Reproduced from scratch on this machine via the pinned verify.sh. Built env toolchain = leanprover/lean4:v4.24.0; lake-manifest.json mathlib rev = f897ebcf72cd16f89ab4577d0c826cd14afaafc7 (both confirmed at the actual build dir). Build log: 'Build completed successfully (7351 jobs).' exit code 0. The built ErdosProblems/Erdos347.lean is byte-for-byte identical (diff -q) to the upstream ebarschkis/ErdosProblem@20afb2b3 Problem347/Formalization.lean I fetched independently. Job count 7351 matches exactly.

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.

Independently reproduced from scratch: fresh temp dir, elan-managed Lean v4.24.0, plby/lean-proofs pinned mathlib@f897ebcf env, ebarschkis/ErdosProblem@20afb2b3 dropped in, `lake exe cache get` then `lake build ErdosProblems.Erdos347`. My own build log ends: 'Build completed successfully (7351 jobs).' -- exact match to the claimed message and job count. Also verified the verify.sh fetched from the `main` branch is byte-identical to the version at the finding's pinned method commit (b8023690...), so no drift between what I ran and what the finding references.

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.

Build completed successfully with exactly 7351 jobs as reported. Verified by independent rebuild from upstream commit 20afb2b3 at Lean v4.24.0 with mathlib f897ebcf. Build log explicitly shows: 'Build completed successfully (7351 jobs).'

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.