{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-04-serre-modularity-real-quadratic-fields-chatgpt-astra/","md":"https://postcutoff.com/e/2026-11-04-serre-modularity-real-quadratic-fields-chatgpt-astra/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":"2026-11-04-serre-modularity-real-quadratic-fields-chatgpt-astra","date":"2026-11-04","date_precision":"day","short_title":"Serre modularity over real quadratic fields, primarily AI-generated","deck":null,"takeaway":"Dieulefait posted two Claude-assisted Fontaine–Mazur modularity papers the same day.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Hexagon 2611.00071: Serre modularity over real quadratic fields","url":"https://hexagonmath.org/abs/2611.00071","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":2,"title":"Hexagon 2611.00067: Fontaine–Mazur for 2-adic representations","url":"https://hexagonmath.org/abs/2611.00067","type":"paper","group":"primary","domain":"hexagonmath.org"},{"n":3,"title":"Hexagon 2611.00096: Fontaine–Mazur, residually reducible mixed case","url":"https://hexagonmath.org/abs/2611.00096","type":"paper","group":"primary","domain":"hexagonmath.org"}],"official":3,"filed":"2026-11-05","updated":"2026-11-05","orgs":["OpenAI","Anthropic"],"title":"Dieulefait, Freitas and Pacetti post a primarily AI-generated proof of Serre's modularity conjecture over 17 real quadratic fields (under GRH)","summary":"On Hexagon, Luis Dieulefait, Nuno Freitas and Ariel Pacetti claim Serre's modularity conjecture over Q(√d) for 17 values of d assuming GRH for Dedekind zeta functions (d = 17 unconditional), in a work declared \"primarily AI-generated\" with ChatGPT 6-Astra and Sol 6.1. Dieulefait posted two Claude-assisted Fontaine–Mazur modularity papers the same day. All are unrefereed.","key_facts":["Hexagon 2611.00071: d ∈ {2,3,5,6,7,10,11,13,17,21,33,37,41,57,65,73,89}; every continuous, absolutely irreducible, totally odd 2-dim mod-p (p odd) representation is modular; d = 17 unconditional","Provenance: 'Primarily AI-generated'; human understanding 'some'; 'the authors used ChatGPT 6-Astra and Sol 6.1 as an assistant in mathematical research and manuscript preparation … exploring proof strategies, checking mathematical arguments …'","Hexagon 2611.00067 (Dieulefait): Fontaine–Mazur for residually reducible 2-adic representations over totally real fields where 2 splits, generalizing an OpenAI result; 'produced with the assistace of Claude'","Hexagon 2611.00096 (Dieulefait): Fontaine–Mazur in the residually reducible mixed case via fully ordinary families; 'the outcome of an interaction with Claude'"],"key_numbers":[],"tags":["math","number-theory","galois-representations","serre-conjecture","gpt-6-astra","gpt-6-1-sol","claude","hexagon"],"science":{"field":"mathematics","subfield":"number theory","problem":"Serre's modularity conjecture over totally real (real quadratic) fields; Fontaine–Mazur conjecture cases","result":"Serre's conjecture over 17 real quadratic fields under GRH (d = 17 unconditional); Fontaine–Mazur modularity in residually reducible 2-adic and mixed cases","open_since":"","ai_system":["ChatGPT 6-Astra","GPT-6.1 Sol","Claude"],"human_role":"Primarily AI-generated by the authors' declaration; partly human-checked","verification":{"key":"none","label":"Unverified claim","text":"Hexagon deposits, unrefereed"},"status":"pending","shock":""},"body_md":"## What happened\n\nThree Hexagon deposits of 4 Nov 2026 come from number theorists who work on modularity. The headline claim, [2611.00071](https://hexagonmath.org/abs/2611.00071), extends Serre's conjecture, proved over Q by Khare–Wintenberger, to 17 real quadratic fields, conditionally on GRH. Its new ingredients are a modularity criterion for 2-adic representations with scalar reduction and integral trace arguments. The authors classify all three works as primarily AI-generated and only partly human-checked.\n\n## Why it matters\n\nSerre's conjecture beyond Q is open in general. The conditional result covers specific fields, so it is not the general conjecture. Hexagon does not judge correctness, and no expert reaction had been found as of 5 Nov.","disputed":[{"label":"Verification","text":"Hexagon deposits, unrefereed","sources":[]}],"related":[{"id":"2026-10-28-kisin-serre-artin-character-conjecture-gpt-astra","url":"https://postcutoff.com/e/2026-10-28-kisin-serre-artin-character-conjecture-gpt-astra/","date":"2026-10-28","date_precision":"day","short_title":"Kisin proves Serre's 1960 Artin-character conjecture with GPT Astra","deck":null,"takeaway":"In 1960 Serre conjectured that a function built from fixed-point multiplicities of a finite group acting on a regular local ring is the character of an ℓ-adic representation. It is the higher-dimensional analogue of the Artin character of local fields. Tomoyuki Abe proved the positive-characteristic case (Inventiones, 2025). On 28 Oct Harvard's Mark Kisin posted the mixed-characteristic case on Hexagon, which finishes the conjecture. He writes that 'extensive use of GPT Astra was made both to arrive at the proofs … and to write a first draft', and that 'significant human effort' went into checking them. Part of the work was done at 'The Overhang', a San Francisco meeting on 9–10 Sept 2026.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-29","updated":"2026-10-29","orgs":["Harvard University","OpenAI"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-05","type":"filed","text":"Created from the Hexagon records"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-05","run":null,"sources_read":"The Hexagon records","updated":"2026-11-05","human_review":null,"version":{"date":"2026-11-05"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":188,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":127,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":218,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":157,"in_training_data":false}],"short_url":null}