theHigherGeometer
@highergeometer.mathstodon.xyz.ap.brid.gy
332 followers 0 following 1.8K posts
rimcræftiga | bespoke constructions in categorified geometry since 2010 | dude [bridged from mathstodon.xyz/@highergeometer on the fediverse by fed.brid.gy ]
![Sept 8 2026 Tweet by Levent Alpöge with a screenshot of an email from him to Tristan Buckmaster on 9/19/25 with subject line "Normal pure math collaboration with ai" and text:
"Hi Tristan
I've been meaning to write you as a shot in the dark, but I saw the following tweet from GDM ([url] which does not name eg you or Javier) and figured why not today! Basically for ideological reasons I fear a world in which corporations are the ones with claim to the deepest pure math work, and since it seems to me there will be only one Millennium Problem solved in the foreseeable future, I wanted to email you on a lark to ask if you'd considered working on the problem in the traditional mathematical way."](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreifvuhx5knivmn43zp34bn3cvhphfxotjb7zctingxgspufz5arpv4)
!["I am happy to have more lower profile people (eg Brieskorn) because I
cannot wish anyone the life experience of Grothendieck. I have read
some Récoltes et sémailles, and in particular looked at the picture of a
cute child in Berlin, and what history did to that child [broken heart emoji] [crying emoji]"
"Yes I know history (and in fact humans) have done and do much worse
to so many kids. But when we talk about him, it seems to me so many
people tend to see the "genius" and not the crying child."](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreigh52oyvus3w425dphrkkzm2uv3fjmton6jgjdygj3n7wks7kfrs4)
![“Large Causal Models from Large Language Models” https://arxiv.org/abs/2512.07796
1. Fabricated (no such paper)
« Citation: Xiaomei He et al. A survey of event causality identification: Taxonomy, resources, and challenges. ACM
Computing Surveys, 2025. Preprint
« No paper of this title by Xiaomei He exists; the only ACM Computing Surveys paper of this name is Qing Cheng,
Zefan Zeng, Xingchen Hu, Yuehang Si, Zhong Liu, A Survey of Event Causality Identification: Taxonomy, Challenges,
Assessment, and Prospects (2026) https://doi.org/10.1145/3756009.
2. Wrong arXiv ID (resolves to an unrelated paper)
« Citation: Zhiting Jin et al. Causal inference and natural language processing: A review. arXiv preprint
arXiv:2012.14366, 2021.
« Resolves to: https://arxiv.org/abs/2012.14366 is Jian Zhang, Cunjing Ge, Feifei Ma, Counting the Number of
Solutions to Constraints (2020).
3. Fabricated (arXiv ID, author, title do not exist)
« Citation: Vladislav Kosoy et al. Do large language models have causal knowledge? arXiv preprint arXiv:2305.00000,
2023.
« Resolution: https://arxiv.org/abs/2305.00000 is not a working arXiv link, the title does not resolve to any paper on a
web search, and an arXiv author search returns no “Vladislav Kosoy”, neither does a Google Scholar search. A
researcher named Eliza Kosoy works in the area.
[truncated]](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreibel2ji6gvqbt3c2xu4epsx3fyscorkym47cosrguuvbgjlgashza)
![“CSQL: Mapping Documents into Causal Databases” https://arxiv.org/abs/2601.08109
1. Wrong first author
« Citation: Abhimanyu Dubey et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024
« The first author of https://arxiv.org/abs/2407.21783 is Aaron Grattafiori, the second author is Abhimanyu Dubey (and then a giant list, hence the et al)
2. Wrong title
« Citation: Prashant Garg and Thiemo Fetzer. Testing causal claims in economics. arXiv preprint arXiv:2501.06873,
2025. URL https://arxiv.org/abs/2501.06873
« Correct title: https://arxiv.org/abs/2501.06873 is Causal Claims in Economics (Garg & Fetzer, 2025); authors and ID
correct, the leading “Testing” is not part of the real title in either v1 or v2.
3. Fabricated (arXiv ID, author, title do not exist)
« Citation: Vladislav Kosoy et al. Do large language models have causal knowledge? arXiv preprint arXiv:2305.00000, 2023
« Resolution: https://arxiv.org/abs/2305.00000 is not a working arXiv link, the title does not resolve to any paper on a
web search, and an arXiv author search returns no “Vladislav Kosoy”, neither does a Google Scholar search. A researcher named Eliza Kosoy works in the area.
4. Wrong arXiv ID (resolves to an unrelated paper)
« Citation: Tuan Le et al. Multi-agent causal discovery using large language models. arXiv preprint arXiv:2404.12345, 2024
« Resolves to: https://arxiv.org/abs/2404.12345 is Shuai Li, Ming Gong, Yu-Hang Li, et al., High spin axion insulator (2024).
[truncated]](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreibxm4nhpb6ra47xglx2fmrq77dn6i74ybzgrvd25choooaaz2nl7i)
![“PROMETHEUS: Automating Deep Causal Research” https://arxiv.org/abs/2605.12835
1. Fabricated (nonexistent DOI, wrong authors/year/volume)
« Citation: Xiaomei He, Yi Guan, and Min Chen. A survey of event causality identification: Taxonomy, resources, and
techniques. ACM Computing Surveys, 55(14s):1-35, 2023. doi:10.1145/3582128.
« The cited DOI does not resolve: https://doi.org/10.1145/3582128 returns HTTP 404.
« Areal paper with a similar title: Qing Cheng, Zefan Zeng, Xingchen Hu, Yuehang Si, Zhong Liu, A Survey of Event
Causality Identification: Taxonomy, Challenges, Assessment, and Prospects, ACM Comput. Surv. 58(3), Art. 59, 2026
https://doi.org/10.1145/3756009 (different authors, year, volume, and subtitle).
2. Wrong arXiv ID (resolves to an unrelated paper)
« Citation: Zhijing Jin, Bernhard Schélkopf, Peter Spirtes, and Kun Zhang. Causal inference and natural language
processing: A survey. arXiv preprint arXiv:2012.14366, 2021.
« Resolves to: https://arxiv.org/abs/2012.14366 is Jian Zhang, Cunjing Ge, Feifei Ma, Counting the Number of
Solutions to Constraints (2020).
3. Wrong author list (real paper, correct ID)
« Citation: Hao Duong Le, Xin Xia, and Zhang Chen. Multi-agent causal discovery using large language models. arXiv
preprint arXiv:2407.15073, 2024.
« Correct author list: https://arxiv.org/abs/2407.15073 is by Hao Duong Le, Xin Xia, Haijie Xu, Chen Zhang, the citation
omits Haijie Xu and renders “Chen Zhang” as “Zhang Chen”.
[truncated]](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreianh3vou6jjejluxmsw7yb3mxis3vo54hztffxohikd2xx6673ocq)
![[A] Mount Allison University
https://mta.ca » ~cat-dist > catlist 2
https://mta.ca/~cat-dist/catlist/1999/zf-010499
Recall that ZERMELO set theory (1908), which is essentially equivalent to the categorists' notion of ELEMENTARY TOPOS with natural numbers ... /~pt/ ...](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreicrohaman6bspfi7ehpi6bw7jztsygplh4uqm2crckjwzzd7oy6hm)
!["Given a sequence X = (x_n) with n = 0,1,2,3,..., Aitken's delta-squared process associates to this sequence the new sequence
[mathematical details]
with [explanatory equations[, Both are the same sequence algebraically but
the latter has improved numerical stability in computational implementation."
the phrase "Both are the same sequence algebraically" is highlighted.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreicjsh2d7z5prosgooub3kxgdnosibywhgi3p7lfnx3ctk7yd2x5cu)
![Screenshot of a mathematics article with Proposition 7.3 stating
"Let C be a quasi-category. The canonical map sd_2 C to C^Delta[1] C."
Text underneath talks about the canonical map "sd_2 C to C^Delta[1]" (no trailing "C"), indicating some text got mangled and the statement compressed.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreihaxaisb7agyoei7wasqyjr6ufunvi76bwzhlu6skojcnkrq75u2a)
!["Verification pays off
- In the course of the verification, I had to prove Expr.hasBoundVar is correct
- This function works by accessing a 64 bit metadata field
- Thad to prove some bit tricks correct, but this worked out alright
- But the metadata calculates the depth of bound variables, which is a priori
unbounded, so this is an overflow situation
- The code was checking for overflow, but it used Lean’s panic function to do
it, and this function doesn’t actually crash the program, because it’s a pure
function with no exit path
- Instead, it returned the default value for the type (0), which is the worst
possible answer in this situation
- By pushing back the counterexample situation to the entry point I was able to
construct a concrete proof of false [#8554]."](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreifsey4mszmcftirynfx3ktii3vptkgfuxixwkgf43b3yjyor5npua)
![A diagram expressing a result in higher category theory, stating that there is a biadjoint biequivalence between ddBicat_s-Cat and BrMonCat. One of the functors, U, is explicit, the theorem is stated that U is a pointwise biequivalence. The corollary is that there exists the functor in the other direction, following "from U being a pointwise biequivalence and [Gurski]".](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreibvnjkl6hghd6uzpp6xbmnqc3na56f4ym3jvbsfl732lvwctl5tbq)
![Peter Scholze — Geometric Langlands, after Gaitsgory, Raskin,...
At its core, the Langlands program seeks to give a description of the vector space of automorphic forms. This is a space of functions on a locally symmetric space X/Gamma, where Gamma = G(Z) subset G(R) is an arithmetic group, equipped with its Hecke symmetries. One seeks a “dual” description, in terms of L-parameters, which are roughly representations of the absolute Galois group with values in the Langlands dual group.
Similar conjectures exist in the function-field case; in this setting, the quotient X/Gamma can be interpreted as the F_p-points of the stack Bun_G of G-bundles on a curve C over F_p. Gaitsgory–Raskin, partly in large collaborations, proved a fine version of Langlands’ conjecture in this setting, in the everywhere unramified case. Notably, they define a vector space on the Galois side, as global sections of a sheaf on the moduli stack of L-parameters, and relate this to the space of automorphic forms, compatibly with the Hecke symmetries.
Their proof is a culmination of many decades of work in the geometric Langlands program, and consists of two key steps: 1) The space of automorphic forms is the trace of Frobenius on a category of l-adic sheaves on Bun_G. 2) This category of l-adic sheaves on Bun_G is equivalent to a category of coherent sheaves on the stack of L-parameters. The starting point for 2) is the observation that this conjecture makes sense for curves over any field, and any[...]](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:3o43hmnayigrgyh6wlyjx6ct/bafkreifnzrmqaq4qh3dg3b463lr67rumjchjlq4lydespmrmtxb477r7ru)
