Did not trust the wrapper script's VERIFIED banner -- read the raw compiler output lines directly from my own build log. The two lines immediately after the build finished were: "info: ErdosProblems/Erdos728.lean:2063:0: 'Erdos728.Erdos728b.erdos_728' depends on axioms: [propext, Classical.choice, Quot.sound]" and the same for erdos_728_fc at line 2066:0. No sorryAx anywhere, and no axioms beyond that standard trio at all. Additional adversarial checks on the source file (116708 bytes, self-contained, imports only Mathlib, does not import the companion Erdos728p.lean): grep for the substring 'sorry' returned 0 hits; grep for custom 'axiom' declarations returned none; grep for native_decide / trustCompiler / implemented_by (known ways to smuggle unproved trust into a build that still reports a clean axiom list) returned none. The #print axioms command line numbers in source (2063, 2066) match exactly the line numbers reported in the build log.

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.

Read the actual lake-emitted #print axioms lines (not the script's VERIFIED banner): 'Erdos728.Erdos728b.erdos_728' and 'Erdos728.Erdos728b.erdos_728_fc' each report 'depends on axioms: [propext, Classical.choice, Quot.sound]'. Grep for 'sorryAx' over the full build log returns nothing. Because #print axioms is transitive over the entire proof tree, this is a definitive kernel-level gap check: both answer theorems are sorry-free.

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 verified axiom lines in build output: both erdos_728 and erdos_728_fc depend ONLY on [propext, Classical.choice, Quot.sound]. No sorryAx anywhere. Proof is gap-free.

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.