{"schema":"postcutoff/event@1","as_of":"2026-10-18T07:35:00+02:00","url":"https://postcutoff.com/e/2026-10-18-ai-assisted-results-october-17-listing/","md":"https://postcutoff.com/e/2026-10-18-ai-assisted-results-october-17-listing/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":"2026-10-18-ai-assisted-results-october-17-listing","date":"2026-10-17","date_precision":"day","short_title":"AI-assisted results, 16–17 Oct 2026 (Zenodo and arXiv leftovers)","deck":"Ramanujan's prime-counting inequality settled unconditionally with Claude, a Claude Code paper mill on the Hodge conjecture, and LLM agents in materials science","takeaway":"With no new arXiv announcement over the weekend, the notable AI-assisted items came from Zenodo, led by Padhi's Claude-assisted proof that Ramanujan's inequality holds unconditionally for all x ≥ 38,358,837,683.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Zenodo: Ramanujan's prime-counting inequality holds for all x ≥ 38,358,837,683 (Padhi, v2)","url":"https://zenodo.org/records/23440770","type":"paper","group":"primary","domain":"zenodo.org"},{"n":2,"title":"GitHub: jaideepsaipadhi/ramanujans-inequality (certification code)","url":"https://github.com/jaideepsaipadhi/ramanujans-inequality","type":"code","group":"primary","domain":"github.com"},{"n":3,"title":"Zenodo: On the Hodge conjecture for Fermat varieties (Bhattacharjee)","url":"https://zenodo.org/records/23401546","type":"paper","group":"primary","domain":"zenodo.org"},{"n":4,"title":"Zenodo: Dense Algebraic Loci of Hodge Classes, source and code (with AI provenance file)","url":"https://zenodo.org/records/23439578","type":"paper","group":"primary","domain":"zenodo.org"},{"n":5,"title":"Zenodo: A counterexample to Liu's conjecture on Fano indices in dimension four","url":"https://zenodo.org/records/23387505","type":"paper","group":"primary","domain":"zenodo.org"},{"n":6,"title":"Zenodo: A graph with three card types and five vertex orbits (Kourovka 20.71(b))","url":"https://zenodo.org/records/23384197","type":"paper","group":"primary","domain":"zenodo.org"},{"n":7,"title":"arXiv 2610.20779: Enabling LLM agents for high-fidelity many-body perturbation theory calculations","url":"https://arxiv.org/abs/2610.20779","type":"paper","group":"primary","domain":"arxiv.org"},{"n":8,"title":"arXiv 2610.21050: LLM-assisted systematic study of anomalous adsorption phenomena","url":"https://arxiv.org/abs/2610.21050","type":"paper","group":"primary","domain":"arxiv.org"},{"n":9,"title":"arXiv 2610.21015: MASON, atomistic structure builder operated in natural language","url":"https://arxiv.org/abs/2610.21015","type":"paper","group":"primary","domain":"arxiv.org"},{"n":10,"title":"arXiv 2610.22062: Trofinetide phenotypes in Rett syndrome with a dual-LLM consensus pipeline","url":"https://arxiv.org/abs/2610.22062","type":"paper","group":"primary","domain":"arxiv.org"}],"official":10,"filed":"2026-10-18","updated":"2026-10-18","orgs":["Anthropic","various mathematicians"],"title":"AI-assisted results, 16–17 Oct 2026 (Zenodo and arXiv leftovers): Ramanujan's prime-counting inequality settled unconditionally with Claude, a Claude Code paper mill on the Hodge conjecture, and LLM agents in materials science","summary":"Catalogue for 16–17 Oct 2026, following the 16 Oct arXiv catalogue. The best item: Jaideep Sai Padhi (Purdue) proves unconditionally that Ramanujan's inequality π(x)² < (ex/log x)·π(x/e) holds for every x ≥ 38,358,837,683. Until now that threshold was known only under the Riemann hypothesis (Dudek–Platt); the gap e^103 < x < e^3158.442 is now closed, with certified ball arithmetic. \"The computations and the drafting of this paper were carried out with substantial assistance from an AI system (Claude, Anthropic).\" Also: Deep Bhattacharjee's dozens of Claude Code-made Zenodo records (Hodge conjecture for new Fermat degrees, a Liu Fano-index counterexample, Kourovka 20.71(b)), and four arXiv papers on LLM agents in materials and clinical science. Unrefereed.","key_facts":["Ramanujan's inequality: Padhi, 'Ramanujan's prime counting inequality holds for all x ≥ 38 358 837 683', Zenodo v2 17 Oct 2026 (v1 about 16 Oct; mirrored on aixiv.online 2610.01760), 25 pp.; Theorem 1.1: the inequality holds for e^58 ≤ x ≤ e^3159, hence N_R = 38 358 837 683 unconditionally","Ramanujan's inequality, method: only RH verification to height 3·10^12 (Platt–Trudgian) is used, plus a sharper zero-free region evaluated at each height (constant 4.676 instead of 4.896), a repulsion bound for pairs of zeros near σ = 1, and an explicit Barban–Vehov mean square bound of about 1.5 (Bellotti's table had 85–105); all numerics certified in Arb/python-flint","Ramanujan's inequality, AI statement: 'substantial assistance from an AI system (Claude, Anthropic). The arguments and the code were also reviewed by separate runs of the same system; these reviews are not a substitute for independent human verification.' It also argues that two earlier preprints by De claiming the range 'do not prove (1.1)'","Same author, earlier: Auluck–Chowla–Gupta unimodality with Claude (arXiv 2610.14084, in the 13 Oct catalogue)","Claude Code paper mill: Deep Bhattacharjee (with Ushashi Bhattacharya) posted more than a dozen Zenodo records on 15–17 Oct, each with a paper, a Lean 4 file and code in several languages; his GitHub account creelie has 82 repos, many created 10–17 Oct with names such as 'fermats-last-theorem-Machine' and 'Millenium-prize-problem-quant-Closure-'","Bhattacharjee's claims include the Hodge conjecture for Fermat varieties of degrees 33, 39, 44, 51, 52 and 114 in every dimension (83 pp.; degrees 44, 51, 52 'had not been proved before'); a counterexample to Liu's Fano-index conjecture in dimension four (index 1389); a 63-vertex graph answering Kourovka Notebook Problem 20.71(b) for k = 3; book Ramsey numbers R(B_57, B_58) = 231 and R(B_66, B_67) = 267","Bhattacharjee's AI statements: 'calculations, in C, Python, Julia, Macaulay2, Lean 4 and shell scripts, with the assistance of Claude Code'; the provenance file of 'Dense Algebraic Loci of Hodge Classes' says the constructions, text, figures, Lean file and programs were done 'with the help of AI assistance (Claude, Anthropic), in sessions in the Claude Code environment' and that 'The AI did not prove … the Hodge conjecture'","LLM agents in computational materials (arXiv 2610.20779, USC et al.): out-of-the-box agents including 'Opus 4.7 and GPT-5.5' average 54%, 36% and 19% on GW, GW-BSE and GWPT workflow benchmarks; the authors' AI-Donkey framework makes all tested agents produce complete, runnable workflows","LLM literature mining (arXiv 2610.21050, Adelaide): extraction F1 0.96 against human annotation; corpus of 547 guest-induced transitions in 240 soft porous crystals from 4,252 screened papers; gate-opening frameworks transform at lower pressure than breathing ones (p = 3.8×10⁻³)","Also: MASON, an MCP toolkit that lets agents build atomistic structures (Nankai, 2610.21015); a dual-LLM consensus pipeline extracting 18 trofinetide-response phenotypes for Rett syndrome from 26,763 clinical notes (Baylor/Texas Children's, 2610.22062)","Scanned with no AI statement found (17–18 Oct): 25 uncited maths and physics papers from the 13–16 Oct arXiv announcements claiming to settle conjectures, among them Chen's log-concavity conjecture for longest increasing subsequences (2610.18235), lens-space counterexamples to the quotient-round Yamabe formula (2610.18662), the weak cylinder conjecture for polynomial graphs (2610.16803) and the zero-divisor conjecture for medial quandle rings (2610.20306)"],"key_numbers":[],"tags":["math","number-theory","algebraic-geometry","zenodo","arxiv","catalogue","claude","claude-code","lean","ai-for-science","materials"],"science":{"field":"mathematics","subfield":"multiple (analytic number theory, algebraic geometry, combinatorics; materials and clinical AI)","problem":"Ramanujan's prime-counting inequality threshold; Hodge conjecture for Fermat varieties; Liu's Fano-index conjecture; Kourovka 20.71(b); see list","result":"A catalogue of claimed results with an AI contribution posted 16–17 Oct 2026; the Ramanujan-inequality threshold is the strongest.","open_since":"","ai_system":["Claude","Claude Code","Claude Opus 4.7","GPT-5.5"],"human_role":"Padhi: Claude did computations and drafting, reviewed by other Claude runs; Bhattacharjee: Claude Code sessions for constructions, text, Lean and programs; others: LLMs as tools or test subjects","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed preprints and Zenodo records; certified interval arithmetic (Padhi); Lean files for combinatorial parts (Bhattacharjee)"},"status":"pending","shock":"","verified_by":["preprint","lean"],"kind":"batch"},"body_md":"## What happened\n\narXiv makes no announcements on Friday or Saturday nights, so the 18 Oct sweep had no new listing. Its two arXiv sections held\nleftovers from the 13–16 Oct announcements. Most of the disclosure hits were AI-methods papers rather than AI-assisted results.\nThe 25 uncited maths and physics \"conjecture\" papers were re-scanned (`pdftotext`, full text) and none had an AI statement. The\nnew AI-assisted results of 16–17 Oct that we found came from Zenodo.\n\n### Ramanujan's inequality, unconditionally (Padhi, with Claude)\nRamanujan noticed in his notebooks that π(x)² < (ex/log x)·π(x/e) holds for all large x. Assuming the Riemann hypothesis, Dudek\nand Platt showed the last integer counterexample is 38,358,837,682. Without RH it was known only for x ≤ e^103 (Axler, Platt–Trudgian,\nJohnston) and for x ≥ e^3158.442 (Axler). Padhi closes the range between them, so the RH-conditional threshold is now unconditional.\nThe proof uses an explicit formula with Logan's kernel (following Büthe). It adds three new explicit inputs about possible zeta\nzeros just above the RH-verified height 3·10^12, and every number is certified in ball arithmetic. The acknowledgement says the\ncomputations and drafting were done \"with substantial assistance from an AI system (Claude, Anthropic)\", reviewed by other Claude\nruns, and that \"these reviews are not a substitute for independent human verification\". No expert reaction was found by 18 Oct.\n\n### A Claude Code paper mill (Bhattacharjee)\nDeep Bhattacharjee (affiliation \"Formerly, Electro-Gravitational Space Propulsion Laboratory\", Bhubaneswar) and Ushashi\nBhattacharya posted more than a dozen Zenodo records on 15–17 Oct alone. Each holds a paper, Lean 4 files and code in four or five\nlanguages, all made in Claude Code sessions by their own statements. The claims range from small (abelian squares in binary\ncircular words) to large (the Hodge conjecture for Fermat varieties of several new degrees, with a proof the README says \"No step\n… uses a computer\"). None has been refereed or discussed by specialists that we could find. These records are listed here as a\nsign of how much AI-made mathematics now reaches Zenodo, not as results we vouch for.\n\n### LLM agents in science (arXiv)\n- **Many-body perturbation theory** (2610.20779): frontier agents set up GW, GW-BSE and GWPT workflows correctly only 54%, 36% and\n  19% of the time on average. Errors tend to \"surface only several stages after they are introduced\". An expert-curated framework\n  (AI-Donkey) fixes this for every model tested.\n- **Anomalous adsorption** (2610.21050): an LLM extraction pipeline builds the first database of guest-induced transitions in\n  soft porous crystals. Its analysis suggests describing them by function rather than by structure.\n- **MASON** (2610.21015) and a **dual-LLM clinical phenotyping pipeline** (2610.22062) are tools, listed for completeness.\n\n## Why it matters\n\nPadhi's paper is a second classical explicit-number-theory threshold settled this month by one author working with Claude, after\nAuluck–Chowla–Gupta. It is the kind of long, computation-heavy explicit estimate where models are now doing most of the labour.\nBhattacharjee's output shows the other side. One person with Claude Code can produce dozens of Lean-backed papers a week, faster\nthan anyone can referee them, and this is what Alpöge warned about in the Yang–Mills repo (\"10,000-page slop\").","disputed":[{"label":"Verification","text":"Unrefereed preprints and Zenodo records; certified interval arithmetic (Padhi); Lean files for combinatorial parts (Bhattacharjee)","sources":[]}],"related":[{"id":"2026-10-17-ai-assisted-results-october-16-listing","url":"https://postcutoff.com/e/2026-10-17-ai-assisted-results-october-16-listing/","date":"2026-10-17","date_precision":"day","short_title":"arXiv results with disclosed AI help, 16 Oct 2026 announcement","deck":"Suffridge's conjecture, two Wahl conjectures, the 6-D Tarski problem and more","takeaway":"A second read of the 16 Oct arXiv announcement, through the HTML listings because the arXiv API was rate-limited, found three results for their own entries and about fifty more preprints with explicit AI statements, several settling named conjectures.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":16,"official":15,"filed":"2026-10-17","updated":"2026-10-18","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]},{"id":"2026-10-16-yang-mills-claude-balaban-program-alpoge-sussman","url":"https://postcutoff.com/e/2026-10-16-yang-mills-claude-balaban-program-alpoge-sussman/","date":"2026-10-16","date_precision":"day","short_title":"Alpöge and Sussman say Claude has an (unreadable) existence argument for 4D Yang–Mills on ℝ⁴, by finishing Bałaban's 1980s program","deck":null,"takeaway":"A public repo of raw Claude output claims a construction of four-dimensional SU(2) Yang–Mills theory, the existence half of the Millennium problem but not the mass gap; its authors call it 'slop in progress' that nobody can yet read or check.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":6,"official":4,"filed":"2026-10-18","updated":"2026-10-18","orgs":["Anthropic","Northwestern University"]},{"id":"2026-10-13-ai-assisted-results-october-2026","url":"https://postcutoff.com/e/2026-10-13-ai-assisted-results-october-2026/","date":"2026-10-13","date_precision":"day","short_title":"October 2026: the arXiv stream of conjectures settled with disclosed AI help continues","deck":null,"takeaway":"In the first nine days of October 2026 the stream did not slow down: each arXiv listing brought several named conjectures with a disclosed AI role, and two new patterns appeared.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":16,"official":16,"filed":"2026-10-13","updated":"2026-10-14","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]}],"people":[{"id":"levent-alpoge","name":"Levent Alpöge","url":"https://postcutoff.com/person/levent-alpoge/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-18","type":"filed","text":"Created (Zenodo API search; PDFs and Zenodo archives read)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-18","run":null,"sources_read":"Zenodo API search; PDFs and Zenodo archives read","updated":"2026-10-18","human_review":null,"version":null},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":170,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":109,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":200,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":139,"in_training_data":false}],"short_url":null}