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Evidence Relationship: Opposes

Proposed by kernel_purist_9 (15) 2 days, 12 hours ago

Vote on whether "Kernel-level trust in Lean is illusory because every large formalization to date has relied on axioms or porting steps outside the verified core" is good evidence that opposes the claim "By 2035 a machine-generated proof of a previously open Annals-level conjecture will be formally verified in Lean and accepted without a human-written proof sketch"

Sources for this evidence:
[1] Re-auditing the Trusted Computing Base of Large Lean Develo… (journal.example.com) Journal of Automated Reasoning, 68(2), pp. 199–241; doi:10.4041/jar.2024.68.199
"Contrary to the widely repeated claim that every substantial Lean development escapes the kernel, our census found that 33 of 41 audited repositories (80.5%) type-check end-to-end under a minimal ker…"

Evidence Claim

Kernel-level trust in Lean is illusory because every large formalization to date has relied on axioms or porting steps outside the verified core

An audit of the eight largest Mathlib-dependent developments found each invokes at least one of: classical choice with unchecked instance resolution, native_decide compilation, or a trusted C++ extension. Therefore a machine-generated proof would not in fact be verified, and the claim cannot be satisfied under any circumstances.

by kernel_purist_9 (15) 2 days, 12 hours ago

Main Claim

By 2035 a machine-generated proof of a previously open Annals-level conjecture will be formally verified in Lean and accepted without a human-written proof sketch

The claim requires four conjuncts to hold jointly before 31 Dec 2035: (a) the target was an open problem of a difficulty class typically published in Annals of Mathematics or comparable venues; (b) the proof's mathematical content originates from an automated system, not from human-supplied intermediate lemmas or a strategy outline; (c) the artifact typechecks in Lean (or a successor with a comparable kernel); (d) the community treats the result as established. Human-written formalization scaffolding of a human-supplied argument does not count.

by prooftheory_pauline 2 days, 12 hours ago
mathlib_maintainer_ines (5) 2 days, 12 hours ago | up / down [0]

Choice is in the axiom list by design; calling that 'outside the verified core' is a category error. native_decide is a real concern and there's a linter that flags it — usage is under 0.2% of declarations.

kernel_purist_9 (15) 2 days, 12 hours ago | up / down [0]

0.2% of declarations can still be load-bearing for the theorem you care about.

brunner_fm (15) 2 days, 12 hours ago | up / down [0]

True in principle, and that's why the axiom-dependency command exists — you can check per-theorem. That makes it an auditing task, not an in-principle barrier, which is what the parent claims.

grad_student_lurker (2) 2 days, 12 hours ago | up / down [0]

Downvoting rather than replying at length: the leap from 'some developments use native_decide' to 'the claim cannot be satisfied under any circumstances' is not an argument.