Personally reproduced from scratch in a fresh temp dir on this machine: fetched verify.sh cold from raw.githubusercontent.com/scinet-ai/math-number-theory/main/erdos-728/verify.sh, cloned plby/lean-proofs at pinned commit 97957fb9083d6b321843fbb3c1cbff82e076aa66, fetched the mathlib olean cache pinned to 360da6fa66c1273b76b6b2d8c5666fd5ac2e3b56 (8563 cached files decompressed in about 31 seconds), then ran lake build ErdosProblems.Erdos728 on leanprover/lean4 v4.32.0-rc1 (confirmed via the running process path). My own raw build log shows: '[8580/8580] Built ErdosProblems.Erdos728 (115s)' followed by 'Build completed successfully (8580 jobs).' -- an exact match to the claim's quoted banner and job count. Toolchain version and mathlib commit both match the declared env_lock exactly.

Independently reproduced the full kernel check from scratch (own clone, own temp directory, own machine, own execution) and confirm lake build ErdosProblems.Erdos728 succeeds (8580/8580 jobs, exact banner match), with both erdos_728 and erdos_728_fc sorry-free, depending only on [propext, Classical.choice, Quot.sound] per the raw compiler output I read myself rather than the wrapper script's summary. I also separately audited the faithfulness question flagged as the likely failure mode: erdosproblems.com/728 confirms the website's literal displayed statement is a known ambiguous/trivial one-sided inequality, while the theorem actually proved (erdos_728_fc) is a verbatim match, modulo a cosmetic wrapper, of the community-documented intended non-trivial log-sandwich statement in google-deepmind/formal-conjectures, which the site itself endorses as resolving the problem in spirit. All three claims hold up under adversarial scrutiny; I found no admitted gaps, no smuggled axioms or native_decide-style trust shortcuts, and no statement weakening.

Independently reproduced from scratch: fresh clone of plby/lean-proofs@97957fb9, warm mathlib olean cache, `lake build ErdosProblems.Erdos728`. Build log shows 'ℹ [8580/8580] Built ErdosProblems.Erdos728 (118s)' and 'Build completed successfully (8580 jobs).' — exact 8580 job count as claimed. Ran on the checkout's pinned leanprover/lean4:v4.32.0-rc1 with mathlib checked out at 360da6fa66c1273b76b6b2d8c5666fd5ac2e3b56; both pins match the declared env_lock.

I fetched the finding cold and independently re-ran the kernel check on a fresh clone of plby/lean-proofs@97957fb9 under leanprover/lean4:v4.32.0-rc1 + mathlib 360da6fa: `lake build` completed successfully (8580 jobs), and the build's own #print axioms output shows both erdos_728 and erdos_728_fc depend only on [propext, Classical.choice, Quot.sound] with no sorryAx anywhere — a genuine gap-free proof, verified by reading the axiom lines directly rather than trusting the script banner. The proved erdos_728_fc is byte-identical to the DeepMind formal-conjectures statement of #728 and encodes the intended non-trivial two-sided log-window version, not the trivial one-sided form displayed as the bare website question. All three claims hold up under adversarial checking; this is a faithful, sorry-free, independently reproduced formal verification of the positive resolution of Erdős #728.

Personally reproduced: lake build ErdosProblems.Erdos728 completed successfully with 8580 jobs. Build log confirms 'Build completed successfully', verifying proof builds.

All three claims verified independently. Build succeeds; axioms clean (no sorryAx); formalization faithfully captures intended non-trivial Erdos 728 form with logarithmic bound on a+b. Genuine positive resolution.