 --> 00:09:51.509 align:start position:0% combination of the four outputs into a single<00:09:48.519> output<00:09:49.000> so<00:09:49.200> the<00:09:49.360> result<00:09:49.880> is<00:09:50.880> a<00:09:51.079> single 00:09:51.509 --> 00:09:51.519 align:start position:0% single output so the result is a single 00:09:51.519 --> 00:09:54.470 align:start position:0% single output so the result is a single proof<00:09:52.320> with<00:09:52.480> a<00:09:52.640> single<00:09:53.000> output<00:09:53.480> this<00:09:53.640> time<00:09:53.959> so 00:09:54.470 --> 00:09:54.480 align:start position:0% proof with a single output this time so 00:09:54.480 --> 00:09:56.750 align:start position:0% proof with a single output this time so let's<00:09:54.680> see<00:09:55.000> what<00:09:55.200> this<00:09:55.399> output<00:09:55.800> could<00:09:56.040> contain 00:09:56.750 --> 00:09:56.760 align:start position:0% let's see what this output could contain 00:09:56.760 --> 00:09:59.590 align:start position:0% let's see what this output could contain okay<00:09:57.720> so<00:09:57.959> for<00:09:58.200> example<00:09:58.720> if<00:09:58.800> we're<00:09:59.000> interested 00:09:59.590 --> 00:09:59.600 align:start position:0% okay so for example if we're interested 00:09:59.600 --> 00:10:02.790 align:start position:0% okay so for example if we're interested in<00:09:59.880> aggregating<00:10:00.519> state<00:10:01.120> diff<00:10:02.120> uh<00:10:02.240> here<00:10:02.360> is<00:10:02.560> an 00:10:02.790 --> 00:10:02.800 align:start position:0% in aggregating state diff uh here is an 00:10:02.800 --> 00:10:05.190 align:start position:0% in aggregating state diff uh here is an example<00:10:03.320> of<00:10:03.519> three<00:10:03.959> state<00:10:04.320> transitions<00:10:05.079> so 00:10:05.190 --> 00:10:05.200 align:start position:0% example of three state transitions so 00:10:05.200 --> 00:10:07.150 align:start position:0% example of three state transitions so we're<00:10:05.399> moving<00:10:05.760> from<00:10:06.000> State<00:10:06.240> one<00:10:06.480> to<00:10:06.680> state<00:10:06.920> two 00:10:07.150 --> 00:10:07.160 align:start position:0% we're moving from State one to state two 00:10:07.160 --> 00:10:09.190 align:start position:0% we're moving from State one to state two to<00:10:07.399> state<00:10:07.640> three<00:10:08.000> and<00:10:08.240> eventually<00:10:08.600> to<00:10:08.839> State 00:10:09.190 --> 00:10:09.200 align:start position:0% to state three and eventually to State 00:10:09.200 --> 00:10:11.910 align:start position:0% to state three and eventually to State four<00:10:10.200> in<00:10:10.360> each<00:10:10.600> transition<00:10:11.240> we<00:10:11.440> generate 00:10:11.910 --> 00:10:11.920 align:start position:0% four in each transition we generate 00:10:11.920 --> 00:10:14.750 align:start position:0% four in each transition we generate State<00:10:12.360> diff<00:10:13.360> so<00:10:13.560> in<00:10:13.680> the<00:10:13.880> first<00:10:14.160> transition 00:10:14.750 --> 00:10:14.760 align:start position:0% State diff so in the first transition 00:10:14.760 --> 00:10:16.750 align:start position:0% State diff so in the first transition you<00:10:14.880> can<00:10:15.040> see<00:10:15.480> that<00:10:15.839> position<00:10:16.200> number<00:10:16.480> three 00:10:16.750 --> 00:10:16.760 align:start position:0% you can see that position number three 00:10:16.760 --> 00:10:19.870 align:start position:0% you can see that position number three has<00:10:16.920> changed<00:10:17.360> from<00:10:17.600> D<00:10:17.920> into<00:10:18.279> X<00:10:19.279> in<00:10:19.399> the<00:10:19.560> second 00:10:19.870 --> 00:10:19.880 align:start position:0% has changed from D into X in the second 00:10:19.880 --> 00:10:22.030 align:start position:0% has changed from D into X in the second transition<00:10:20.480> we're<00:10:20.720> touching<00:10:21.279> positions<00:10:21.800> five 00:10:22.030 --> 00:10:22.040 align:start position:0% transition we're touching positions five 00:10:22.040 --> 00:10:24.990 align:start position:0% transition we're touching positions five and<00:10:22.240> six<00:10:23.200> and<00:10:23.480> in<00:10:23.600> the<00:10:23.760> last<00:10:24.000> transition<00:10:24.640> the 00:10:24.990 --> 00:10:25.000 align:start position:0% and six and in the last transition the 00:10:25.000 --> 00:10:27.230 align:start position:0% and six and in the last transition the fourth<00:10:25.320> transition<00:10:25.800> from<00:10:26.800> the<00:10:26.920> third 00:10:27.230 --> 00:10:27.240 align:start position:0% fourth transition from the third 00:10:27.240 --> 00:10:28.949 align:start position:0% fourth transition from the third transition<00:10:27.680> from<00:10:28.040> state<00:10:28.320> three<00:10:28.560> to<00:10:28.720> State 00:10:28.949 --> 00:10:28.959 align:start position:0% transition from state three to State 00:10:28.959 --> 00:10:30.350 align:start position:0% transition from state three to State four 00:10:30.350 --> 00:10:30.360 align:start position:0% four 00:10:30.360 --> 00:10:32.509 align:start position:0% four uh<00:10:30.480> we're<00:10:30.680> changing<00:10:31.399> position<00:10:31.760> three<00:10:32.160> again 00:10:32.509 --> 00:10:32.519 align:start position:0% uh we're changing position three again 00:10:32.519 --> 00:10:35.350 align:start position:0% uh we're changing position three again and<00:10:32.800> position<00:10:33.200> six<00:10:33.640> again<00:10:33.920> so<00:10:34.120> the<00:10:34.320> result<00:10:34.839> is 00:10:35.350 --> 00:10:35.360 align:start position:0% and position six again so the result is 00:10:35.360 --> 00:10:36.269 align:start position:0% and position six again so the result is the 00:10:36.269 --> 00:10:36.279 align:start position:0% the 00:10:36.279 --> 00:10:40.310 align:start position:0% the state<00:10:37.279> called<00:10:37.600> S4<00:10:38.240> on<00:10:38.399> the<00:10:38.560> bottom<00:10:38.839> of<00:10:38.959> the 00:10:40.310 --> 00:10:40.320 align:start position:0% state called S4 on the bottom of the 00:10:40.320 --> 00:10:42.990 align:start position:0% state called S4 on the bottom of the slide<00:10:41.320> but<00:10:41.480> if<00:10:41.600> you<00:10:41.760> look<00:10:42.040> at<00:10:42.200> the<00:10:42.440> resulting 00:10:42.990 --> 00:10:43.000 align:start position:0% slide but if you look at the resulting 00:10:43.000 --> 00:10:47.389 align:start position:0% slide but if you look at the resulting stative<00:10:43.760> between<00:10:44.440> S1<00:10:45.399> and<00:10:45.760> S4<00:10:46.760> there<00:10:46.880> are<00:10:47.040> only 00:10:47.389 --> 00:10:47.399 align:start position:0% stative between S1 and S4 there are only 00:10:47.399 --> 00:10:50.590 align:start position:0% stative between S1 and S4 there are only three<00:10:47.920> changes<00:10:48.920> so<00:10:49.079> there's<00:10:49.399> no<00:10:49.720> reason<00:10:50.240> to 00:10:50.590 --> 00:10:50.600 align:start position:0% three changes so there's no reason to 00:10:50.600 --> 00:10:54.030 align:start position:0% three changes so there's no reason to transmit<00:10:51.600> three<00:10:51.920> statives<00:10:52.720> with<00:10:52.920> six<00:10:53.320> changes 00:10:54.030 --> 00:10:54.040 align:start position:0% transmit three statives with six changes 00:10:54.040 --> 00:10:56.790 align:start position:0% transmit three statives with six changes as<00:10:54.160> in<00:10:54.399> this<00:10:54.959> example<00:10:55.959> so<00:10:56.200> one<00:10:56.360> of<00:10:56.480> the<00:10:56.600> things 00:10:56.790 --> 00:10:56.800 align:start position:0% as in this example so one of the things 00:10:56.800 --> 00:10:58.949 align:start position:0% as in this example so one of the things that<00:10:56.959> we<00:10:57.079> can<00:10:57.240> do<00:10:57.480> in<00:10:57.639> the<00:10:57.839> squashing<00:10:58.519> proof 00:10:58.949 --> 00:10:58.959 align:start position:0% that we can do in the squashing proof 00:10:58.959 --> 00:11:01.110 align:start position:0% that we can do in the squashing proof this<00:10:59.360> final<00:10:59.680> step<00:10:59.920> of<00:11:00.079> applicative<00:11:00.519> recursion 00:11:01.110 --> 00:11:01.120 align:start position:0% this final step of applicative recursion 00:11:01.120 --> 00:11:03.590 align:start position:0% this final step of applicative recursion is<00:11:01.399> joining<00:11:01.959> the<00:11:02.120> outputs<00:11:02.680> together<00:11:03.079> into<00:11:03.360> a 00:11:03.590 --> 00:11:03.600 align:start position:0% is joining the outputs together into a 00:11:03.600 --> 00:11:07.269 align:start position:0% is joining the outputs together into a single<00:11:04.480> more<00:11:04.839> concise<00:11:05.880> output<00:11:06.880> now<00:11:07.040> in 00:11:07.269 --> 00:11:07.279 align:start position:0% single more concise output now in 00:11:07.279 --> 00:11:09.870 align:start position:0% single more concise output now in reality<00:11:07.800> for<00:11:08.079> validity<00:11:08.519> rollups<00:11:09.240> it<00:11:09.399> happens 00:11:09.870 --> 00:11:09.880 align:start position:0% reality for validity rollups it happens 00:11:09.880 --> 00:11:12.030 align:start position:0% reality for validity rollups it happens quite<00:11:10.079> a<00:11:10.279> lot<00:11:10.720> that<00:11:10.880> the<00:11:11.079> same<00:11:11.440> positions<00:11:11.880> in 00:11:12.030 --> 00:11:12.040 align:start position:0% quite a lot that the same positions in 00:11:12.040 --> 00:11:13.910 align:start position:0% quite a lot that the same positions in the<00:11:12.200> state<00:11:12.480> are<00:11:12.680> changed<00:11:13.120> multiple<00:11:13.600> times 00:11:13.910 --> 00:11:13.920 align:start position:0% the state are changed multiple times 00:11:13.920 --> 00:11:15.949 align:start position:0% the state are changed multiple times even<00:11:14.200> within<00:11:14.440> a<00:11:14.600> block<00:11:15.320> and<00:11:15.480> certainly 00:11:15.949 --> 00:11:15.959 align:start position:0% even within a block and certainly 00:11:15.959 --> 00:11:17.949 align:start position:0% even within a block and certainly between<00:11:16.399> blocks<00:11:17.079> especially<00:11:17.480> if<00:11:17.639> there<00:11:17.760> are 00:11:17.949 --> 00:11:17.959 align:start position:0% between blocks especially if there are 00:11:17.959 --> 00:11:21.710 align:start position:0% between blocks especially if there are many<00:11:18.200> many<00:11:18.519> blocks<00:11:19.440> or<00:11:19.720> large<00:11:20.200> blocks<00:11:21.200> so<00:11:21.519> this 00:11:21.710 --> 00:11:21.720 align:start position:0% many many blocks or large blocks so this 00:11:21.720 --> 00:11:24.550 align:start position:0% many many blocks or large blocks so this kind<00:11:21.959> of<00:11:22.440> uh<00:11:22.720> aggregation<00:11:23.480> is<00:11:23.720> very<00:11:24.079> very<00:11:24.399> is 00:11:24.550 --> 00:11:24.560 align:start position:0% kind of uh aggregation is very very is 00:11:24.560 --> 00:11:27.190 align:start position:0% kind of uh aggregation is very very is very<00:11:24.760> important<00:11:25.160> to<00:11:25.600> improve<00:11:26.079> efficiency<00:11:26.760> of 00:11:27.190 --> 00:11:27.200 align:start position:0% very important to improve efficiency of 00:11:27.200 --> 00:11:30.750 align:start position:0% very important to improve efficiency of State<00:11:27.519> div<00:11:27.800> transmitted<00:11:28.279> to<00:11:28.399> the<00:11:28.519> blockchain 00:11:30.750 --> 00:11:30.760 align:start position:0% State div transmitted to the blockchain 00:11:30.760 --> 00:11:32.670 align:start position:0% State div transmitted to the blockchain but<00:11:30.959> also<00:11:31.279> other<00:11:31.560> things<00:11:31.760> can<00:11:31.880> be<00:11:32.079> done<00:11:32.560> and 00:11:32.670 --> 00:11:32.680 align:start position:0% but also other things can be done and 00:11:32.680 --> 00:11:35.949 align:start position:0% but also other things can be done and I'll<00:11:32.920> go<00:11:33.040> into<00:11:33.279> examples<00:11:33.680> in<00:11:33.800> a<00:11:33.959> moment<00:11:34.680> so<00:11:34.959> now 00:11:35.949 --> 00:11:35.959 align:start position:0% I'll go into examples in a moment so now 00:11:35.959 --> 00:11:38.470 align:start position:0% I'll go into examples in a moment so now uh<00:11:36.120> validity<00:11:36.560> rollup<00:11:36.959> looks<00:11:37.279> like<00:11:37.560> this<00:11:38.320> you 00:11:38.470 --> 00:11:38.480 align:start position:0% uh validity rollup looks like this you 00:11:38.480 --> 00:11:40.430 align:start position:0% uh validity rollup looks like this you have<00:11:38.639> the<00:11:39.079> transactions<00:11:40.079> as<00:11:40.160> you<00:11:40.279> know 00:11:40.430 --> 00:11:40.440 align:start position:0% have the transactions as you know 00:11:40.440 --> 00:11:42.069 align:start position:0% have the transactions as you know they're<00:11:40.680> sequenced<00:11:41.200> and 00:11:42.069 --> 00:11:42.079 align:start position:0% they're sequenced and 00:11:42.079 --> 00:11:46.150 align:start position:0% they're sequenced and executed<00:11:43.079> put<00:11:43.279> into<00:11:44.000> blocks<00:11:45.000> for<00:11:45.519> every<00:11:45.880> set 00:11:46.150 --> 00:11:46.160 align:start position:0% executed put into blocks for every set 00:11:46.160 --> 00:11:49.670 align:start position:0% executed put into blocks for every set of<00:11:46.399> blocks<00:11:47.079> we<00:11:47.399> create<00:11:47.760> a<00:11:47.959> recursive<00:11:48.680> proof 00:11:49.670 --> 00:11:49.680 align:start position:0% of blocks we create a recursive proof 00:11:49.680 --> 00:11:51.750 align:start position:0% of blocks we create a recursive proof then<00:11:50.200> we<00:11:50.320> do<00:11:50.519> the<00:11:50.680> applicative<00:11:51.160> recursion 00:11:51.750 --> 00:11:51.760 align:start position:0% then we do the applicative recursion 00:11:51.760 --> 00:11:53.470 align:start position:0% then we do the applicative recursion because<00:11:52.120> all<00:11:52.320> these<00:11:52.519> proofs<00:11:52.839> relate<00:11:53.160> to<00:11:53.360> the 00:11:53.470 --> 00:11:53.480 align:start position:0% because all these proofs relate to the 00:11:53.480 --> 00:11:55.269 align:start position:0% because all these proofs relate to the same<00:11:53.720> application<00:11:54.240> the<00:11:54.360> same<00:11:54.560> rollup<00:11:54.959> in<00:11:55.079> this 00:11:55.269 --> 00:11:55.279 align:start position:0% same application the same rollup in this 00:11:55.279 --> 00:11:58.470 align:start position:0% same application the same rollup in this case<00:11:55.880> so<00:11:56.040> we<00:11:56.120> can<00:11:56.320> do<00:11:56.680> that<00:11:57.680> and<00:11:57.839> this<00:11:58.040> single 00:11:58.470 --> 00:11:58.480 align:start position:0% case so we can do that and this single 00:11:58.480 --> 00:12:01.350 align:start position:0% case so we can do that and this single proof<00:11:59.320> with<00:11:59.519> the<00:11:59.880> aggregated<00:12:00.639> output<00:12:01.200> a 00:12:01.350 --> 00:12:01.360 align:start position:0% proof with the aggregated output a 00:12:01.360 --> 00:12:03.629 align:start position:0% proof with the aggregated output a single<00:12:01.760> output<00:12:02.240> is<00:12:02.399> sent<00:12:02.639> to<00:12:02.800> the<00:12:02.959> verifier<00:12:03.440> on 00:12:03.629 --> 00:12:03.639 align:start position:0% single output is sent to the verifier on 00:12:03.639 --> 00:12:06.509 align:start position:0% single output is sent to the verifier on layer<00:12:03.920> one<00:12:04.440> so<00:12:04.639> we<00:12:04.880> pay<00:12:05.160> for<00:12:05.519> verification 00:12:06.509 --> 00:12:06.519 align:start position:0% layer one so we pay for verification 00:12:06.519 --> 00:12:08.629 align:start position:0% layer one so we pay for verification just<00:12:06.720> like<00:12:06.880> we<00:12:07.040> paid<00:12:07.320> for<00:12:07.600> ver<00:12:07.920> verification 00:12:08.629 --> 00:12:08.639 align:start position:0% just like we paid for ver verification 00:12:08.639 --> 00:12:10.629 align:start position:0% just like we paid for ver verification in<00:12:08.760> the<00:12:08.920> previous<00:12:09.320> example<00:12:09.720> using<00:12:10.279> simple 00:12:10.629 --> 00:12:10.639 align:start position:0% in the previous example using simple 00:12:10.639 --> 00:12:13.590 align:start position:0% in the previous example using simple recursive<00:12:11.360> proving<00:12:12.360> but<00:12:12.600> now<00:12:13.040> instead<00:12:13.399> of 00:12:13.590 --> 00:12:13.600 align:start position:0% recursive proving but now instead of 00:12:13.600 --> 00:12:17.389 align:start position:0% recursive proving but now instead of doing<00:12:14.000> a<00:12:14.120> state<00:12:14.639> update<00:12:15.639> per<00:12:15.959> block<00:12:16.839> we<00:12:16.959> can<00:12:17.160> do 00:12:17.389 --> 00:12:17.399 align:start position:0% doing a state update per block we can do 00:12:17.399 --> 00:12:20.750 align:start position:0% doing a state update per block we can do a<00:12:17.560> state<00:12:17.920> update<00:12:18.720> per<00:12:19.519> recursive<00:12:20.240> cycle<00:12:20.680> if 00:12:20.750 --> 00:12:20.760 align:start position:0% a state update per recursive cycle if 00:12:20.760 --> 00:12:24.670 align:start position:0% a state update per recursive cycle if you<00:12:20.920> like<00:12:21.120> for<00:12:21.680> multiple<00:12:22.199> blocks<00:12:22.880> together 00:12:24.670 --> 00:12:24.680 align:start position:0% you like for multiple blocks together 00:12:24.680 --> 00:12:27.310 align:start position:0% you like for multiple blocks together simultaneously<00:12:25.680> so<00:12:25.880> what<00:12:26.040> does<00:12:26.639> uh<00:12:26.880> this<00:12:27.079> look 00:12:27.310 --> 00:12:27.320 align:start position:0% simultaneously so what does uh this look 00:12:27.320 --> 00:12:30.269 align:start position:0% simultaneously so what does uh this look like<00:12:27.519> so<00:12:27.720> we<00:12:27.839> have<00:12:28.000> the<00:12:28.160> recursive<00:12:29.040> uh<00:12:29.360> uh<00:12:29.639> appc 00:12:30.269 --> 00:12:30.279 align:start position:0% like so we have the recursive uh uh appc 00:12:30.279 --> 00:12:33.069 align:start position:0% like so we have the recursive uh uh appc applicative<00:12:30.720> recursion 00:12:33.069 --> 00:12:33.079 align:start position:0% applicative recursion 00:12:33.079 --> 00:12:35.710 align:start position:0% applicative recursion recursion<00:12:34.079> per<00:12:34.320> recursion<00:12:34.880> we<00:12:35.079> verify<00:12:35.519> appr 00:12:35.710 --> 00:12:35.720 align:start position:0% recursion per recursion we verify appr 00:12:35.720 --> 00:12:38.790 align:start position:0% recursion per recursion we verify appr proof<00:12:36.040> and<00:12:36.360> per<00:12:36.639> recursion<00:12:37.600> we<00:12:37.839> publish<00:12:38.600> the 00:12:38.790 --> 00:12:38.800 align:start position:0% proof and per recursion we publish the 00:12:38.800 --> 00:12:41.670 align:start position:0% proof and per recursion we publish the aggregate<00:12:39.320> State<00:12:39.680> diff<00:12:40.120> in<00:12:40.680> one<00:12:40.920> or<00:12:41.079> more 00:12:41.670 --> 00:12:41.680 align:start position:0% aggregate State diff in one or more 00:12:41.680 --> 00:12:44.990 align:start position:0% aggregate State diff in one or more blobs<00:12:42.680> and<00:12:43.000> update<00:12:43.440> the<00:12:43.680> state<00:12:44.079> on<00:12:44.320> the<00:12:44.680> on<00:12:44.800> the 00:12:44.990 --> 00:12:45.000 align:start position:0% blobs and update the state on the on the 00:12:45.000 --> 00:12:46.910 align:start position:0% blobs and update the state on the on the contract<00:12:45.560> that<00:12:45.720> tracks<00:12:46.160> the<00:12:46.360> state<00:12:46.600> of<00:12:46.760> the 00:12:46.910 --> 00:12:46.920 align:start position:0% contract that tracks the state of the 00:12:46.920 --> 00:12:51.230 align:start position:0% contract that tracks the state of the rollup<00:12:47.920> with<00:12:48.120> a<00:12:48.639> single<00:12:49.639> state<00:12:50.040> update<00:12:51.040> that 00:12:51.230 --> 00:12:51.240 align:start position:0% rollup with a single state update that 00:12:51.240 --> 00:12:52.990 align:start position:0% rollup with a single state update that updates<00:12:51.639> the<00:12:51.800> state<00:12:52.040> to<00:12:52.199> the<00:12:52.399> final<00:12:52.720> State 00:12:52.990 --> 00:12:53.000 align:start position:0% updates the state to the final State 00:12:53.000 --> 00:12:55.350 align:start position:0% updates the state to the final State we've<00:12:53.240> reached<00:12:53.600> after<00:12:53.959> multiple<00:12:54.399> blocks<00:12:55.240> and 00:12:55.350 --> 00:12:55.360 align:start position:0% we've reached after multiple blocks and 00:12:55.360 --> 00:12:57.670 align:start position:0% we've reached after multiple blocks and of<00:12:55.480> course<00:12:55.680> we<00:12:55.760> can<00:12:55.959> include<00:12:56.360> messaging<00:12:56.959> as 00:12:57.670 --> 00:12:57.680 align:start position:0% of course we can include messaging as 00:12:57.680 --> 00:13:00.389 align:start position:0% of course we can include messaging as before<00:12:58.680> so<00:12:58.880> the<00:12:59.240> more<00:12:59.399> blocks<00:12:59.800> we<00:12:59.959> have<00:13:00.120> Pro 00:13:00.389 --> 00:13:00.399 align:start position:0% before so the more blocks we have Pro 00:13:00.399 --> 00:13:02.870 align:start position:0% before so the more blocks we have Pro recursion<00:13:01.120> the<00:13:01.279> lower<00:13:01.839> layer<00:13:02.160> one<00:13:02.440> cost<00:13:02.680> will 00:13:02.870 --> 00:13:02.880 align:start position:0% recursion the lower layer one cost will 00:13:02.880 --> 00:13:06.670 align:start position:0% recursion the lower layer one cost will be<00:13:03.839> and<00:13:04.040> this<00:13:04.240> basically<00:13:04.600> skills<00:13:05.680> infinitely 00:13:06.670 --> 00:13:06.680 align:start position:0% be and this basically skills infinitely 00:13:06.680 --> 00:13:09.670 align:start position:0% be and this basically skills infinitely uh<00:13:06.880> depending<00:13:07.480> on<00:13:07.720> the<00:13:07.920> latency<00:13:08.519> you<00:13:08.720> require 00:13:09.670 --> 00:13:09.680 align:start position:0% uh depending on the latency you require 00:13:09.680 --> 00:13:12.269 align:start position:0% uh depending on the latency you require uh<00:13:09.800> to<00:13:09.959> layer<00:13:10.680> one 00:13:12.269 --> 00:13:12.279 align:start position:0% uh to layer one 00:13:12.279 --> 00:13:15.310 align:start position:0% uh to layer one um<00:13:13.279> and<00:13:13.760> uh<00:13:14.079> this<00:13:14.240> is<00:13:14.480> actually<00:13:14.839> what<00:13:14.959> we<00:13:15.160> are 00:13:15.310 --> 00:13:15.320 align:start position:0% um and uh this is actually what we are 00:13:15.320 --> 00:13:18.230 align:start position:0% um and uh this is actually what we are doing<00:13:15.839> currently<00:13:16.839> on<00:13:17.040> our<00:13:17.240> rollup<00:13:17.880> uh<00:13:18.000> called 00:13:18.230 --> 00:13:18.240 align:start position:0% doing currently on our rollup uh called 00:13:18.240 --> 00:13:20.389 align:start position:0% doing currently on our rollup uh called Stark 00:13:20.389 --> 00:13:20.399 align:start position:0% Stark 00:13:20.399 --> 00:13:23.629 align:start position:0% Stark net<00:13:21.399> what<00:13:21.560> else<00:13:21.800> can<00:13:21.959> be<00:13:22.120> done<00:13:22.560> in<00:13:22.760> this<00:13:23.160> uh 00:13:23.629 --> 00:13:23.639 align:start position:0% net what else can be done in this uh 00:13:23.639 --> 00:13:25.590 align:start position:0% net what else can be done in this uh applicative<00:13:24.160> squashing<00:13:24.800> or<00:13:24.959> if<00:13:25.079> you<00:13:25.240> like<00:13:25.399> an 00:13:25.590 --> 00:13:25.600 align:start position:0% applicative squashing or if you like an 00:13:25.600 --> 00:13:26.670 align:start position:0% applicative squashing or if you like an applicative 00:13:26.670 --> 00:13:26.680 align:start position:0% applicative 00:13:26.680 --> 00:13:30.949 align:start position:0% applicative recursion<00:13:27.680> so<00:13:28.519> the<00:13:28.680> basic<00:13:29.560> uh<00:13:29.959> aggregation<00:13:30.760> of 00:13:30.949 --> 00:13:30.959 align:start position:0% recursion so the basic uh aggregation of 00:13:30.959 --> 00:13:34.189 align:start position:0% recursion so the basic uh aggregation of State<00:13:31.279> diffs<00:13:31.760> as<00:13:31.880> I<00:13:32.199> mentioned<00:13:33.199> is<00:13:33.440> just<00:13:33.880> uh<00:13:34.040> a 00:13:34.189 --> 00:13:34.199 align:start position:0% State diffs as I mentioned is just uh a 00:13:34.199 --> 00:13:35.949 align:start position:0% State diffs as I mentioned is just uh a straightforward<00:13:34.920> aggregation<00:13:35.600> but<00:13:35.680> you<00:13:35.800> can 00:13:35.949 --> 00:13:35.959 align:start position:0% straightforward aggregation but you can 00:13:35.959 --> 00:13:37.949 align:start position:0% straightforward aggregation but you can also<00:13:36.199> do<00:13:36.440> more<00:13:36.680> sophisticated<00:13:37.399> things<00:13:37.800> for 00:13:37.949 --> 00:13:37.959 align:start position:0% also do more sophisticated things for 00:13:37.959 --> 00:13:39.670 align:start position:0% also do more sophisticated things for instance<00:13:38.320> if<00:13:38.399> you<00:13:38.519> want<00:13:38.680> to<00:13:38.880> represent<00:13:39.440> your 00:13:39.670 --> 00:13:39.680 align:start position:0% instance if you want to represent your 00:13:39.680 --> 00:13:42.269 align:start position:0% instance if you want to represent your state<00:13:40.480> in<00:13:40.600> a<00:13:40.720> more<00:13:40.959> efficient<00:13:41.399> way<00:13:41.600> so<00:13:41.839> utilize 00:13:42.269 --> 00:13:42.279 align:start position:0% state in a more efficient way so utilize 00:13:42.279 --> 00:13:44.350 align:start position:0% state in a more efficient way so utilize your<00:13:42.440> blobs<00:13:42.839> more<00:13:43.079> efficiently<00:13:44.079> you<00:13:44.199> can 00:13:44.350 --> 00:13:44.360 align:start position:0% your blobs more efficiently you can 00:13:44.360 --> 00:13:45.910 align:start position:0% your blobs more efficiently you can Implement<00:13:44.760> for<00:13:44.920> instance<00:13:45.240> a<00:13:45.440> compression 00:13:45.910 --> 00:13:45.920 align:start position:0% Implement for instance a compression 00:13:45.920 --> 00:13:49.509 align:start position:0% Implement for instance a compression algorithm<00:13:46.440> on<00:13:46.600> this<00:13:46.959> data<00:13:47.959> uh<00:13:48.199> just<00:13:48.959> deflating 00:13:49.509 --> 00:13:49.519 align:start position:0% algorithm on this data uh just deflating 00:13:49.519 --> 00:13:51.990 align:start position:0% algorithm on this data uh just deflating the<00:13:49.720> data<00:13:50.000> into<00:13:50.360> much<00:13:50.639> smaller<00:13:51.120> form<00:13:51.800> which 00:13:51.990 --> 00:13:52.000 align:start position:0% the data into much smaller form which 00:13:52.000 --> 00:13:56.310 align:start position:0% the data into much smaller form which allows<00:13:52.399> you<00:13:53.040> to<00:13:54.040> uh<00:13:54.320> include<00:13:55.199> more<00:13:55.560> blocks<00:13:56.160> on 00:13:56.310 --> 00:13:56.320 align:start position:0% allows you to uh include more blocks on 00:13:56.320 --> 00:13:58.110 align:start position:0% allows you to uh include more blocks on your<00:13:56.560> applicative<00:13:57.040> recursion<00:13:57.600> of<00:13:57.759> course 00:13:58.110 --> 00:13:58.120 align:start position:0% your applicative recursion of course 00:13:58.120 --> 00:14:01.910 align:start position:0% your applicative recursion of course eventually<00:13:59.199> when<00:13:59.440> all<00:13:59.600> the<00:13:59.720> blobs<00:14:00.079> fill<00:14:00.639> up<00:14:01.639> uh 00:14:01.910 --> 00:14:01.920 align:start position:0% eventually when all the blobs fill up uh 00:14:01.920 --> 00:14:04.030 align:start position:0% eventually when all the blobs fill up uh you<00:14:02.079> may<00:14:02.320> reach<00:14:02.519> a<00:14:02.720> state<00:14:03.000> where<00:14:03.240> blob<00:14:03.600> prices 00:14:04.030 --> 00:14:04.040 align:start position:0% you may reach a state where blob prices 00:14:04.040 --> 00:14:06.189 align:start position:0% you may reach a state where blob prices could<00:14:04.240> go<00:14:04.560> up<00:14:04.800> or<00:14:05.000> you<00:14:05.160> have<00:14:05.399> more<00:14:05.639> blobs<00:14:06.000> than 00:14:06.189 --> 00:14:06.199 align:start position:0% could go up or you have more blobs than 00:14:06.199 --> 00:14:07.790 align:start position:0% could go up or you have more blobs than could<00:14:06.360> fit<00:14:06.560> in<00:14:06.680> a<00:14:06.800> single<00:14:07.120> transaction<00:14:07.600> and 00:14:07.790 --> 00:14:07.800 align:start position:0% could fit in a single transaction and 00:14:07.800 --> 00:14:09.470 align:start position:0% could fit in a single transaction and things<00:14:08.040> like<00:14:08.240> that<00:14:08.839> that<00:14:09.000> is<00:14:09.120> something<00:14:09.360> you 00:14:09.470 --> 00:14:09.480 align:start position:0% things like that that is something you 00:14:09.480 --> 00:14:10.790 align:start position:0% things like that that is something you want<00:14:09.600> to<00:14:09.759> avoid<00:14:10.000> so<00:14:10.160> that's<00:14:10.320> a<00:14:10.440> point<00:14:10.639> where 00:14:10.790 --> 00:14:10.800 align:start position:0% want to avoid so that's a point where 00:14:10.800 --> 00:14:12.509 align:start position:0% want to avoid so that's a point where you<00:14:10.880> want<00:14:11.000> to<00:14:11.199> cut<00:14:11.440> off<00:14:11.959> the<00:14:12.120> applicative 00:14:12.509 --> 00:14:12.519 align:start position:0% you want to cut off the applicative 00:14:12.519 --> 00:14:14.310 align:start position:0% you want to cut off the applicative recursion<00:14:13.040> so<00:14:13.199> it's<00:14:13.320> not<00:14:13.519> really<00:14:13.720> infinite<00:14:14.199> as 00:14:14.310 --> 00:14:14.320 align:start position:0% recursion so it's not really infinite as 00:14:14.320 --> 00:14:17.150 align:start position:0% recursion so it's not really infinite as I<00:14:14.440> mentioned<00:14:15.199> before<00:14:16.199> in<00:14:16.399> addition<00:14:16.880> as<00:14:17.000> I 00:14:17.150 --> 00:14:17.160 align:start position:0% I mentioned before in addition as I 00:14:17.160 --> 00:14:19.310 align:start position:0% I mentioned before in addition as I mentioned<00:14:17.920> you<00:14:18.040> can<00:14:18.399> uh<00:14:18.519> remove<00:14:18.839> the<00:14:18.959> need<00:14:19.199> to 00:14:19.310 --> 00:14:19.320 align:start position:0% mentioned you can uh remove the need to 00:14:19.320 --> 00:14:22.629 align:start position:0% mentioned you can uh remove the need to do<00:14:19.560> update<00:14:19.880> States<00:14:20.240> per<00:14:20.639> block<00:14:21.639> and<00:14:22.360> if<00:14:22.480> you 00:14:22.629 --> 00:14:22.639 align:start position:0% do update States per block and if you 00:14:22.639 --> 00:14:25.230 align:start position:0% do update States per block and if you like<00:14:22.920> you<00:14:23.079> can<00:14:23.279> generalize<00:14:23.920> this<00:14:24.120> into<00:14:24.320> a<00:14:24.519> con 00:14:25.230 --> 00:14:25.240 align:start position:0% like you can generalize this into a con 00:14:25.240 --> 00:14:27.990 align:start position:0% like you can generalize this into a con into<00:14:25.440> a<00:14:25.639> concept<00:14:26.199> of<00:14:26.839> segmenting<00:14:27.560> a<00:14:27.759> very 00:14:27.990 --> 00:14:28.000 align:start position:0% into a concept of segmenting a very 00:14:28.000 --> 00:14:31.710 align:start position:0% into a concept of segmenting a very large<00:14:28.639> computer<00:14:29.279> ation<00:14:30.079> into<00:14:30.519> multiple 00:14:31.710 --> 00:14:31.720 align:start position:0% large computer ation into multiple 00:14:31.720 --> 00:14:36.189 align:start position:0% large computer ation into multiple segments<00:14:32.720> so<00:14:33.279> if<00:14:33.440> you<00:14:34.160> prove<00:14:35.160> that<00:14:35.480> you've 00:14:36.189 --> 00:14:36.199 align:start position:0% segments so if you prove that you've 00:14:36.199 --> 00:14:38.829 align:start position:0% segments so if you prove that you've executed<00:14:36.680> a<00:14:36.880> program<00:14:37.480> from<00:14:37.759> some<00:14:38.079> State<00:14:38.399> a<00:14:38.639> to 00:14:38.829 --> 00:14:38.839 align:start position:0% executed a program from some State a to 00:14:38.839 --> 00:14:41.870 align:start position:0% executed a program from some State a to some<00:14:39.079> State<00:14:39.399> B<00:14:40.320> and<00:14:40.560> then<00:14:41.000> you've<00:14:41.279> executed 00:14:41.870 --> 00:14:41.880 align:start position:0% some State B and then you've executed 00:14:41.880 --> 00:14:43.710 align:start position:0% some State B and then you've executed the<00:14:42.000> same<00:14:42.279> program<00:14:42.600> or<00:14:42.800> continuation<00:14:43.399> of<00:14:43.519> the 00:14:43.710 --> 00:14:43.720 align:start position:0% the same program or continuation of the 00:14:43.720 --> 00:14:47.310 align:start position:0% the same program or continuation of the program<00:14:44.120> from<00:14:44.360> State<00:14:44.680> B<00:14:44.920> to<00:14:45.199> State<00:14:45.440> C<00:14:46.199> Etc<00:14:47.199> an 00:14:47.310 --> 00:14:47.320 align:start position:0% program from State B to State C Etc an 00:14:47.320 --> 00:14:49.350 align:start position:0% program from State B to State C Etc an applicative<00:14:47.759> recursion<00:14:48.240> or<00:14:48.440> the<00:14:48.639> squashing 00:14:49.350 --> 00:14:49.360 align:start position:0% applicative recursion or the squashing 00:14:49.360 --> 00:14:51.710 align:start position:0% applicative recursion or the squashing mechanism<00:14:50.360> can<00:14:50.600> ensure<00:14:51.199> that<00:14:51.399> you've 00:14:51.710 --> 00:14:51.720 align:start position:0% mechanism can ensure that you've 00:14:51.720 --> 00:14:54.189 align:start position:0% mechanism can ensure that you've actually<00:14:52.079> proven<00:14:52.680> the<00:14:53.079> complete<00:14:53.600> execution 00:14:54.189 --> 00:14:54.199 align:start position:0% actually proven the complete execution 00:14:54.199 --> 00:14:56.550 align:start position:0% actually proven the complete execution of<00:14:54.440> this<00:14:54.720> program<00:14:55.160> from<00:14:55.399> State<00:14:55.680> a<00:14:56.040> all<00:14:56.199> the<00:14:56.320> way 00:14:56.550 --> 00:14:56.560 align:start position:0% of this program from State a all the way 00:14:56.560 --> 00:14:59.829 align:start position:0% of this program from State a all the way through<00:14:56.839> State<00:14:57.079> C<00:14:57.360> or<00:14:57.560> Zed<00:14:57.839> or<00:14:58.000> whatever<00:14:59.440> uh<00:14:59.600> so 00:14:59.829 --> 00:14:59.839 align:start position:0% through State C or Zed or whatever uh so 00:14:59.839 --> 00:15:01.430 align:start position:0% through State C or Zed or whatever uh so this<00:14:59.959> is<00:15:00.120> the<00:15:00.399> generalization<00:15:01.120> of<00:15:01.240> the 00:15:01.430 --> 00:15:01.440 align:start position:0% this is the generalization of the 00:15:01.440 --> 00:15:03.829 align:start position:0% this is the generalization of the concept<00:15:01.759> of<00:15:01.920> applicative<00:15:02.399> recursion<00:15:03.399> and<00:15:03.720> you 00:15:03.829 --> 00:15:03.839 align:start position:0% concept of applicative recursion and you 00:15:03.839 --> 00:15:06.710 align:start position:0% concept of applicative recursion and you may<00:15:04.040> have<00:15:04.240> more<00:15:04.480> ideas<00:15:04.959> here<00:15:05.240> and<00:15:05.680> uh<00:15:06.399> the<00:15:06.519> more 00:15:06.710 --> 00:15:06.720 align:start position:0% may have more ideas here and uh the more 00:15:06.720 --> 00:15:10.949 align:start position:0% may have more ideas here and uh the more creative<00:15:07.240> you<00:15:07.440> get<00:15:08.120> the<00:15:08.199> more<00:15:08.399> interesting<00:15:08.839> it 00:15:10.949 --> 00:15:10.959 align:start position:0% creative you get the more interesting it 00:15:10.959 --> 00:15:14.230 align:start position:0% creative you get the more interesting it gets<00:15:11.959> so<00:15:12.639> basically<00:15:13.040> if<00:15:13.120> you<00:15:13.240> think<00:15:13.480> about<00:15:13.720> it 00:15:14.230 --> 00:15:14.240 align:start position:0% gets so basically if you think about it 00:15:14.240 --> 00:15:15.790 align:start position:0% gets so basically if you think about it uh<00:15:14.399> the<00:15:14.519> whole<00:15:14.759> concept<00:15:15.160> of<00:15:15.279> recursive 00:15:15.790 --> 00:15:15.800 align:start position:0% uh the whole concept of recursive 00:15:15.800 --> 00:15:19.069 align:start position:0% uh the whole concept of recursive proving<00:15:16.199> applicative<00:15:16.800> proving<00:15:17.800> is<00:15:18.440> are<00:15:18.600> a<00:15:18.720> few 00:15:19.069 --> 00:15:19.079 align:start position:0% proving applicative proving is are a few 00:15:19.079 --> 00:15:21.790 align:start position:0% proving applicative proving is are a few examples<00:15:19.959> of<00:15:20.480> offchain<00:15:21.040> proving<00:15:21.480> so<00:15:21.680> these 00:15:21.790 --> 00:15:21.800 align:start position:0% examples of offchain proving so these 00:15:21.800 --> 00:15:24.749 align:start position:0% examples of offchain proving so these are<00:15:22.040> proofs<00:15:22.560> that<00:15:22.680> are<00:15:22.839> never<00:15:23.360> submitted<00:15:24.360> to<00:15:24.560> a 00:15:24.749 --> 00:15:24.759 align:start position:0% are proofs that are never submitted to a 00:15:24.759 --> 00:15:26.310 align:start position:0% are proofs that are never submitted to a verifier<00:15:25.199> on<00:15:25.360> layer<00:15:25.600> one<00:15:25.839> so<00:15:26.000> basically 00:15:26.310 --> 00:15:26.320 align:start position:0% verifier on layer one so basically 00:15:26.320 --> 00:15:27.710 align:start position:0% verifier on layer one so basically they're<00:15:26.560> only<00:15:26.759> submitted<00:15:27.199> to<00:15:27.320> a<00:15:27.480> new 00:15:27.710 --> 00:15:27.720 align:start position:0% they're only submitted to a new 00:15:27.720 --> 00:15:30.150 align:start position:0% they're only submitted to a new statement<00:15:28.160> that<00:15:28.399> verifies<00:15:29.040> them<00:15:29.319> off<00:15:29.560> chain 00:15:30.150 --> 00:15:30.160 align:start position:0% statement that verifies them off chain 00:15:30.160 --> 00:15:32.470 align:start position:0% statement that verifies them off chain completely<00:15:31.160> and<00:15:31.279> there<00:15:31.399> are<00:15:31.600> other<00:15:31.920> examples 00:15:32.470 --> 00:15:32.480 align:start position:0% completely and there are other examples 00:15:32.480 --> 00:15:34.629 align:start position:0% completely and there are other examples that<00:15:32.600> are<00:15:32.759> useful<00:15:33.240> in<00:15:33.600> in<00:15:33.759> this<00:15:33.959> context<00:15:34.480> and 00:15:34.629 --> 00:15:34.639 align:start position:0% that are useful in in this context and 00:15:34.639 --> 00:15:37.269 align:start position:0% that are useful in in this context and I'll<00:15:34.880> talk<00:15:35.079> about<00:15:35.279> a<00:15:35.399> few<00:15:35.560> of<00:15:35.839> these<00:15:36.839> so<00:15:37.040> one 00:15:37.269 --> 00:15:37.279 align:start position:0% I'll talk about a few of these so one 00:15:37.279 --> 00:15:39.189 align:start position:0% I'll talk about a few of these so one example<00:15:37.720> could<00:15:37.920> be<00:15:38.160> for<00:15:38.360> instance<00:15:38.800> for<00:15:39.000> a 00:15:39.189 --> 00:15:39.199 align:start position:0% example could be for instance for a 00:15:39.199 --> 00:15:42.829 align:start position:0% example could be for instance for a privacy<00:15:39.720> preserving<00:15:40.800> uh<00:15:41.800> uh<00:15:42.000> exchange<00:15:42.639> for 00:15:42.829 --> 00:15:42.839 align:start position:0% privacy preserving uh uh exchange for 00:15:42.839 --> 00:15:44.870 align:start position:0% privacy preserving uh uh exchange for example<00:15:43.319> so<00:15:43.519> let's<00:15:43.720> say<00:15:43.920> you<00:15:44.120> have<00:15:44.279> an 00:15:44.870 --> 00:15:44.880 align:start position:0% example so let's say you have an 00:15:44.880 --> 00:15:47.790 align:start position:0% example so let's say you have an exchange<00:15:45.880> on<00:15:46.079> your<00:15:46.440> rollup<00:15:47.440> on<00:15:47.639> the 00:15:47.790 --> 00:15:47.800 align:start position:0% exchange on your rollup on the 00:15:47.800 --> 00:15:50.350 align:start position:0% exchange on your rollup on the blockchain<00:15:48.319> itself<00:15:48.920> typically<00:15:49.360> exchanges 00:15:50.350 --> 00:15:50.360 align:start position:0% blockchain itself typically exchanges 00:15:50.360 --> 00:15:51.990 align:start position:0% blockchain itself typically exchanges that<00:15:50.480> are<00:15:50.639> on<00:15:50.920> chain<00:15:51.279> they<00:15:51.440> expose<00:15:51.839> the 00:15:51.990 --> 00:15:52.000 align:start position:0% that are on chain they expose the 00:15:52.000 --> 00:15:53.509 align:start position:0% that are on chain they expose the positions<00:15:52.399> of<00:15:52.560> their 00:15:53.509 --> 00:15:53.519 align:start position:0% positions of their 00:15:53.519 --> 00:15:56.309 align:start position:0% positions of their users<00:15:54.519> uh<00:15:54.720> some<00:15:54.920> users<00:15:55.360> are<00:15:55.639> very<00:15:55.880> sensitive 00:15:56.309 --> 00:15:56.319 align:start position:0% users uh some users are very sensitive 00:15:56.319 --> 00:15:58.189 align:start position:0% users uh some users are very sensitive to<00:15:56.480> this<00:15:56.680> information<00:15:57.240> because<00:15:57.480> it<00:15:57.600> divulges 00:15:58.189 --> 00:15:58.199 align:start position:0% to this information because it divulges 00:15:58.199 --> 00:16:00.670 align:start position:0% to this information because it divulges a<00:15:58.360> trading<00:15:58.639> Str<00:15:59.000> strategies<00:16:00.000> so<00:16:00.199> what<00:16:00.319> you<00:16:00.440> can 00:16:00.670 --> 00:16:00.680 align:start position:0% a trading Str strategies so what you can 00:16:00.680 --> 00:16:05.949 align:start position:0% a trading Str strategies so what you can do<00:16:01.480> is<00:16:01.720> basically<00:16:02.480> have<00:16:03.160> a<00:16:03.639> user<00:16:04.639> who<00:16:04.839> knows<00:16:05.839> uh 00:16:05.949 --> 00:16:05.959 align:start position:0% do is basically have a user who knows uh 00:16:05.959 --> 00:16:06.990 align:start position:0% do is basically have a user who knows uh their<00:16:06.120> own 00:16:06.990 --> 00:16:07.000 align:start position:0% their own 00:16:07.000 --> 00:16:11.910 align:start position:0% their own position<00:16:08.000> uh<00:16:08.639> execute<00:16:09.639> uh<00:16:10.120> some<00:16:10.959> order<00:16:11.720> on 00:16:11.910 --> 00:16:11.920 align:start position:0% position uh execute uh some order on 00:16:11.920 --> 00:16:12.870 align:start position:0% position uh execute uh some order on their 00:16:12.870 --> 00:16:12.880 align:start position:0% their 00:16:12.880 --> 00:16:15.749 align:start position:0% their position<00:16:13.880> while<00:16:14.160> keeping<00:16:14.519> the<00:16:14.680> position 00:16:15.749 --> 00:16:15.759 align:start position:0% position while keeping the position 00:16:15.759 --> 00:16:18.670 align:start position:0% position while keeping the position encrypted<00:16:16.759> on<00:16:17.120> the<00:16:17.560> on<00:16:17.680> the<00:16:17.800> rollup<00:16:18.240> itself<00:16:18.560> or 00:16:18.670 --> 00:16:18.680 align:start position:0% encrypted on the on the rollup itself or 00:16:18.680 --> 00:16:21.230 align:start position:0% encrypted on the on the rollup itself or on<00:16:18.800> the<00:16:18.920> blockchain<00:16:19.319> if<00:16:19.399> you<00:16:19.560> like<00:16:20.519> so<00:16:20.800> in<00:16:21.000> this 00:16:21.230 --> 00:16:21.240 align:start position:0% on the blockchain if you like so in this 00:16:21.240 --> 00:16:23.269 align:start position:0% on the blockchain if you like so in this example<00:16:21.680> if<00:16:21.759> I<00:16:21.880> go<00:16:22.040> over<00:16:22.199> the<00:16:22.399> diagram<00:16:23.079> you 00:16:23.269 --> 00:16:23.279 align:start position:0% example if I go over the diagram you 00:16:23.279 --> 00:16:25.509 align:start position:0% example if I go over the diagram you keep<00:16:23.519> you<00:16:23.680> store<00:16:24.279> encrypted<00:16:24.880> positions<00:16:25.360> on 00:16:25.509 --> 00:16:25.519 align:start position:0% keep you store encrypted positions on 00:16:25.519 --> 00:16:29.710 align:start position:0% keep you store encrypted positions on the<00:16:26.120> blockchain<00:16:27.120> every<00:16:27.399> user<00:16:28.399> uh<00:16:28.959> is<00:16:29.279> involved 00:16:29.710 --> 00:16:29.720 align:start position:0% the blockchain every user uh is involved 00:16:29.720 --> 00:16:31.389 align:start position:0% the blockchain every user uh is involved in<00:16:29.839> the<00:16:29.920> encryption<00:16:30.440> of<00:16:30.639> this<00:16:31.000> of<00:16:31.199> this 00:16:31.389 --> 00:16:31.399 align:start position:0% in the encryption of this of this 00:16:31.399 --> 00:16:34.389 align:start position:0% in the encryption of this of this position<00:16:31.800> by<00:16:31.920> using<00:16:32.199> their<00:16:32.399> own<00:16:32.759> key<00:16:33.759> they<00:16:33.920> can 00:16:34.389 --> 00:16:34.399 align:start position:0% position by using their own key they can 00:16:34.399 --> 00:16:37.910 align:start position:0% position by using their own key they can read<00:16:34.720> the<00:16:34.839> encrypted<00:16:35.639> position<00:16:36.639> decrypt<00:16:37.199> it 00:16:37.910 --> 00:16:37.920 align:start position:0% read the encrypted position decrypt it 00:16:37.920 --> 00:16:39.949 align:start position:0% read the encrypted position decrypt it and<00:16:38.120> then<00:16:38.600> execute<00:16:39.000> an<00:16:39.160> order<00:16:39.440> on<00:16:39.600> their<00:16:39.720> own 00:16:39.949 --> 00:16:39.959 align:start position:0% and then execute an order on their own 00:16:39.959 --> 00:16:42.350 align:start position:0% and then execute an order on their own position<00:16:40.360> and<00:16:40.560> encrypt<00:16:41.000> the<00:16:41.319> resulting<00:16:41.839> or 00:16:42.350 --> 00:16:42.360 align:start position:0% position and encrypt the resulting or 00:16:42.360 --> 00:16:45.910 align:start position:0% position and encrypt the resulting or the<00:16:42.519> resulting<00:16:43.279> position<00:16:44.279> now<00:16:44.480> if<00:16:44.639> they<00:16:44.959> prove 00:16:45.910 --> 00:16:45.920 align:start position:0% the resulting position now if they prove 00:16:45.920 --> 00:16:47.749 align:start position:0% the resulting position now if they prove to<00:16:46.160> a<00:16:46.360> contract<00:16:46.839> that 00:16:47.749 --> 00:16:47.759 align:start position:0% to a contract that 00:16:47.759 --> 00:16:51.629 align:start position:0% to a contract that executes<00:16:48.759> um<00:16:49.800> trades<00:16:50.800> that<00:16:51.079> this<00:16:51.240> would<00:16:51.440> be 00:16:51.629 --> 00:16:51.639 align:start position:0% executes um trades that this would be 00:16:51.639 --> 00:16:53.710 align:start position:0% executes um trades that this would be the<00:16:51.800> result<00:16:52.120> of<00:16:52.279> their<00:16:52.440> encrypted<00:16:53.040> position 00:16:53.710 --> 00:16:53.720 align:start position:0% the result of their encrypted position 00:16:53.720 --> 00:16:56.749 align:start position:0% the result of their encrypted position if<00:16:54.360> for<00:16:54.600> instance<00:16:55.079> they<00:16:55.240> get<00:16:55.480> a<00:16:55.600> little<00:16:55.759> more<00:16:56.040> e 00:16:56.749 --> 00:16:56.759 align:start position:0% if for instance they get a little more e 00:16:56.759 --> 00:16:59.990 align:start position:0% if for instance they get a little more e selling<00:16:57.680> a<00:16:57.800> little<00:16:58.000> bit<00:16:58.199> of<00:16:58.399> Bitcoin 00:16:59.990 --> 00:17:00.000 align:start position:0% selling a little bit of Bitcoin 00:17:00.000 --> 00:17:02.949 align:start position:0% selling a little bit of Bitcoin uh<00:17:00.480> then<00:17:01.360> a<00:17:01.560> trading<00:17:02.079> contract<00:17:02.560> or<00:17:02.720> if<00:17:02.800> you 00:17:02.949 --> 00:17:02.959 align:start position:0% uh then a trading contract or if you 00:17:02.959 --> 00:17:05.590 align:start position:0% uh then a trading contract or if you like<00:17:03.160> an<00:17:03.439> exchange<00:17:04.439> can<00:17:04.679> accept<00:17:05.039> that<00:17:05.240> proof 00:17:05.590 --> 00:17:05.600 align:start position:0% like an exchange can accept that proof 00:17:05.600 --> 00:17:08.390 align:start position:0% like an exchange can accept that proof without<00:17:06.240> actually<00:17:06.559> knowing<00:17:07.280> the<00:17:07.520> contents<00:17:08.199> of 00:17:08.390 --> 00:17:08.400 align:start position:0% without actually knowing the contents of 00:17:08.400 --> 00:17:11.710 align:start position:0% without actually knowing the contents of the<00:17:08.600> current<00:17:09.360> position<00:17:10.360> so<00:17:10.600> of<00:17:10.760> course<00:17:11.559> this 00:17:11.710 --> 00:17:11.720 align:start position:0% the current position so of course this 00:17:11.720 --> 00:17:14.189 align:start position:0% the current position so of course this does<00:17:11.959> divulge<00:17:12.480> some<00:17:12.760> information<00:17:13.400> because<00:17:14.039> uh 00:17:14.189 --> 00:17:14.199 align:start position:0% does divulge some information because uh 00:17:14.199 --> 00:17:16.630 align:start position:0% does divulge some information because uh we<00:17:14.319> are<00:17:14.439> telling<00:17:14.880> the<00:17:15.000> exchange<00:17:15.839> uh<00:17:16.199> by<00:17:16.439> how 00:17:16.630 --> 00:17:16.640 align:start position:0% we are telling the exchange uh by how 00:17:16.640 --> 00:17:18.990 align:start position:0% we are telling the exchange uh by how much<00:17:17.360> how<00:17:17.520> much<00:17:17.679> we<00:17:17.799> are<00:17:17.959> selling<00:17:18.480> and<00:17:18.880> how 00:17:18.990 --> 00:17:19.000 align:start position:0% much how much we are selling and how 00:17:19.000 --> 00:17:22.270 align:start position:0% much how much we are selling and how much<00:17:19.199> we<00:17:19.319> are<00:17:19.839> buying<00:17:20.839> but<00:17:21.199> anyone<00:17:21.679> looking<00:17:22.120> at 00:17:22.270 --> 00:17:22.280 align:start position:0% much we are buying but anyone looking at 00:17:22.280 --> 00:17:25.029 align:start position:0% much we are buying but anyone looking at the<00:17:22.520> position<00:17:23.079> of<00:17:23.199> a<00:17:23.400> given<00:17:23.880> uh<00:17:24.000> user<00:17:24.760> wouldn't 00:17:25.029 --> 00:17:25.039 align:start position:0% the position of a given uh user wouldn't 00:17:25.039 --> 00:17:27.390 align:start position:0% the position of a given uh user wouldn't be<00:17:25.199> able<00:17:25.400> to<00:17:25.600> decipher<00:17:26.319> the<00:17:26.520> current<00:17:26.919> strategy 00:17:27.390 --> 00:17:27.400 align:start position:0% be able to decipher the current strategy 00:17:27.400 --> 00:17:30.510 align:start position:0% be able to decipher the current strategy of<00:17:27.559> this<00:17:27.720> Trader<00:17:29.000> so<00:17:29.480> this<00:17:29.600> is<00:17:29.799> one<00:17:30.080> example 00:17:30.510 --> 00:17:30.520 align:start position:0% of this Trader so this is one example 00:17:30.520 --> 00:17:32.950 align:start position:0% of this Trader so this is one example where<00:17:30.679> proofs<00:17:31.039> can<00:17:31.200> be<00:17:31.440> combined<00:17:32.440> into<00:17:32.799> a 00:17:32.950 --> 00:17:32.960 align:start position:0% where proofs can be combined into a 00:17:32.960 --> 00:17:35.510 align:start position:0% where proofs can be combined into a blockchain<00:17:33.679> in<00:17:33.799> order<00:17:34.039> to<00:17:34.280> create<00:17:34.840> a<00:17:35.200> more 00:17:35.510 --> 00:17:35.520 align:start position:0% blockchain in order to create a more 00:17:35.520 --> 00:17:36.630 align:start position:0% blockchain in order to create a more private 00:17:36.630 --> 00:17:36.640 align:start position:0% private 00:17:36.640 --> 00:17:39.110 align:start position:0% private environment<00:17:37.640> uh<00:17:37.960> by<00:17:38.120> using<00:17:38.559> client<00:17:38.960> side 00:17:39.110 --> 00:17:39.120 align:start position:0% environment uh by using client side 00:17:39.120 --> 00:17:40.909 align:start position:0% environment uh by using client side proving<00:17:39.440> in<00:17:39.600> this<00:17:39.799> example<00:17:40.600> there<00:17:40.720> are 00:17:40.909 --> 00:17:40.919 align:start position:0% proving in this example there are 00:17:40.919 --> 00:17:43.590 align:start position:0% proving in this example there are variants<00:17:41.360> of<00:17:41.559> this<00:17:41.919> concept<00:17:42.919> uh<00:17:43.080> where<00:17:43.400> we 00:17:43.590 --> 00:17:43.600 align:start position:0% variants of this concept uh where we 00:17:43.600 --> 00:17:45.470 align:start position:0% variants of this concept uh where we trust<00:17:43.960> the<00:17:44.160> exchange<00:17:44.720> with<00:17:44.919> our<00:17:45.120> private 00:17:45.470 --> 00:17:45.480 align:start position:0% trust the exchange with our private 00:17:45.480 --> 00:17:47.430 align:start position:0% trust the exchange with our private information<00:17:46.160> and<00:17:46.400> then<00:17:46.679> all<00:17:46.840> the<00:17:47.000> positions 00:17:47.430 --> 00:17:47.440 align:start position:0% information and then all the positions 00:17:47.440 --> 00:17:49.230 align:start position:0% information and then all the positions can<00:17:47.559> be<00:17:47.720> encrypted<00:17:48.200> and<00:17:48.360> decrypted<00:17:48.919> by<00:17:49.080> the 00:17:49.230 --> 00:17:49.240 align:start position:0% can be encrypted and decrypted by the 00:17:49.240 --> 00:17:52.590 align:start position:0% can be encrypted and decrypted by the exchange<00:17:50.240> as<00:17:50.480> part<00:17:50.640> of<00:17:51.000> uh<00:17:51.240> proving<00:17:52.240> uh<00:17:52.440> but 00:17:52.590 --> 00:17:52.600 align:start position:0% exchange as part of uh proving uh but 00:17:52.600 --> 00:17:55.710 align:start position:0% exchange as part of uh proving uh but this<00:17:52.720> is<00:17:52.960> one<00:17:53.200> interesting<00:17:53.720> example<00:17:54.720> U<00:17:55.559> that 00:17:55.710 --> 00:17:55.720 align:start position:0% this is one interesting example U that 00:17:55.720 --> 00:17:59.149 align:start position:0% this is one interesting example U that can<00:17:55.919> also<00:17:56.159> be<00:17:56.320> implemented<00:17:56.960> on<00:17:57.559> uh<00:17:57.840> rollups<00:17:58.840> or 00:17:59.149 --> 00:17:59.159 align:start position:0% can also be implemented on uh rollups or 00:17:59.159 --> 00:18:01.350 align:start position:0% can also be implemented on uh rollups or blockchains<00:18:00.120> as<00:18:00.280> long<00:18:00.520> as<00:18:00.679> you<00:18:00.919> have<00:18:01.200> a 00:18:01.350 --> 00:18:01.360 align:start position:0% blockchains as long as you have a 00:18:01.360 --> 00:18:05.230 align:start position:0% blockchains as long as you have a contract<00:18:01.799> that<00:18:01.919> can<00:18:02.280> verify<00:18:03.280> uh<00:18:03.960> proofs<00:18:04.960> uh<00:18:05.080> on 00:18:05.230 --> 00:18:05.240 align:start position:0% contract that can verify uh proofs uh on 00:18:05.240 --> 00:18:07.070 align:start position:0% contract that can verify uh proofs uh on Stark<00:18:05.640> net<00:18:05.840> we<00:18:05.960> have<00:18:06.159> contracts<00:18:06.559> verifying 00:18:07.070 --> 00:18:07.080 align:start position:0% Stark net we have contracts verifying 00:18:07.080 --> 00:18:10.149 align:start position:0% Stark net we have contracts verifying Stark<00:18:07.559> proofs<00:18:08.559> uh<00:18:08.679> we<00:18:08.799> also<00:18:09.039> have<00:18:09.400> a<00:18:09.640> contract 00:18:10.149 --> 00:18:10.159 align:start position:0% Stark proofs uh we also have a contract 00:18:10.159 --> 00:18:12.669 align:start position:0% Stark proofs uh we also have a contract verifying<00:18:10.919> gross<00:18:11.240> extin<00:18:11.720> proofs<00:18:12.080> so<00:18:12.360> you<00:18:12.559> have 00:18:12.669 --> 00:18:12.679 align:start position:0% verifying gross extin proofs so you have 00:18:12.679 --> 00:18:15.310 align:start position:0% verifying gross extin proofs so you have a<00:18:12.919> choice<00:18:13.880> of<00:18:14.080> building<00:18:14.440> your<00:18:14.640> application<00:18:15.120> on 00:18:15.310 --> 00:18:15.320 align:start position:0% a choice of building your application on 00:18:15.320 --> 00:18:17.909 align:start position:0% a choice of building your application on top<00:18:15.480> of<00:18:15.600> that<00:18:15.760> and<00:18:15.919> Stark<00:18:16.280> net 00:18:17.909 --> 00:18:17.919 align:start position:0% top of that and Stark net 00:18:17.919 --> 00:18:20.990 align:start position:0% top of that and Stark net today<00:18:18.919> another<00:18:19.320> example<00:18:19.799> is<00:18:19.919> for<00:18:20.120> scaling 00:18:20.990 --> 00:18:21.000 align:start position:0% today another example is for scaling 00:18:21.000 --> 00:18:23.270 align:start position:0% today another example is for scaling blockchains<00:18:22.000> and<00:18:22.159> this<00:18:22.280> will<00:18:22.480> be<00:18:22.640> my<00:18:22.960> final 00:18:23.270 --> 00:18:23.280 align:start position:0% blockchains and this will be my final 00:18:23.280 --> 00:18:27.190 align:start position:0% blockchains and this will be my final slide<00:18:23.640> so<00:18:23.840> for<00:18:24.080> everyone<00:18:24.880> uh<00:18:25.880> uh<00:18:26.360> pressed<00:18:26.679> for 00:18:27.190 --> 00:18:27.200 align:start position:0% slide so for everyone uh uh pressed for 00:18:27.200 --> 00:18:30.710 align:start position:0% slide so for everyone uh uh pressed for time<00:18:28.200> um<00:18:29.120> this<00:18:29.280> is<00:18:29.400> a<00:18:29.600> little<00:18:29.840> bit<00:18:30.120> more 00:18:30.710 --> 00:18:30.720 align:start position:0% time um this is a little bit more 00:18:30.720 --> 00:18:33.789 align:start position:0% time um this is a little bit more sophisticated<00:18:31.720> but<00:18:31.880> the<00:18:32.039> idea<00:18:32.480> is<00:18:32.840> let's<00:18:33.120> say 00:18:33.789 --> 00:18:33.799 align:start position:0% sophisticated but the idea is let's say 00:18:33.799 --> 00:18:36.390 align:start position:0% sophisticated but the idea is let's say I<00:18:33.960> have<00:18:34.080> a<00:18:34.600> bottleneck<00:18:35.600> in<00:18:35.720> terms<00:18:36.000> of<00:18:36.200> the 00:18:36.390 --> 00:18:36.400 align:start position:0% I have a bottleneck in terms of the 00:18:36.400 --> 00:18:39.630 align:start position:0% I have a bottleneck in terms of the capacity<00:18:36.960> of<00:18:37.120> sequencing<00:18:37.640> and<00:18:38.360> execution<00:18:39.360> of 00:18:39.630 --> 00:18:39.640 align:start position:0% capacity of sequencing and execution of 00:18:39.640 --> 00:18:42.270 align:start position:0% capacity of sequencing and execution of what's<00:18:39.919> going<00:18:40.200> on<00:18:40.440> in<00:18:40.679> the<00:18:40.960> in<00:18:41.080> the<00:18:41.200> rollup<00:18:42.200> I 00:18:42.270 --> 00:18:42.280 align:start position:0% what's going on in the in the rollup I 00:18:42.280 --> 00:18:44.669 align:start position:0% what's going on in the in the rollup I want<00:18:42.480> to<00:18:42.919> Outsource<00:18:43.600> sequencing<00:18:44.159> to<00:18:44.360> someone 00:18:44.669 --> 00:18:44.679 align:start position:0% want to Outsource sequencing to someone 00:18:44.679 --> 00:18:47.630 align:start position:0% want to Outsource sequencing to someone else<00:18:45.120> if<00:18:45.240> you<00:18:45.440> like<00:18:46.080> or<00:18:46.280> I<00:18:46.400> want<00:18:46.600> to<00:18:46.799> Shard<00:18:47.400> my 00:18:47.630 --> 00:18:47.640 align:start position:0% else if you like or I want to Shard my 00:18:47.640 --> 00:18:50.830 align:start position:0% else if you like or I want to Shard my layer<00:18:48.200> my<00:18:48.559> uh<00:18:48.720> validity<00:18:49.159> rollup<00:18:50.120> so<00:18:50.360> that 00:18:50.830 --> 00:18:50.840 align:start position:0% layer my uh validity rollup so that 00:18:50.840 --> 00:18:53.510 align:start position:0% layer my uh validity rollup so that different<00:18:51.159> sequencers<00:18:51.919> can<00:18:52.120> run<00:18:52.760> together<00:18:53.240> in 00:18:53.510 --> 00:18:53.520 align:start position:0% different sequencers can run together in 00:18:53.520 --> 00:18:55.870 align:start position:0% different sequencers can run together in parallel<00:18:54.240> sequencing<00:18:54.880> different<00:18:55.320> parts<00:18:55.720> of 00:18:55.870 --> 00:18:55.880 align:start position:0% parallel sequencing different parts of 00:18:55.880 --> 00:18:57.789 align:start position:0% parallel sequencing different parts of the<00:18:56.000> rollup<00:18:56.480> or<00:18:56.679> different<00:18:57.039> contracts<00:18:57.520> if<00:18:57.640> you 00:18:57.789 --> 00:18:57.799 align:start position:0% the rollup or different contracts if you 00:18:57.799 --> 00:19:00.669 align:start position:0% the rollup or different contracts if you like<00:18:58.400> some<00:18:58.880> segregation<00:18:59.640> of 00:19:00.669 --> 00:19:00.679 align:start position:0% like some segregation of 00:19:00.679 --> 00:19:02.990 align:start position:0% like some segregation of transactions<00:19:01.679> so<00:19:01.880> in<00:19:02.039> this<00:19:02.320> context<00:19:02.799> you 00:19:02.990 --> 00:19:03.000 align:start position:0% transactions so in this context you 00:19:03.000 --> 00:19:04.549 align:start position:0% transactions so in this context you basically<00:19:03.400> what<00:19:03.480> you<00:19:03.640> see<00:19:03.880> here<00:19:04.000> is<00:19:04.200> something 00:19:04.549 --> 00:19:04.559 align:start position:0% basically what you see here is something 00:19:04.559 --> 00:19:07.029 align:start position:0% basically what you see here is something that<00:19:04.720> looks<00:19:05.000> like<00:19:05.159> two<00:19:05.480> rollups<00:19:06.480> but<00:19:06.679> they<00:19:06.799> are 00:19:07.029 --> 00:19:07.039 align:start position:0% that looks like two rollups but they are 00:19:07.039 --> 00:19:08.630 align:start position:0% that looks like two rollups but they are actually<00:19:07.360> the<00:19:07.480> same<00:19:07.720> rollup<00:19:08.200> so<00:19:08.320> you<00:19:08.440> have 00:19:08.630 --> 00:19:08.640 align:start position:0% actually the same rollup so you have 00:19:08.640 --> 00:19:11.789 align:start position:0% actually the same rollup so you have multiple<00:19:09.039> sequencers<00:19:09.880> each<00:19:10.600> executing<00:19:11.559> part 00:19:11.789 --> 00:19:11.799 align:start position:0% multiple sequencers each executing part 00:19:11.799 --> 00:19:15.350 align:start position:0% multiple sequencers each executing part of<00:19:11.960> the<00:19:12.200> sequencing<00:19:13.200> for<00:19:13.480> the<00:19:14.000> rollup<00:19:15.000> and 00:19:15.350 --> 00:19:15.360 align:start position:0% of the sequencing for the rollup and 00:19:15.360 --> 00:19:17.710 align:start position:0% of the sequencing for the rollup and proving<00:19:15.919> this<00:19:16.200> sequencing<00:19:16.799> is<00:19:17.039> correct<00:19:17.400> using 00:19:17.710 --> 00:19:17.720 align:start position:0% proving this sequencing is correct using 00:19:17.720 --> 00:19:20.990 align:start position:0% proving this sequencing is correct using the<00:19:17.919> validity<00:19:18.960> concept<00:19:19.960> where<00:19:20.159> the<00:19:20.360> output<00:19:20.840> of 00:19:20.990 --> 00:19:21.000 align:start position:0% the validity concept where the output of 00:19:21.000 --> 00:19:23.190 align:start position:0% the validity concept where the output of this<00:19:21.200> proof<00:19:21.640> is<00:19:21.840> the<00:19:22.240> state<00:19:22.640> diff<00:19:22.880> or<00:19:23.039> the 00:19:23.190 --> 00:19:23.200 align:start position:0% this proof is the state diff or the 00:19:23.200 --> 00:19:25.070 align:start position:0% this proof is the state diff or the changes<00:19:23.600> to<00:19:23.760> the<00:19:23.960> state<00:19:24.240> in<00:19:24.400> the<00:19:24.559> areas<00:19:24.960> that 00:19:25.070 --> 00:19:25.080 align:start position:0% changes to the state in the areas that 00:19:25.080 --> 00:19:27.909 align:start position:0% changes to the state in the areas that they're<00:19:25.400> responsible<00:19:26.240> for<00:19:27.240> an<00:19:27.400> underlying 00:19:27.909 --> 00:19:27.919 align:start position:0% they're responsible for an underlying 00:19:27.919 --> 00:19:29.549 align:start position:0% they're responsible for an underlying sequencer<00:19:28.520> that<00:19:28.760> which<00:19:28.880> is<00:19:29.000> the<00:19:29.159> validity 00:19:29.549 --> 00:19:29.559 align:start position:0% sequencer that which is the validity 00:19:29.559 --> 00:19:32.510 align:start position:0% sequencer that which is the validity rollup<00:19:29.960> sequencer<00:19:30.480> can<00:19:30.720> verify<00:19:31.240> these<00:19:31.520> proofs 00:19:32.510 --> 00:19:32.520 align:start position:0% rollup sequencer can verify these proofs 00:19:32.520 --> 00:19:34.430 align:start position:0% rollup sequencer can verify these proofs completely<00:19:33.240> remaining<00:19:33.600> on<00:19:33.760> the<00:19:33.880> rollup 00:19:34.430 --> 00:19:34.440 align:start position:0% completely remaining on the rollup 00:19:34.440 --> 00:19:36.029 align:start position:0% completely remaining on the rollup doesn't<00:19:34.720> have<00:19:35.159> these<00:19:35.320> proofs<00:19:35.559> don't<00:19:35.760> need<00:19:35.919> to 00:19:36.029 --> 00:19:36.039 align:start position:0% doesn't have these proofs don't need to 00:19:36.039 --> 00:19:37.190 align:start position:0% doesn't have these proofs don't need to be<00:19:36.159> sent<00:19:36.440> to 00:19:37.190 --> 00:19:37.200 align:start position:0% be sent to 00:19:37.200 --> 00:19:39.990 align:start position:0% be sent to ethereum<00:19:38.200> and<00:19:38.360> by<00:19:38.520> verifying<00:19:39.000> these<00:19:39.200> proofs 00:19:39.990 --> 00:19:40.000 align:start position:0% ethereum and by verifying these proofs 00:19:40.000 --> 00:19:42.789 align:start position:0% ethereum and by verifying these proofs uh<00:19:40.280> this<00:19:40.480> centralized<00:19:41.120> or<00:19:41.320> this<00:19:41.760> rollup 00:19:42.789 --> 00:19:42.799 align:start position:0% uh this centralized or this rollup 00:19:42.799 --> 00:19:45.310 align:start position:0% uh this centralized or this rollup sequencer<00:19:43.799> can<00:19:44.120> accept<00:19:44.480> the<00:19:44.679> state<00:19:44.960> diffs 00:19:45.310 --> 00:19:45.320 align:start position:0% sequencer can accept the state diffs 00:19:45.320 --> 00:19:47.270 align:start position:0% sequencer can accept the state diffs coming<00:19:45.600> from<00:19:45.840> these<00:19:46.080> various<00:19:46.400> shards<00:19:46.960> or<00:19:47.159> what 00:19:47.270 --> 00:19:47.280 align:start position:0% coming from these various shards or what 00:19:47.280 --> 00:19:51.270 align:start position:0% coming from these various shards or what we<00:19:47.480> call<00:19:48.000> ZK<00:19:48.600> threads<00:19:49.600> and<00:19:49.799> when<00:19:50.039> we<00:19:50.320> combine 00:19:51.270 --> 00:19:51.280 align:start position:0% we call ZK threads and when we combine 00:19:51.280 --> 00:19:53.789 align:start position:0% we call ZK threads and when we combine the<00:19:51.440> state<00:19:51.760> of<00:19:51.919> all<00:19:52.080> the<00:19:52.240> threads<00:19:52.679> we<00:19:52.919> result 00:19:53.789 --> 00:19:53.799 align:start position:0% the state of all the threads we result 00:19:53.799 --> 00:19:56.750 align:start position:0% the state of all the threads we result in<00:19:54.039> a<00:19:54.200> single<00:19:54.600> state<00:19:55.240> of<00:19:55.400> a<00:19:55.520> single<00:19:55.799> rollup 00:19:56.750 --> 00:19:56.760 align:start position:0% in a single state of a single rollup 00:19:56.760 --> 00:19:59.909 align:start position:0% in a single state of a single rollup that<00:19:56.960> can<00:19:57.320> be<00:19:58.320> as<00:19:58.480> in<00:19:58.760> the<00:19:58.880> previous<00:19:59.240> story 00:19:59.909 --> 00:19:59.919 align:start position:0% that can be as in the previous story 00:19:59.919 --> 00:20:02.110 align:start position:0% that can be as in the previous story transmitted<00:20:00.520> to<00:20:00.679> ethereum<00:20:01.440> with<00:20:01.679> various 00:20:02.110 --> 00:20:02.120 align:start position:0% transmitted to ethereum with various 00:20:02.120 --> 00:20:03.029 align:start position:0% transmitted to ethereum with various kinds<00:20:02.320> of 00:20:03.029 --> 00:20:03.039 align:start position:0% kinds of 00:20:03.039 --> 00:20:05.789 align:start position:0% kinds of proving<00:20:04.039> uh<00:20:04.159> resulting<00:20:04.600> in<00:20:04.720> a<00:20:04.880> unified<00:20:05.679> uh 00:20:05.789 --> 00:20:05.799 align:start position:0% proving uh resulting in a unified uh 00:20:05.799 --> 00:20:08.270 align:start position:0% proving uh resulting in a unified uh rollup<00:20:06.720> that<00:20:06.919> has<00:20:07.159> all<00:20:07.320> the<00:20:07.480> state<00:20:07.840> computed 00:20:08.270 --> 00:20:08.280 align:start position:0% rollup that has all the state computed 00:20:08.280 --> 00:20:10.270 align:start position:0% rollup that has all the state computed by<00:20:08.440> multiple<00:20:08.880> sequencers<00:20:09.799> so<00:20:09.960> here<00:20:10.120> we 00:20:10.270 --> 00:20:10.280 align:start position:0% by multiple sequencers so here we 00:20:10.280 --> 00:20:12.230 align:start position:0% by multiple sequencers so here we utilize<00:20:11.000> uh<00:20:11.120> validity 00:20:12.230 --> 00:20:12.240 align:start position:0% utilize uh validity 00:20:12.240 --> 00:20:16.830 align:start position:0% utilize uh validity proofs<00:20:13.240> uh<00:20:13.400> in<00:20:13.520> order<00:20:13.840> to<00:20:14.120> scale<00:20:15.000> a 00:20:16.830 --> 00:20:16.840 align:start position:0% proofs uh in order to scale a 00:20:16.840 --> 00:20:19.669 align:start position:0% proofs uh in order to scale a rollup<00:20:17.840> that's<00:20:18.039> it<00:20:18.440> I<00:20:18.520> think<00:20:18.679> I<00:20:18.799> have<00:20:19.360> 3 00:20:19.669 --> 00:20:19.679 align:start position:0% rollup that's it I think I have 3 00:20:19.679 --> 00:20:25.350 align:start position:0% rollup that's it I think I have 3 seconds 00:20:25.350 --> 00:20:25.360 align:start position:0% 00:20:25.360 --> 00:20:27.950 align:start position:0% left<00:20:26.360> thank<00:20:26.559> you<00:20:26.720> we<00:20:26.840> have<00:20:27.280> now<00:20:27.559> a<00:20:27.679> few 00:20:27.950 --> 00:20:27.960 align:start position:0% left thank you we have now a few 00:20:27.960 --> 00:20:31.510 align:start position:0% left thank you we have now a few questions<00:20:28.880> could<00:20:29.080> you 00:20:31.510 --> 00:20:31.520 align:start position:0% questions could you 00:20:31.520 --> 00:20:33.669 align:start position:0% questions could you question<00:20:32.520> so<00:20:32.720> I<00:20:32.840> think<00:20:33.000> the<00:20:33.159> first<00:20:33.400> question 00:20:33.669 --> 00:20:33.679 align:start position:0% question so I think the first question 00:20:33.679 --> 00:20:36.630 align:start position:0% question so I think the first question is<00:20:34.200> how<00:20:34.360> is<00:20:34.559> aggregating<00:20:35.200> State<00:20:35.840> differ<00:20:36.320> from 00:20:36.630 --> 00:20:36.640 align:start position:0% is how is aggregating State differ from 00:20:36.640 --> 00:20:39.750 align:start position:0% is how is aggregating State differ from multiple<00:20:37.120> blocks<00:20:37.919> and<00:20:38.640> is<00:20:38.799> it<00:20:39.159> better<00:20:39.480> than 00:20:39.750 --> 00:20:39.760 align:start position:0% multiple blocks and is it better than 00:20:39.760 --> 00:20:42.990 align:start position:0% multiple blocks and is it better than increasing<00:20:40.200> the<00:20:40.360> block<00:20:40.640> time 00:20:42.990 --> 00:20:43.000 align:start position:0% 00:20:43.000 --> 00:20:46.789 align:start position:0% itself<00:20:44.159> um<00:20:45.159> aggregating<00:20:45.799> state<00:20:46.280> is<00:20:46.480> better 00:20:46.789 --> 00:20:46.799 align:start position:0% itself um aggregating state is better 00:20:46.799 --> 00:20:48.110 align:start position:0% itself um aggregating state is better than<00:20:47.000> multiple 00:20:48.110 --> 00:20:48.120 align:start position:0% than multiple 00:20:48.120 --> 00:20:50.270 align:start position:0% than multiple blocks 00:20:50.270 --> 00:20:50.280 align:start position:0% blocks 00:20:50.280 --> 00:20:53.990 align:start position:0% blocks uh<00:20:51.280> no<00:20:52.039> uh<00:20:52.440> multiple<00:20:52.960> blocks<00:20:53.320> is<00:20:53.480> better<00:20:53.760> than 00:20:53.990 --> 00:20:54.000 align:start position:0% uh no uh multiple blocks is better than 00:20:54.000 --> 00:20:56.029 align:start position:0% uh no uh multiple blocks is better than having<00:20:54.240> a<00:20:54.400> single<00:20:54.799> aggregate<00:20:55.280> block<00:20:55.679> I'll<00:20:55.919> put 00:20:56.029 --> 00:20:56.039 align:start position:0% having a single aggregate block I'll put 00:20:56.039 --> 00:20:58.950 align:start position:0% having a single aggregate block I'll put it<00:20:56.280> that<00:20:56.440> way<00:20:57.240> why<00:20:57.960> because<00:20:58.240> what<00:20:58.400> use<00:20:58.600> users 00:20:58.950 --> 00:20:58.960 align:start position:0% it that way why because what use users 00:20:58.960 --> 00:21:02.110 align:start position:0% it that way why because what use users really<00:20:59.200> want<00:20:59.679> is<00:20:59.960> finality<00:21:00.559> on<00:21:00.720> Layer<00:21:01.039> Two<00:21:01.919> on 00:21:02.110 --> 00:21:02.120 align:start position:0% really want is finality on Layer Two on 00:21:02.120 --> 00:21:04.149 align:start position:0% really want is finality on Layer Two on the<00:21:02.280> validity<00:21:02.679> roll<00:21:02.919> up<00:21:03.120> itself<00:21:03.400> so<00:21:03.679> response 00:21:04.149 --> 00:21:04.159 align:start position:0% the validity roll up itself so response 00:21:04.159 --> 00:21:07.909 align:start position:0% the validity roll up itself so response times<00:21:04.520> go<00:21:04.799> down<00:21:05.440> the<00:21:05.640> smaller<00:21:06.080> the<00:21:06.240> block<00:21:06.919> is 00:21:07.909 --> 00:21:07.919 align:start position:0% times go down the smaller the block is 00:21:07.919 --> 00:21:09.710 align:start position:0% times go down the smaller the block is uh<00:21:08.159> of<00:21:08.320> course<00:21:08.600> if<00:21:08.760> we<00:21:08.880> would<00:21:09.120> wait<00:21:09.320> for<00:21:09.520> an 00:21:09.710 --> 00:21:09.720 align:start position:0% uh of course if we would wait for an 00:21:09.720 --> 00:21:11.590 align:start position:0% uh of course if we would wait for an hour<00:21:10.039> to<00:21:10.240> aggregate<00:21:10.720> lots<00:21:10.919> of<00:21:11.080> transactions 00:21:11.590 --> 00:21:11.600 align:start position:0% hour to aggregate lots of transactions 00:21:11.600 --> 00:21:14.110 align:start position:0% hour to aggregate lots of transactions in<00:21:11.720> a<00:21:11.960> block<00:21:12.960> then<00:21:13.080> we<00:21:13.200> would<00:21:13.440> had<00:21:13.720> you<00:21:14.000> we 00:21:14.110 --> 00:21:14.120 align:start position:0% in a block then we would had you we 00:21:14.120 --> 00:21:16.110 align:start position:0% in a block then we would had you we would<00:21:14.360> have<00:21:14.679> huge<00:21:15.000> blocks<00:21:15.480> and<00:21:15.640> the<00:21:15.799> basic 00:21:16.110 --> 00:21:16.120 align:start position:0% would have huge blocks and the basic 00:21:16.120 --> 00:21:18.070 align:start position:0% would have huge blocks and the basic validity<00:21:16.559> roll<00:21:16.799> up<00:21:16.960> would<00:21:17.120> work<00:21:17.400> but<00:21:17.600> finality 00:21:18.070 --> 00:21:18.080 align:start position:0% validity roll up would work but finality 00:21:18.080 --> 00:21:20.070 align:start position:0% validity roll up would work but finality on<00:21:18.240> Layer<00:21:18.480> Two<00:21:18.760> would<00:21:18.880> be<00:21:19.080> very 00:21:20.070 --> 00:21:20.080 align:start position:0% on Layer Two would be very 00:21:20.080 --> 00:21:22.750 align:start position:0% on Layer Two would be very slow<00:21:21.080> I<00:21:21.200> also<00:21:21.400> want<00:21:21.520> to<00:21:21.679> answer<00:21:22.159> of<00:21:22.360> about 00:21:22.750 --> 00:21:22.760 align:start position:0% slow I also want to answer of about 00:21:22.760 --> 00:21:24.390 align:start position:0% slow I also want to answer of about about<00:21:23.080> proving 00:21:24.390 --> 00:21:24.400 align:start position:0% about proving 00:21:24.400 --> 00:21:28.269 align:start position:0% about proving cost<00:21:25.480> um<00:21:26.480> it's<00:21:26.600> a<00:21:26.760> good<00:21:26.960> question<00:21:27.320> because<00:21:27.880> uh 00:21:28.269 --> 00:21:28.279 align:start position:0% cost um it's a good question because uh 00:21:28.279 --> 00:21:30.549 align:start position:0% cost um it's a good question because uh in<00:21:28.640> the<00:21:28.760> past<00:21:29.039> people<00:21:29.400> thought<00:21:30.240> uh<00:21:30.360> that 00:21:30.549 --> 00:21:30.559 align:start position:0% in the past people thought uh that 00:21:30.559 --> 00:21:34.350 align:start position:0% in the past people thought uh that proving<00:21:31.080> I<00:21:31.240> remember<00:21:31.840> back<00:21:32.039> in<00:21:32.480> 2017<00:21:33.480> or 00:21:34.350 --> 00:21:34.360 align:start position:0% proving I remember back in 2017 or 00:21:34.360 --> 00:21:37.549 align:start position:0% proving I remember back in 2017 or 2018<00:21:35.360> uh<00:21:35.559> the<00:21:35.679> number<00:21:36.080> thrown<00:21:36.640> at<00:21:36.840> people<00:21:37.320> was 00:21:37.549 --> 00:21:37.559 align:start position:0% 2018 uh the number thrown at people was 00:21:37.559 --> 00:21:40.390 align:start position:0% 2018 uh the number thrown at people was that<00:21:38.039> proving<00:21:38.520> a<00:21:38.760> statement<00:21:39.279> was<00:21:39.600> something 00:21:40.390 --> 00:21:40.400 align:start position:0% that proving a statement was something 00:21:40.400 --> 00:21:44.789 align:start position:0% that proving a statement was something like<00:21:41.080> four<00:21:41.440> orders<00:21:41.840> of<00:21:42.159> magnitude<00:21:43.159> uh<00:21:43.600> less<00:21:44.320> uh 00:21:44.789 --> 00:21:44.799 align:start position:0% like four orders of magnitude uh less uh 00:21:44.799 --> 00:21:47.070 align:start position:0% like four orders of magnitude uh less uh performant<00:21:45.480> than<00:21:45.760> actually<00:21:46.120> executing<00:21:46.720> that 00:21:47.070 --> 00:21:47.080 align:start position:0% performant than actually executing that 00:21:47.080 --> 00:21:49.269 align:start position:0% performant than actually executing that statement<00:21:48.080> at<00:21:48.240> starkware<00:21:48.840> I<00:21:48.919> think<00:21:49.080> our 00:21:49.269 --> 00:21:49.279 align:start position:0% statement at starkware I think our 00:21:49.279 --> 00:21:51.549 align:start position:0% statement at starkware I think our initial<00:21:49.679> prover<00:21:50.159> reached<00:21:50.600> about<00:21:50.960> two<00:21:51.200> orders 00:21:51.549 --> 00:21:51.559 align:start position:0% initial prover reached about two orders 00:21:51.559 --> 00:21:53.470 align:start position:0% initial prover reached about two orders of<00:21:51.840> magnitude<00:21:52.840> H<00:21:52.960> which<00:21:53.080> is<00:21:53.200> called<00:21:53.360> the 00:21:53.470 --> 00:21:53.480 align:start position:0% of magnitude H which is called the 00:21:53.480 --> 00:21:56.070 align:start position:0% of magnitude H which is called the stoneover<00:21:54.279> and<00:21:54.480> today<00:21:54.880> we're<00:21:55.120> talking<00:21:55.520> about 00:21:56.070 --> 00:21:56.080 align:start position:0% stoneover and today we're talking about 00:21:56.080 --> 00:21:56.909 align:start position:0% stoneover and today we're talking about a 00:21:56.909 --> 00:21:56.919 align:start position:0% a 00:21:56.919 --> 00:21:59.909 align:start position:0% a Stover<00:21:57.919> where<00:21:58.600> execution<00:21:59.000> of<00:21:59.120> the<00:21:59.320> statement 00:21:59.909 --> 00:21:59.919 align:start position:0% Stover where execution of the statement 00:21:59.919 --> 00:22:02.549 align:start position:0% Stover where execution of the statement is<00:22:00.600> almost<00:22:01.159> the<00:22:01.360> same<00:22:01.760> as<00:22:01.960> proving<00:22:02.360> the 00:22:02.549 --> 00:22:02.559 align:start position:0% is almost the same as proving the 00:22:02.559 --> 00:22:04.669 align:start position:0% is almost the same as proving the statement<00:22:03.039> so<00:22:03.360> the<00:22:03.600> cost<00:22:03.880> of<00:22:04.080> proving<00:22:04.480> has 00:22:04.669 --> 00:22:04.679 align:start position:0% statement so the cost of proving has 00:22:04.679 --> 00:22:06.789 align:start position:0% statement so the cost of proving has gone<00:22:04.960> down<00:22:05.360> very<00:22:05.600> very<00:22:05.880> significantly<00:22:06.640> well 00:22:06.789 --> 00:22:06.799 align:start position:0% gone down very very significantly well 00:22:06.799 --> 00:22:08.510 align:start position:0% gone down very very significantly well it's<00:22:07.000> not<00:22:07.200> the<00:22:07.360> same<00:22:07.679> of<00:22:07.840> course<00:22:08.120> you<00:22:08.279> still 00:22:08.510 --> 00:22:08.520 align:start position:0% it's not the same of course you still 00:22:08.520 --> 00:22:10.990 align:start position:0% it's not the same of course you still have<00:22:08.679> an<00:22:08.880> overhead<00:22:09.880> but<00:22:10.039> to<00:22:10.200> prove<00:22:10.520> statements 00:22:10.990 --> 00:22:11.000 align:start position:0% have an overhead but to prove statements 00:22:11.000 --> 00:22:13.430 align:start position:0% have an overhead but to prove statements today<00:22:11.559> costs<00:22:12.279> very<00:22:12.600> very 00:22:13.430 --> 00:22:13.440 align:start position:0% today costs very very 00:22:13.440 --> 00:22:17.149 align:start position:0% today costs very very little<00:22:14.440> uh<00:22:14.960> so<00:22:15.679> all<00:22:15.960> this<00:22:16.200> recursive<00:22:16.760> proving 00:22:17.149 --> 00:22:17.159 align:start position:0% little uh so all this recursive proving 00:22:17.159 --> 00:22:20.430 align:start position:0% little uh so all this recursive proving for<00:22:17.360> instance<00:22:18.360> is<00:22:18.559> done<00:22:18.960> within<00:22:19.440> seconds 00:22:20.430 --> 00:22:20.440 align:start position:0% for instance is done within seconds 00:22:20.440 --> 00:22:22.789 align:start position:0% for instance is done within seconds every<00:22:20.720> recursive<00:22:21.279> step<00:22:21.640> so<00:22:21.880> you<00:22:22.039> get<00:22:22.360> a<00:22:22.600> very 00:22:22.789 --> 00:22:22.799 align:start position:0% every recursive step so you get a very 00:22:22.799 --> 00:22:24.590 align:start position:0% every recursive step so you get a very quick<00:22:23.000> finality<00:22:23.600> even<00:22:23.799> of<00:22:23.919> the<00:22:24.080> recursive 00:22:24.590 --> 00:22:24.600 align:start position:0% quick finality even of the recursive 00:22:24.600 --> 00:22:26.710 align:start position:0% quick finality even of the recursive proof<00:22:25.000> and<00:22:25.200> of<00:22:25.360> course<00:22:25.600> that<00:22:25.760> doesn't<00:22:26.080> cost 00:22:26.710 --> 00:22:26.720 align:start position:0% proof and of course that doesn't cost 00:22:26.720 --> 00:22:30.750 align:start position:0% proof and of course that doesn't cost much<00:22:27.720> okay<00:22:28.080> um<00:22:28.240> we<00:22:28.360> have<00:22:28.760> still<00:22:29.159> time<00:22:29.559> so<00:22:30.520> um 00:22:30.750 --> 00:22:30.760 align:start position:0% much okay um we have still time so um 00:22:30.760 --> 00:22:32.350 align:start position:0% much okay um we have still time so um what's<00:22:30.919> the<00:22:31.120> current<00:22:31.400> transaction<00:22:31.919> finality 00:22:32.350 --> 00:22:32.360 align:start position:0% what's the current transaction finality 00:22:32.360 --> 00:22:35.950 align:start position:0% what's the current transaction finality on<00:22:32.440> Stark<00:22:32.760> net<00:22:33.000> if<00:22:33.200> you<00:22:33.880> uh<00:22:34.200> can<00:22:35.200> yes<00:22:35.640> currently 00:22:35.950 --> 00:22:35.960 align:start position:0% on Stark net if you uh can yes currently 00:22:35.960 --> 00:22:37.909 align:start position:0% on Stark net if you uh can yes currently on<00:22:36.080> starnet<00:22:36.600> you<00:22:36.679> get<00:22:36.880> finality<00:22:37.360> on<00:22:37.480> Layer<00:22:37.720> Two 00:22:37.909 --> 00:22:37.919 align:start position:0% on starnet you get finality on Layer Two 00:22:37.919 --> 00:22:40.190 align:start position:0% on starnet you get finality on Layer Two within<00:22:38.200> two<00:22:38.480> seconds<00:22:39.039> two<00:22:39.200> seconds<00:22:39.799> and<00:22:39.960> this 00:22:40.190 --> 00:22:40.200 align:start position:0% within two seconds two seconds and this 00:22:40.200 --> 00:22:42.230 align:start position:0% within two seconds two seconds and this two<00:22:40.480> seconds<00:22:40.799> will<00:22:41.000> be<00:22:41.279> preserved<00:22:41.919> in<00:22:42.039> a 00:22:42.230 --> 00:22:42.240 align:start position:0% two seconds will be preserved in a 00:22:42.240 --> 00:22:44.710 align:start position:0% two seconds will be preserved in a decentralized<00:22:43.080> environment<00:22:43.880> where<00:22:44.240> actually 00:22:44.710 --> 00:22:44.720 align:start position:0% decentralized environment where actually 00:22:44.720 --> 00:22:46.750 align:start position:0% decentralized environment where actually block<00:22:45.039> times<00:22:45.320> will<00:22:45.480> go<00:22:45.679> down<00:22:45.840> to<00:22:46.120> 2<00:22:46.400> seconds 00:22:46.750 --> 00:22:46.760 align:start position:0% block times will go down to 2 seconds 00:22:46.760 --> 00:22:49.390 align:start position:0% block times will go down to 2 seconds and<00:22:46.919> we<00:22:47.000> will<00:22:47.240> continue<00:22:47.640> to<00:22:47.919> prove<00:22:48.840> every 00:22:49.390 --> 00:22:49.400 align:start position:0% and we will continue to prove every 00:22:49.400 --> 00:22:51.630 align:start position:0% and we will continue to prove every block<00:22:50.400> so<00:22:50.640> that's<00:22:50.840> where<00:22:51.000> we<00:22:51.120> can<00:22:51.320> go<00:22:51.480> with 00:22:51.630 --> 00:22:51.640 align:start position:0% block so that's where we can go with 00:22:51.640 --> 00:22:53.870 align:start position:0% block so that's where we can go with this 00:22:53.870 --> 00:22:53.880 align:start position:0% 00:22:53.880 --> 00:22:56.789 align:start position:0% technology<00:22:54.880> and<00:22:55.240> maybe<00:22:55.880> could<00:22:56.120> this<00:22:56.320> be<00:22:56.480> used 00:22:56.789 --> 00:22:56.799 align:start position:0% technology and maybe could this be used 00:22:56.799 --> 00:22:58.710 align:start position:0% technology and maybe could this be used for<00:22:57.000> Crossroad<00:22:57.520> lab<00:22:57.760> Communications<00:22:58.520> through 00:22:58.710 --> 00:22:58.720 align:start position:0% for Crossroad lab Communications through 00:22:58.720 --> 00:23:03.710 align:start position:0% for Crossroad lab Communications through a<00:22:58.880> shared<00:23:00.159> approver<00:23:01.240> absolutely<00:23:02.240> uh<00:23:02.520> in<00:23:02.799> fact 00:23:03.710 --> 00:23:03.720 align:start position:0% a shared approver absolutely uh in fact 00:23:03.720 --> 00:23:06.110 align:start position:0% a shared approver absolutely uh in fact in<00:23:03.880> Stark<00:23:04.279> net<00:23:04.520> to<00:23:04.799> in<00:23:05.159> starkware<00:23:05.840> I<00:23:05.919> should 00:23:06.110 --> 00:23:06.120 align:start position:0% in Stark net to in starkware I should 00:23:06.120 --> 00:23:08.750 align:start position:0% in Stark net to in starkware I should say<00:23:06.520> today<00:23:07.400> we<00:23:07.600> already<00:23:08.039> have<00:23:08.240> a<00:23:08.360> shared 00:23:08.750 --> 00:23:08.760 align:start position:0% say today we already have a shared 00:23:08.760 --> 00:23:10.950 align:start position:0% say today we already have a shared prover<00:23:09.200> it's<00:23:09.360> called<00:23:09.640> sharp<00:23:10.440> sharp<00:23:10.760> for 00:23:10.950 --> 00:23:10.960 align:start position:0% prover it's called sharp sharp for 00:23:10.960 --> 00:23:14.549 align:start position:0% prover it's called sharp sharp for shared<00:23:11.320> proving<00:23:12.320> and<00:23:12.520> we<00:23:12.679> use<00:23:12.960> it<00:23:13.760> for<00:23:14.080> many 00:23:14.549 --> 00:23:14.559 align:start position:0% shared proving and we use it for many 00:23:14.559 --> 00:23:17.549 align:start position:0% shared proving and we use it for many systems<00:23:15.120> together<00:23:15.440> so<00:23:15.600> we<00:23:15.760> use<00:23:16.000> it<00:23:16.440> for<00:23:17.279> public 00:23:17.549 --> 00:23:17.559 align:start position:0% systems together so we use it for public 00:23:17.559 --> 00:23:21.029 align:start position:0% systems together so we use it for public Stark<00:23:18.000> net<00:23:18.400> we<00:23:18.559> use<00:23:18.799> it<00:23:19.120> for<00:23:19.679> private<00:23:20.000> Stark<00:23:20.520> X 00:23:21.029 --> 00:23:21.039 align:start position:0% Stark net we use it for private Stark X 00:23:21.039 --> 00:23:23.909 align:start position:0% Stark net we use it for private Stark X instances<00:23:21.600> we<00:23:21.880> are<00:23:22.480> layer<00:23:22.720> 2<00:23:23.000> platforms<00:23:23.480> for 00:23:23.909 --> 00:23:23.919 align:start position:0% instances we are layer 2 platforms for 00:23:23.919 --> 00:23:26.669 align:start position:0% instances we are layer 2 platforms for exchanges<00:23:24.919> we<00:23:25.080> use<00:23:25.279> it<00:23:25.520> for<00:23:25.799> app<00:23:26.039> chains<00:23:26.480> of 00:23:26.669 --> 00:23:26.679 align:start position:0% exchanges we use it for app chains of 00:23:26.679 --> 00:23:29.909 align:start position:0% exchanges we use it for app chains of Stark<00:23:27.080> net<00:23:27.720> and<00:23:27.960> all<00:23:28.120> of<00:23:28.279> the<00:23:28.840> com<00:23:29.559> all<00:23:29.720> of 00:23:29.909 --> 00:23:29.919 align:start position:0% Stark net and all of the com all of 00:23:29.919 --> 00:23:32.110 align:start position:0% Stark net and all of the com all of these<00:23:30.279> proofs<00:23:30.640> are<00:23:30.919> combined<00:23:31.400> into<00:23:31.720> single 00:23:32.110 --> 00:23:32.120 align:start position:0% these proofs are combined into single 00:23:32.120 --> 00:23:34.110 align:start position:0% these proofs are combined into single recursive<00:23:32.679> proofs<00:23:33.520> some<00:23:33.679> of<00:23:33.799> them<00:23:33.960> are 00:23:34.110 --> 00:23:34.120 align:start position:0% recursive proofs some of them are 00:23:34.120 --> 00:23:36.029 align:start position:0% recursive proofs some of them are applicative<00:23:34.600> recursion<00:23:35.240> some<00:23:35.400> of<00:23:35.559> them<00:23:35.760> are 00:23:36.029 --> 00:23:36.039 align:start position:0% applicative recursion some of them are 00:23:36.039 --> 00:23:37.750 align:start position:0% applicative recursion some of them are regular<00:23:36.480> recursion<00:23:37.000> and<00:23:37.159> all<00:23:37.279> of<00:23:37.440> this<00:23:37.600> is 00:23:37.750 --> 00:23:37.760 align:start position:0% regular recursion and all of this is 00:23:37.760 --> 00:23:40.990 align:start position:0% regular recursion and all of this is submitted<00:23:38.279> in<00:23:38.440> a<00:23:38.640> single<00:23:39.360> proof<00:23:39.799> attesting<00:23:40.360> to 00:23:40.990 --> 00:23:41.000 align:start position:0% submitted in a single proof attesting to 00:23:41.000 --> 00:23:43.950 align:start position:0% submitted in a single proof attesting to a<00:23:41.200> huge<00:23:41.600> number<00:23:41.960> of<00:23:42.200> execution<00:23:42.799> steps<00:23:43.600> across 00:23:43.950 --> 00:23:43.960 align:start position:0% a huge number of execution steps across 00:23:43.960 --> 00:23:45.870 align:start position:0% a huge number of execution steps across multiple<00:23:44.480> systems<00:23:44.880> so<00:23:45.080> of<00:23:45.200> course<00:23:45.480> this<00:23:45.640> could 00:23:45.870 --> 00:23:45.880 align:start position:0% multiple systems so of course this could 00:23:45.880 --> 00:23:48.070 align:start position:0% multiple systems so of course this could also<00:23:46.120> be<00:23:46.279> used<00:23:47.000> for<00:23:47.240> messaging<00:23:47.760> between 00:23:48.070 --> 00:23:48.080 align:start position:0% also be used for messaging between 00:23:48.080 --> 00:23:50.230 align:start position:0% also be used for messaging between different 00:23:50.230 --> 00:23:50.240 align:start position:0% different 00:23:50.240 --> 00:23:53.549 align:start position:0% different rollups<00:23:51.240> uh<00:23:51.440> do<00:23:51.640> we<00:23:51.799> have<00:23:52.039> any<00:23:52.240> questions<00:23:52.679> from 00:23:53.549 --> 00:23:53.559 align:start position:0% rollups uh do we have any questions from 00:23:53.559 --> 00:23:58.159 align:start position:0% rollups uh do we have any questions from the<00:23:54.559> audience<00:23:55.080> no<00:23:55.559> okay<00:23:55.919> uh