GENESIS R300.1 – Validating Frontier Claims in AI-Assisted Mathematics: An exploratory case study on formal verification, semantic fidelity, multi-model review and human-in-the-loop governance
Abstract
Between May and October 2026, OpenAI announced several mathematical breakthroughs: a disproof of the Erdős unit distance conjecture, a claimed resolution of Clay alternatives C/D for the Navier–Stokes equations with external forcing, a quasi-Riemann hypothesis (zero-free half-plane Re s > 7/8) for ζ and Dirichlet L-functions, the "Ten Advances", and a catalogue of 722 manuscripts (719 after withdrawals). Session GENESIS R300.1 asked how likely it is that these problems have actually been solved, and how such claims can be reviewed in a traceable, correctable and transferable way.
A team of five AI systems (Claude Opus 5.5 as primary architect; Sol 6.1/ChatGPT, Perplexity Pro, Mistral-Vibe and Grok as review nodes) and one human decision-maker (HITL) worked in four rounds from 16 to 19 October 2026. The claims were decomposed into 17 review entries. Provenance, formal evidence (Lean 4 kernel checks), statement faithfulness and expert assessment were examined on separate paths and combined in an approved HITL gate.
Part A – Results: The Erdős disproof is solved on solid grounds (independent human-verified reconstruction by nine authors). The quasi-RH for ζ and Dirichlet L and Navier–Stokes C/D as a formal theorem are strongly supported but not conclusively verified: the formal chains are statically consistent but were not reproduced by the team, and a human PDE sign-off is missing for Navier–Stokes. The Ten Advances are supported with reservations (chapter 8 on hold). No success rate can be derived for the catalogue; three withdrawn manuscripts remain unsupported. Six dated forecasts with deadlines up to the end of 2027 and pre-registered resolution criteria (K1.0) form a prospectively evaluable register.
Part B – Method: The session produced the validation protocol R300-VEP v0.3 (six review stages P0–P5, two separate review paths, five review measures, four reproduction levels, 14 evidence aggregation rules, process rules V1–V6, forecast register) and the first full application of the behaviour anchor GENESIS-R900-I10. The main observation: in the documented process, the primary architect was the most conspicuous source of wrong objections that were passed on to other nodes; they were caught only in cross-review. This motivates candidate rule V8 (enforced handover contracts and an evidence graph) for testing in R300.2. Because roles differed and there was no comparison condition, no error-rate comparison between models and no proof of the anchor's effect is claimed.
Nature of this work: an exploratory, AI-assisted evidence synthesis and protocol case study. It is not an original mathematical publication and not a certification of the results examined. Mathematical judgements rest on human expert sources, third-party formal checks and static checks; no Lean build was run by the team. All AI contributions are disclosed and were directed and approved by the human author. Data state: freeze of 19 October 2026.
Contents: report in German (working original) and English (v1.2); dataset v1.1 with node submissions, triage and catalogue scripts (reproduced byte-identically against openai/math commit 1581d4c), forecast resolution criteria K1.0, peer-review findings register, summarised annex of session documents, the canonical behaviour anchor JSON, README, MANIFEST.json and SHA256SUMS. Dataset files and annexes are in German.
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BibTeX
@misc{fuerste2026genesis,
title = {{GENESIS R300.1 – Validating Frontier Claims in AI-Assisted Mathematics: An exploratory case study on formal verification, semantic fidelity, multi-model review and human-in-the-loop governance}},
author = {Dietmar Fuerste},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23482824},
url = {https://zenodo.org/records/23482824},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GENESIS R300.1 – Validating Frontier Claims in AI-Assisted Mathematics: An exploratory case study on formal verification, semantic fidelity, multi-model review and human-in-the-loop governance
AU - Dietmar Fuerste
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23482824
UR - https://zenodo.org/records/23482824
AB - Between May and October 2026, OpenAI announced several mathematical breakthroughs: a disproof of the Erdős unit distance conjecture, a claimed resolution of Clay alternatives C/D for the Navier–Stokes equations with external forcing, a quasi-Riemann hypothesis (zero-free half-plane Re s > 7/8) for ζ and Dirichlet L-functions, the "Ten Advances", and a catalogue of 722 manuscripts (719 after withdrawals). Session GENESIS R300.1 asked how likely it is that these problems have actually been solved, and how such claims can be reviewed in a traceable, correctable and transferable way. A team of five AI systems (Claude Opus 5.5 as primary architect; Sol 6.1/ChatGPT, Perplexity Pro, Mistral-Vibe and Grok as review nodes) and one human decision-maker (HITL) worked in four rounds from 16 to 19 October 2026. The claims were decomposed into 17 review entries. Provenance, formal evidence (Lean 4 kernel checks), statement faithfulness and expert assessment were examined on separate paths and combined in an approved HITL gate. Part A – Results: The Erdős disproof is solved on solid grounds (independent human-verified reconstruction by nine authors). The quasi-RH for ζ and Dirichlet L and Navier–Stokes C/D as a formal theorem are strongly supported but not conclusively verified: the formal chains are statically consistent but were not reproduced by the team, and a human PDE sign-off is missing for Navier–Stokes. The Ten Advances are supported with reservations (chapter 8 on hold). No success rate can be derived for the catalogue; three withdrawn manuscripts remain unsupported. Six dated forecasts with deadlines up to the end of 2027 and pre-registered resolution criteria (K1.0) form a prospectively evaluable register. Part B – Method: The session produced the validation protocol R300-VEP v0.3 (six review stages P0–P5, two separate review paths, five review measures, four reproduction levels, 14 evidence aggregation rules, process rules V1–V6, forecast register) and the first full application of the behaviour anchor GENESIS-R900-I10. The main observation: in the documented process, the primary architect was the most conspicuous source of wrong objections that were passed on to other nodes; they were caught only in cross-review. This motivates candidate rule V8 (enforced handover contracts and an evidence graph) for testing in R300.2. Because roles differed and there was no comparison condition, no error-rate comparison between models and no proof of the anchor's effect is claimed. Nature of this work: an exploratory, AI-assisted evidence synthesis and protocol case study. It is not an original mathematical publication and not a certification of the results examined. Mathematical judgements rest on human expert sources, third-party formal checks and static checks; no Lean build was run by the team. All AI contributions are disclosed and were directed and approved by the human author. Data state: freeze of 19 October 2026. Contents: report in German (working original) and English (v1.2); dataset v1.1 with node submissions, triage and catalogue scripts (reproduced byte-identically against openai/math commit 1581d4c), forecast resolution criteria K1.0, peer-review findings register, summarised annex of session documents, the canonical behaviour anchor JSON, README, MANIFEST.json and SHA256SUMS. Dataset files and annexes are in German.
ER -