Matteo Capucci

Mathematician (category theory for general systems theory & cybernetics), socialist, aspiring psycohistorian, meme enjoyer (shitpost is not endorsement).
Currently: ARIA double grantee, 🇮🇹 based, finishing my PhD @mspstrath
Custodian of CT Zulip, email me for an invite.

Pronouns: he/him
Website: https://matteocapucci.eu

Public Key

npub1lezrwa7qdjfwnfqhyumqr47nyrs2c7vw24p8ddq8uuzn7r7uk9uqkv3yeq

NIP-05 Address

mc_at_mathstodon.xyz@momostr.pink

Profile Code

nprofile1qqs0u3phwlqxeyhf5stjwdsp6lfjpc9v0x892snkksr7wpflplwtz7qpz3mhxue69uhhyetvv9ujuerpd46hxtnfduqs6amnwvaz7tmwdaejumr0dsrhjku4

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relay.damus.io

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npub1lezrwa7qdjfwnfqhyumqr47nyrs2c7vw24p8ddq8uuzn7r7uk9uqkv3yeq

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Last Notes

2026-08-26 10:05:54 UTC

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hehe :)

2026-08-25 10:14:13 UTC

be not afraid
https://media.mathstodon.xyz/media_attachments/files/117/155/615/578/766/198/original/8c5a6e6270bc637a.png

2026-08-21 00:27:21 UTC

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if everything goes to plan, it should be done within a month. then reviewers will bite away, and we'll see how long that takes. hopefully not too much longer!

2026-08-21 00:25:34 UTC

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and needless to say, so much stuff is inspired or directly taken from the community's work, the list is too long!

2026-08-21 00:23:47 UTC

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so glad to have you as a beta tester :) I hope it's gonna get less challenging to read when we are done refining the thing.
we are currently attacking a massive to-do list of ~600 items. we spent most of last week just reading through each other's parts and heavily annotating them. there's quite a bit of writing missing, and tons of copyedits.
we are doing this at David Jazz's parents house in Portugal, which has helped making the whole process less stressful!
also, let me mention that the thesis will also feature two contributed chapters, one from [@ayegill](https://schelling.pt/@ayegill ) (about continuous-time SDEs) and one by Diptarko Roy and Gregory Neustroev, on 'supermartingale certificates for Markov processes'. having heavy-duty stochastic systems in the framework is quite a reality check (if far from definitive), and Dip and Greg's exposition gives a glimpse of where one could go with some ingenuity.

2026-08-21 00:14:41 UTC

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oh wow for a moment I thought it was comparing *increase* of all those countries (and was pretty relieved by seeing how good Italy was doing) but no 🤯

2026-08-15 17:14:20 UTC

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ah damn. though I mean *real* \infty-category theorists (ie (\infty,\infty))

2026-08-15 16:27:04 UTC

in 10 years, \infty-category theorists will look at 1-category theorists the way 1-category theorists look at set theorist

2026-08-14 19:31:46 UTC

so in his latest post (https://xenaproject.wordpress.com/2026/08/13/the-annals-challenge/) Buzzard makes the point that the process of formalizing math usually yields insight on the math itself, which seems very reasonable!
I thought I could ask the chatbots about examples of that, but then why not ask here?
formalizers, blow my mind!

2026-08-11 08:35:03 UTC

this is wild https://arxiv.org/abs/2608.08421
https://media.mathstodon.xyz/media_attachments/files/117/075/952/568/809/717/original/e73e77361536aa35.png

2026-06-09 07:57:17 UTC

the language spoken by aibros on X is noticeably diverging from the rest of english and it's so bizarre

2026-05-22 07:25:34 UTC

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yeah indeed, but it's been known to work. thanks for the notes :D

2026-05-22 07:16:42 UTC

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is this a quasicrystal? it's the projection of a high-dimensional lattice so it's not unlikely

2026-04-29 08:19:25 UTC

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you should write 'huger numbers', where you list all the numbers from Elwes' book but + 1

2026-04-07 08:11:21 UTC

got an automated email from a guy who runs a website posting slopified versions of papers from the arxiv. my last preprint with David was promptly fed to it, with my and David's name under it. "if you find any errors, just reply to this email". the rage is immense.

2026-03-14 11:43:48 UTC

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is it bad to emancipate such an institution from a private US university?
the CEO salary is quite embarrassing though, I agree

2026-03-04 20:06:32 UTC

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uh I should re-read that... there is definitely something interesting brewing...

2026-03-04 17:13:35 UTC

This paper is uber-cool, linking Shannon entropy to groupoid cardinality (it's also short and elementary, worth a read!).
**Homotopy Cardinality and Entropy**
Andrés Ortiz-Muñoz
We explore connections between homotopy type theory and information theory through homotopy cardinality. We define probability types and random variable types, prove that homotopy cardinality respects dependent sums under truncation and decidability hypotheses, and show that it does not respect dependent products in general. Using the power series expansion of the logarithm, expressed type-theoretically through deloopings of finite cyclic groups, we formulate Shannon entropy as the homotopy cardinality of a type and derive the chain rule for entropy under a trivial-action hypothesis.
https://arxiv.org/abs/2501.10672
A very interesting aspect about this is that in Bayesian probability, the only accepted way to build a prior is through the so-called *principle of indifference*, namely the evident fact that 'equivalent' outcomes should be assigned the same probability. That is, one *starts* from a 1-truncated groupoid! And these are precisely the ones with the required properties in the preprint.

2026-01-27 07:40:42 UTC

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yikes.

2025-12-15 11:27:15 UTC

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damn the case seems pretty strong then :O

2025-12-15 11:02:16 UTC

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🤯 It never occurred to me the explanation could be this simple!

2025-12-15 04:08:17 UTC

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I've always been puzzled by the claim the universe might be BH, there something I must be missing: how can the universe be so small and massive to be a BH and yet it contains many things that are less dense than one??

2025-12-10 12:14:16 UTC

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🤷

2025-12-10 10:54:19 UTC

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weird, it never appeared on my timeline. I suspect you might have 'quiet' posts on, meaning your posts are public but do not appear on timelines (I learned of this when I tried to quote boost your AI-in-math toot)

2025-12-07 17:28:02 UTC

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uh yeah this was supposed to be a quote-boost of that toot of yours. let me fix that!

2025-12-07 15:23:55 UTC

A corollary to this is that in the near future we might see easily-automated puzzle-solving lose status compared to human-guided theory-building. I wonder how this will change the social reality of mathematics, especially in the eye of the general public, where puzzle-solving is disproportionately represented...

2025-11-28 14:03:04 UTC

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I really like this idea of defining virus as non-living stage of a living organism, the virocell. I'm also very entertained by matters stretching our definitions of 'life' and 'organism'. Thanks for the pointers!

2025-11-23 17:28:45 UTC

uh is the author ok
https://media.mathstodon.xyz/media_attachments/files/115/600/189/130/402/397/original/e972674a992b0154.png

2025-11-21 09:21:27 UTC

further proof most academic publishing industry is completely parasitic https://arxiv.org/abs/2511.01675
https://media.mathstodon.xyz/media_attachments/files/115/586/945/103/544/575/original/7d2bd1a8f80e0e7c.png

2025-11-20 09:12:42 UTC

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Thanks! Today and tomorrow. No problem if you're busy! :)

2025-11-19 16:10:16 UTC

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Thanks for the publicity John, though, for completeness, I should mentioned that me and Jason Brown will also be authoring the thesis, and a few more people will be involved as contributors too. Also, plenty more people will be working on tools that directly or indirectly build on top of (1) and (2), including software and innovative model checking techniques, among others.
If you're free in the next couple of days, I'll still be around Edinburgh and I'd be happy to meet up!

2025-11-04 10:42:00 UTC

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Indeed... it also seems his (and Cox's) derivation of the laws of probability from 'logical axioms' is wrong (though one of these axioms is 'it should adhere to common sense', so I'd say the attempt was doomed from the start).
Instead, here's a nice paper fixing the proof (and much more readable):
> http://arxiv.org/abs/1507.06597
I love how they incorporate a 'monoidality' axiom, saying that the probability law on XxY should be a composite of those of X and Y, using the same operation one uses for conjunction. I wonder if one could phrase their theorem as a uniqueness theorem for Markov functors from free Markov categories with conditionals into BR... much like your paper with Fritz and Leinster did for entropy...

2025-11-03 09:10:43 UTC

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he follows such an observation with this take, which is quite funny given that the most interesting developments in logic in the last century or so came from dropping axioms from classical logic (first lem to get intuitionistic logic, then weakening/contraction to get linear logic). and I wouldn't say IL and LL are just musings of the ivory tower dwellers, since they say quite important things about computation, and e.g. make implication---which Jaynes rightly criticizes for being very unintuitive---much more adherent to intuition
https://media.mathstodon.xyz/media_attachments/files/115/484/971/418/792/136/original/7c984f5c918be84c.png

2025-11-03 09:06:20 UTC

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also insane how sharp Jaynes is about statistics compared to his logical takes, which are at best shallow and at worst just plain wrong---here he complains about the syllogism on the right by apparently saying it is not intuitionistically valid, except it is (it's again *modus ponens*/cut rule):
https://media.mathstodon.xyz/media_attachments/files/115/484/961/846/568/536/original/e1bf761756880334.png
https://media.mathstodon.xyz/media_attachments/files/115/484/964/705/030/595/original/c11bd37359a5f73f.png

2025-11-03 08:37:40 UTC

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also insane the distrust Jaynes has towards... infinite sets?
https://media.mathstodon.xyz/media_attachments/files/115/484/853/122/101/170/original/66879179b80454d3.png

2025-11-03 08:07:32 UTC

insane that 'The Logic of Science' came out in 2003

2025-10-29 08:13:24 UTC

very cool finding: planetary tidal forcing on the solar dynami might explain various short period cycles in solar magnetic activity:
https://phys.org/news/2025-08-planets-subdue-solar.html
this might interest @npub1nf4…nqe4, the paper is quite readable (though I understand very little in the way of solar dynamics): at some point they compare the forcing effect they find to secondary beats in music theory!

2025-10-25 20:49:05 UTC

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https://youtu.be/P4iiNpkClRU?si=khmdlB0RsE729DlQ enjoy the ride!

2025-10-25 09:28:16 UTC

day ruined by learning of Sabine Hossenfelder's last video contains a very stupid invective about CT...

2025-09-08 19:00:55 UTC

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"We at Holon Labs argue that the prevailing object-centric worldview, rooted in set theory, became dominant not just because of its mathematical elegance, but because it perfectly mirrored the needs of an industrial civilization focused on discrete products, quantifiable assets, and manageable parts"
uh great I didn't know one can just 'argue' historical facts lol

2025-08-27 10:59:14 UTC

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in my case I do add the type in the label, but it still doesn't pick it up (apparently due to a conflict with amsmath)

2025-08-26 17:25:38 UTC

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it looks like cleveref used to rely on a way to alias counters that broke in the latest version, someone gave a fix here https://tex.stackexchange.com/a/750232/124018
I'm curious what Tom came up with though, since the conflict with amsmath is pretty conspicuous

2025-08-26 14:23:53 UTC

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somehow cleveref is broken despite not having been updated in 7 years wtf

2025-08-26 14:00:19 UTC

> update texlive
> regret it

2025-08-03 18:48:17 UTC

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maybe the other 7 hours are all Eastern religions lol

2025-08-01 08:36:52 UTC

kinda crazy to think space has its own wind, weather, and thus erosion: gas and dust clouds, as well as small compact objects, can be consumed away by stellar wind
https://en.wikipedia.org/wiki/Photoevaporation

2025-07-07 10:18:20 UTC

guys is it too abstract to witness your existentials
https://media.mathstodon.xyz/media_attachments/files/114/811/433/751/958/917/original/fe4c625d983ec8d2.jpg

2025-04-14 11:34:53 UTC

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🤯 amazing!

2025-04-08 17:08:25 UTC

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how the heck do you discern between a stable isotope and one with a gazillion years halflife??

2025-02-08 08:49:15 UTC

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after reading (half of) this now the theorem feels completely trivial so I say good job!

2024-12-01 16:01:43 UTC

freezing cold take: if I have to 'login through my institution' to read it, it's not open-access

2024-11-16 15:36:47 UTC

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yeah I gave it for granted connected component in a directed graph meant forward-connected, but probably should've specified that

2024-11-15 15:26:39 UTC

crackpot papers form a connected component of the citation graph.
corollary: if a paper cites (attributing credibility) a crackpot paper, then it's crackpot too.
helps shortening reviewing time...

2024-08-29 15:11:15 UTC

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I was indeed tempted to include this extra interpretation of natural number lol do you think one can make it as 'elementary' as cardinals/ordinals? i.e. do 'dimensional numbers' answer to some basic intuition, which could be appealed to without introducing homotopy theory?

2024-08-29 12:27:57 UTC

the dilemma of starting natural numbers at 0 or 1 stems from the fact they abstract both cardinal (which start at 0) and ordinal (which start at 1) numbers. so I guess the best answer is 'it depends'.