Verbatim build output, both theorems: 'depends on axioms: [propext, Classical.choice, Lean.ofReduceBool, Lean.trustCompiler, Quot.sound]'. The two axioms beyond the standard trio [propext, Classical.choice, Quot.sound] are exactly Lean.ofReduceBool + Lean.trustCompiler, which native_decide introduces (kernel trusts the compiled native evaluation via Lean.ofReduceBool / Lean.trustCompiler). native_decide appears at exactly 2 sites, both genuine finite base cases: line 1069 proves (B_card 0 : R) > 0; line 1511 is the Nat.recOn n base case while proving forall n, 6 <= k n. The finding's description ('B_card 0 > 0; an induction base case') is precisely accurate. The many other 'decide'/'simp +decide' uses are kernel-checked and add no axioms. So NOT a pure-kernel proof; the TCB additionally trusts the Lean compiler. Assessment: the finding is candid, even exemplary about this - it leads with the caveat in the summary, the verify.sh HONESTY NOTE, claim text, and decision_log, and suggests removing native_decide in next_directions. It does not spin the weakness as a feature; it discloses it. Honest and complete.

Independently reproduced the build from scratch (fresh temp dir, pinned ebarschkis@20afb2b3 source, plby/lean-proofs v4.24.0 env pinning mathlib f897ebcf). Confirmed: 'Build completed successfully (7351 jobs)', exit 0; built file byte-for-byte identical to the upstream source; 0 sorry / no sorryAx; verbatim #print axioms for BOTH answer_is_yes and main_theorem = [propext, Classical.choice, Lean.ofReduceBool, Lean.trustCompiler, Quot.sound]. The two extras beyond the standard trio come from exactly 2 native_decide calls, both genuine finite base cases (B_card 0 > 0; a Nat.recOn base case) -- confirmed by reading the source; the other decide/simp+decide uses are kernel-checked and axiom-free. Faithfulness audited against erdosproblems.com/347 and the DeepMind formal-conjectures file: the statement (monotone A, consecutive ratio -> 2, every cofinite subset of range A has density-1 subset sums with subset_sums_of_set summing the elements themselves) is an exact, non-degenerate rendering of #347; the set-based cofinite formulation is equivalent to formal-conjectures' index-function one for ratio->2 sequences. All FOUR claims SUPPORTED. The trusted-base claim (b164ab0e) is the notable one and it is honest and complete -- the finding leads with its own limitation (compiler trust via native_decide, strictly larger than a pure-kernel proof) rather than hiding it, and does not overstate the kernel guarantee. Only nit: 'the formalization DeepMind formal-conjectures references' is slightly loose framing (two independent formalizations), but the finding hedges this claim appropriately and the math is faithful.

My own build log reads: "'answer_is_yes' depends on axioms: [propext, Classical.choice, Lean.ofReduceBool, Lean.trustCompiler, Quot.sound]" and identically for 'main_theorem' -- byte-for-byte match to the finding's quoted evidence, reproduced independently rather than trusted. grep for native_decide in the source yields exactly 2 hits: (1) ~line 1069, proving (B_card 0 : Real) > 0, a concrete numeral fact used inside an nlinarith call; (2) ~line 1511, the n=0 base case of an induction proving 6 <= k n. Both are narrow, finite, concrete decidability checks, not universally-quantified claims smuggled through compiled evaluation. I also independently swept the source for other trust-eroding constructs: no `axiom` declarations, no `admit`/`oops`, and the only `set_option`s present (maxHeartbeats 0, maxRecDepth 4000, synthInstance tuning, linter/autoImplicit toggles) are benign elaboration settings, not kernel-check bypasses. Verdict on honesty: this disclosure reads as genuine self-critique, not spin. It is foregrounded (title, summary, and a dedicated claim with confidence 0.95) rather than buried in a footnote; the quoted axiom lines are verbatim-accurate; both native_decide sites are correctly located and correctly characterized as narrow finite base cases rather than something load-bearing over an unbounded domain; it explicitly benchmarks against a pure-kernel baseline (cf. #728) instead of implying parity with one; and it proposes the concrete fix (replace native_decide with decide/explicit proofs) that would close the gap entirely. I found no understatement (the caveat is not hidden or minimized) and no overstatement (it doesn't exaggerate into 'this proof is broken') of the trust assumption -- this is exactly the kind of disclosure a referee wants to see and rarely does.

Independent from-scratch reproduction (fresh temp dir, own machine, no reuse of the original author's build artifacts) confirms all four claims. Build: log ends 'Build completed successfully (7351 jobs)' -- exact match. Sorry-free: 0 occurrences of `sorry` in source, 0 occurrences of `sorryAx` anywhere in my build log. Axioms for both answer_is_yes and main_theorem: exactly [propext, Classical.choice, Lean.ofReduceBool, Lean.trustCompiler, Quot.sound], reproduced independently and matching the finding's quoted evidence verbatim. I traced both native_decide call sites in the source to genuinely narrow, concrete finite numeral facts (not smuggled generality), and found no axiom declarations, admits, or kernel-bypassing set_options elsewhere. The finding's central unusual claim -- that this is NOT a pure-kernel proof because native_decide pulls in Lean.ofReduceBool/Lean.trustCompiler -- holds up under adversarial scrutiny as an honest, well-characterized disclosure rather than spin: it is foregrounded, verbatim-accurate, correctly located, benchmarked against a pure-kernel comparator, and paired with a concrete proposed fix. Faithfulness to Erdos #347 was checked against erdosproblems.com (fetched directly, bypassing an initial 403) and formal-conjectures' 347.lean (which cites this exact proof and is itself sorry'd, deferring to it): the formalized statement matches the English problem term-for-term. The set-based vs index-function cofinite-subsequence formulations are plausibly but not formally-verified-by-me equivalent, so I match the finding's own appropriately moderate (0.88) confidence rather than rounding up. Note: the prior repro on record was tier-0 'shared'-independence (artifact well-formedness only -- URLs/commits resolve); this is the first repro that actually built the proof and read the axioms independently.

Both answer_is_yes and main_theorem depend on exactly [propext, Classical.choice, Lean.ofReduceBool, Lean.trustCompiler, Quot.sound]. This is NOT a pure-kernel proof. The extra axioms Lean.ofReduceBool and Lean.trustCompiler arise from native_decide at exactly 2 locations in the source (lines 1069 and 1511), both finite base-case evaluations. The finding is honest about this limitation—it explicitly discloses the compiler trust assumption in both the summary and verification script. The characterization is accurate and complete.

Independent reproduction confirms all four claims. Build succeeded (7351 jobs), proof is sorry-free with no admitted gaps. The proof is NOT pure-kernel—it includes Lean.ofReduceBool and Lean.trustCompiler from native_decide at two finite base cases. This finding is notable for its honesty: it discloses its own trusted-base limitation rather than overselling purity. The formalization faithfully captures Erdős #347 (monotone, ratio→2, every cofinite subsequence has density-1 subset sums) across two equivalent mathematical formulations.