{"schema":"postcutoff/event@1","as_of":"2026-11-15T00:33:00+01:00","url":"https://postcutoff.com/e/2026-11-13-qiyue-tang-gpt-6-pro-representation-theory-conjectures/","md":"https://postcutoff.com/e/2026-11-13-qiyue-tang-gpt-6-pro-representation-theory-conjectures/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-11-13-qiyue-tang-gpt-6-pro-representation-theory-conjectures","date":"2026-11-13","date_precision":"day","short_title":"Six unchecked GPT-6-Pro proofs of named conjectures (Qiyue Tang)","deck":null,"takeaway":"In one day a Tsinghua contributor posted AI-written proofs of several well-known conjectures in representation theory and geometry, each produced in GPT-6-Pro sessions of 2 to 110 hours. Every deposit declares that no human has checked or understood it; reviews by the Rethlas system are promised later.","category":"science","category_label":"Science & math","importance":3,"confidence":"low","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Hexagon 2611.00426: A proof of Brauer's k(B)-conjecture at the prime two","url":"https://hexagonmath.org/abs/2611.00426","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":2,"title":"Hexagon 2611.00427: A proof of the Hausel–Rodriguez-Villegas conjecture","url":"https://hexagonmath.org/abs/2611.00427","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":3,"title":"Hexagon 2611.00411: A proof of Lusztig's conjectures for extended affine Weyl groups","url":"https://hexagonmath.org/abs/2611.00411","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":4,"title":"Hexagon 2611.00406: A proof of Lusztig's connectedness conjecture in finite type","url":"https://hexagonmath.org/abs/2611.00406","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":5,"title":"Hexagon 2611.00408: A proof of the scheme-theoretic Humphreys conjectures","url":"https://hexagonmath.org/abs/2611.00408","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":6,"title":"Hexagon 2611.00409: The Shapiro–Shapiro conjecture for ordered positive flags","url":"https://hexagonmath.org/abs/2611.00409","type":"paper","group":"primary","domain":"hexagonmath.org"}],"official":6,"filed":"2026-11-14","updated":"2026-11-14","orgs":["OpenAI","Tsinghua University"],"title":"Qiyue Tang deposits six GPT-6-Pro papers on Hexagon claiming Brauer's k(B)-conjecture at p = 2, the Hausel–Rodriguez-Villegas conjecture, Lusztig's P1–P15 for extended affine Weyl groups and three more; none checked by a human","summary":"On 13 Nov 2026 Qiyue Tang posted six papers to Hexagon, all 'Primarily AI-generated' with the declaration 'None of this contribution has been checked and understood by any human'. They claim: Brauer's k(B)-conjecture for 2-blocks (2611.00426), the Hausel–Rodriguez-Villegas conjecture on mixed Hodge polynomials of twisted GL_n character varieties (2611.00427), Lusztig's conjectures P1–P15 for extended affine Weyl groups with positive weights (2611.00411), Lusztig's connectedness conjecture for left cells in finite Weyl groups (2611.00406), the scheme-theoretic Humphreys conjectures (2611.00408) and the Shapiro–Shapiro conjecture for ordered positive flags (2611.00409). GPT-6-Pro did the research, review and writing.","key_facts":["Brauer's k(B)-conjecture (1954), p = 2 case: 'every 2-block of a finite group has at most as many ordinary irreducible characters as the order of its defect groups'; 'GPT-6-Pro was used during approximately 29 hours of documented research sessions' ([2611.00426](https://hexagonmath.org/abs/2611.00426))","Hausel–Rodriguez-Villegas conjecture: 'two research sessions totalling approximately 22 hours' ([2611.00427](https://hexagonmath.org/abs/2611.00427))","Lusztig's P1–P15 for extended affine Weyl groups with positive integer weights: 'more than 110 hours of documented research-session time across fourteen rounds' ([2611.00411](https://hexagonmath.org/abs/2611.00411)); Lusztig's connectedness conjecture in finite type, every equal-parameter Kazhdan–Lusztig left cell connected by simple left multiplications, from 'approximately 88 hours' over twelve sessions ([2611.00406](https://hexagonmath.org/abs/2611.00406))","Scheme-theoretic Humphreys conjectures for p above the Coxeter number, 'approximately 2.11 hours' ([2611.00408](https://hexagonmath.org/abs/2611.00408)); Shapiro–Shapiro conjecture for ordered totally positive flags, '10.9 hours' ([2611.00409](https://hexagonmath.org/abs/2611.00409))","Each provenance statement ends: 'A review by Rethlas-OSV will be added later' (Rethlas: an agent system by Liang Xiao and Bin Dong's group). Hexagon does not judge correctness; no arXiv copies, Lean files or expert reactions found by 14 Nov","Context: Tang has posted dozens of such deposits since October (e.g. Kamnitzer's MV = theta conjecture, Gorenstein symmetry; see the 29 Oct, 4 Nov and 10 Nov listings). The positive-flag Shapiro–Shapiro case and some Lusztig cases may overlap known results (Mukhin–Tarasov–Varchenko proved the original Shapiro conjecture; Lusztig's P1–P15 are known in the equal-parameter case); the deposits' novelty claims are unchecked"],"key_numbers":[],"tags":["math","representation-theory","group-theory","algebraic-geometry","hexagon","gpt-6-pro","unverified","ai-generated"],"science":{"field":"mathematics","subfield":"representation theory / algebraic geometry","problem":"Brauer's k(B)-conjecture (p = 2), Hausel–Rodriguez-Villegas conjecture, Lusztig's P1–P15 and connectedness conjectures, Humphreys conjectures, Shapiro–Shapiro conjecture (positive flags)","result":"Claimed proofs, all AI-generated and unchecked by humans","open_since":"1954","ai_system":["GPT-6 Pro"],"human_role":"Contributor ran and deposited GPT-6-Pro research sessions; declares no human understanding","verification":{"key":"none","label":"Unverified claim","text":"Unverified claim (Hexagon deposits, no human check, no Lean)"},"status":"pending","shock":""},"body_md":"## What happened\n\nQiyue Tang, listed on Hexagon as a Tsinghua mathematician, deposited six papers on 13 Nov, each titled as a proof of a named\nconjecture. Each says GPT-6-Pro did the research, checked the arguments and polished the text, gives the session time, and states\nthat no human has checked or understood the contribution.\n\n## Why it matters\n\nBrauer's k(B)-conjecture and the Hausel–Rodriguez-Villegas conjecture are well known; a correct proof of either would be major. As\ndeposited, these are unverified model outputs. The batch shows how fast claims on famous problems now appear compared with the\ncapacity to check them, the problem MathHelm (2026-11-13-mathhelm-forum-ai-generated-papers) was set up to address.","disputed":[{"label":"Verification","text":"Unverified claim (Hexagon deposits, no human check, no Lean)","sources":[]}],"related":[{"id":"2026-11-14-ai-assisted-results-november-14-listing","url":"https://postcutoff.com/e/2026-11-14-ai-assisted-results-november-14-listing/","date":"2026-11-14","date_precision":"day","short_title":"AI-assisted results, 14 Nov","deck":null,"takeaway":"arXiv posted no new listing after 13 Nov (it announces Sunday to Thursday), so this sweep is mostly Hexagon's 13 Nov deposits, older arXiv papers not yet catalogued, and the week's commentary. Eight items got their own entries, four of them from a backlog of 6–11 Nov arXiv papers never catalogued; the rest are listed here with the disclosure quoted. All are unrefereed.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":14,"official":13,"filed":"2026-11-14","updated":"2026-11-14","orgs":["OpenAI","Anthropic","Google DeepMind","various researchers"]},{"id":"2026-11-10-ai-assisted-results-november-10-listing","url":"https://postcutoff.com/e/2026-11-10-ai-assisted-results-november-10-listing/","date":"2026-11-10","date_precision":"day","short_title":"AI-assisted results, 10 Nov: arXiv and Hexagon","deck":null,"takeaway":"Own entries today: X_ns+(121) (two AI proofs) and the Benjamini–Schramm p_c < p_u claims. Below: a catalogue of the rest, quoted from Hexagon provenance and arXiv PDFs; nothing here is refereed.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":82,"official":82,"filed":"2026-11-10","updated":"2026-11-10","orgs":["OpenAI","Anthropic","various researchers"]},{"id":"2026-10-29-ai-assisted-results-october-29-listing-3","url":"https://postcutoff.com/e/2026-10-29-ai-assisted-results-october-29-listing-3/","date":"2026-10-29","date_precision":"day","short_title":"AI-assisted results, 29 Oct (part 3): Hexagon's evening batch","deck":null,"takeaway":"Hexagon published 58 new works on 28–29 Oct that we had not cited. Four have their own entries: the claimed sharp Berry–Esseen constant (Kołodziejek–Rodziewicz), the existence of the q-colourability threshold (Aronow–Lopatto, machine-written), deterministic factoring in N^o(1) (Rudich–Rousseau, Lean, ideas by Claude) and the refutation of Moschovakis's uniform-process lower bounds for gcd (Davies, Lean). Others claim the quantum Jellium = uniform-electron-gas energy (Csirik), C₂-cofiniteness of all finite-group orbifolds (Riesen), analytic floating bodies of equilibrium in every dimension ≥ 3 (Price–de Groot, GPT-6 Pro) and Cowling's conjecture for almost connected groups (Arhancet). From the backlog: S(13) = 45 comparators for sorting 13 inputs and an area law for 3D U(1) Wilson lattice gauge theory (Tomar, Lean), Enomoto's settlement of the third Brauer–Thrall conjecture over algebraically closed fields (GPT-6 Astra) and Soberón's counterexample to Matschke's table conjecture.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":22,"official":22,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI","Anthropic","Google","various researchers"]},{"id":"2026-10-06-hexagon-repository-llm-assisted-math","url":"https://postcutoff.com/e/2026-10-06-hexagon-repository-llm-assisted-math/","date":"2026-10-06","date_precision":"day","short_title":"Hexagon launches: a new arXiv-style repository for LLM-assisted mathematics papers","deck":null,"takeaway":"It is the first dedicated infrastructure for AI-generated mathematics backed by leading mathematicians, and it accepts work that no human claims to understand.","category":"research","category_label":"Research","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":2,"official":2,"filed":"2026-10-07","updated":"2026-10-29","orgs":["Hexagon Mathematics Foundation"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-14","type":"filed","text":"Created (science agent; all six Hexagon records and provenance statements read via the Hexagon API)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-14","run":null,"sources_read":"Science agent; all six Hexagon records and provenance statements read via the Hexagon API","updated":"2026-11-14","human_review":null,"version":null},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":197,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":136,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":227,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":166,"in_training_data":false}],"short_url":null}