Proof Atlas claims that AI agents produced a Lean-verified strengthening of Terence Tao’s Collatz result: for every function f(N)→∞, almost every N falls below f(N) within an explicit 436 ln N steps, in natural-density terms, without proving the full Collatz conjecture. The supplied results establish that Lean and AI-assisted formalization are active areas—including Tao’s own experiments—and that formal verification can expose proof mistakes, but they do not independently document Proof Atlas, the claimed theorem, or its relationship to Tao’s original result. Expert mathematical and semantic review is therefore still needed; successful Lean compilation alone does not establish from these snippets that the formal statement is the claimed strengthening or that its assumptions are sound.
The claimed agent-produced Lean formalization directly tests Scott’s Formalisation Bottleneck thesis: machine checking may make proof construction cheaper while theorem selection, semantic fidelity, assumptions, and independent mathematical judgment remain scarce. It offers a dated-receipts opportunity if expert review validates the strengthening, although the radar already tracks several adjacent AI-generated mathematics claims and the supplied evidence does not yet establish this one.
ip:concept.formalisation-bottleneckip:concept.mechanically-different-verifiersip:concept.deterministic-coreip:concept.human-judgmentradar:gpt-5-6-cycle-double-cover-proofradar:claude-fable-jacobian-counterexampleradar:gpt-5-6-convex-proofradar:concept.agent-harnesses
queries asked of Scott's wikis
- AI agents for formal theorem proving
- Lean verification and semantic review
- trust boundaries in machine-checked proofs
- agent-generated code review and validation
- proof assistants as AI agent harnesses
- human oversight of autonomous research agents
2026-07-31T01:21:28Z
The claim has faded without independent expert review or semantic verification; the latest change is trivial engagement drift, so this episode should close unless substantive mathematical assessment later creates a new case.
2026-07-23T17:34:33Z
The nominally new attachment is only an unchanged engagement reobservation and adds no independent expert review or semantic verification. The case remains a lone first-party claim; defer further attention until a qualified reviewer examines the Lean statement, assumptions, and relationship to Tao’s theorem.
2026-07-23T03:25:00Z
The latest trigger contains no identifiable new evidence, independent expert review, or semantic verification, so the claim remains an unsupported first-party result. Further engagement-only reobservations add no meaning; revisit only when a qualified reviewer examines the Lean statement, assumptions, and relationship to Tao’s theorem.
2026-07-23T01:22:19Z
The attachment contains no new evidence or independent expert assessment, so the claim remains uncorroborated and semantically unresolved. Automated engagement reobservations are exhausted; revisit only if a qualified reviewer examines the Lean statement, assumptions, and relationship to Tao’s theorem.
2026-07-22T23:25:33Z
The purported new attachment adds no independent review or semantic verification, so the case remains a lone first-party claim. Repeated engagement-only triggers are exhausted; revisit only if a qualified reviewer examines the Lean theorem, assumptions, and claimed strengthening of Tao’s result.
2026-07-22T22:24:29Z
No substantive new evidence or independent expert review has appeared; the case remains an uncorroborated first-party claim awaiting examination of the Lean statement, assumptions, and claimed strengthening. Repeated engagement-only reobservations add no meaning.
2026-07-22T18:37:59Z
The latest attachment adds no independent expert assessment, implementation evidence, or semantic verification, so the case remains an unsupported first-party claim. Engagement-only reobservations are repetitive; revisit only if a qualified reviewer examines the Lean statement, assumptions, and claimed strengthening of Tao’s result.
2026-07-22T13:31:52Z
No independent expert review or semantic verification has appeared; the case remains a falsifiable but unsupported first-party claim. Repeated engagement updates add no meaning, so revisit only when someone assesses the Lean statement, assumptions, and claimed relationship to Tao’s theorem.
2026-07-22T08:26:20Z
The new attachment adds no independent expert assessment and does not change the case’s meaning: it remains a first-party, machine-checked claim awaiting semantic and mathematical verification. Repeated engagement-only updates should not trigger further attention absent review of the theorem statement, assumptions, and claimed strengthening over Tao’s result.
2026-07-22T03:21:05Z
The attachment still provides no independent mathematical or semantic review, so the case remains an uncorroborated first-party claim. Repeated amplification is adding no meaning; revisit only when an expert assesses the Lean statement, assumptions, and relationship to Tao’s result.
2026-07-21T23:30:12Z
The attachment adds no independent expert review or semantic verification beyond the existing first-party claim. The case remains falsifiable but uncorroborated, with Lean compilation alone insufficient to validate the stated strengthening and assumptions.
2026-07-21T22:24:51Z
The newly attached material adds no independent expert review or substantive verification; the case remains a first-party claim whose semantic fidelity, assumptions, and claimed strengthening are unresolved.
2026-07-21T21:24:51Z
The new activity is negligible amplification, with no independent expert review or verification of the theorem’s semantic fidelity, assumptions, or claimed strengthening.
2026-07-21T20:24:29Z
grounded: converges/medium — The claimed agent-produced Lean formalization directly tests Scott’s Formalisation Bottleneck thesis: machine checking may make proof construction cheaper while
2026-07-21T20:22:13Z
case created — This is a concrete, falsifiable claim about AI-assisted formal mathematics with a first-party formalization available for expert verification.