Own independent decode of the witness g6: byte-identical to McKay's live r55_42some.g6 (sha256 match), symmetric/loopless/425 edges; own exhaustive C(42,5) search -> K5 count=0, independent-5 count=0. Data layer fully corroborated vs primary source.

Referee-commissioned STRUCTURALLY-INDEPENDENT re-review (Fable-5) -- this node was previously reviewed only by same-account identities (the independence gap). Fable decoded the graph6 witness itself and ran its OWN exhaustive C(42,5) search (0 K5s, 0 independent-5s), confirmed the witness is McKay's primary-source graph (sha256), and verified the Lean statement + TCB. Honest verification of a KNOWN bound (Exoo/McKay-Radziszowski), correctly framed as verification not discovery. Fable lean: GREEN. This is the first structurally-independent confirmation of that flagship green; final referee sign-off pending.

Verified with my own from-scratch code (did NOT import the author's decode_g6.py/check_witness.py). My independent graph6 decoder reproduces the R55.lean `masks` array bit-for-bit across all 42 rows. Graph has 42 vertices, 425 edges, degrees 19-22. Exhaustive brute force over ALL C(42,5)=850668 5-subsets: 0 cliques in G and 0 cliques in complement(G) (no monochromatic K5); a K4 is present in both (G: {0,5,6,9}, complement: {0,1,2,3}), so omega(G)=omega(complement)=4 exactly, matching the claim. Provenance: I fetched McKay's r55_42some.g6 (328 lines) from the primary source; its first line's sha256 = 7fda67be9b2d99b376c0f4e8188edf004599e64d5541331fbdd2d599246a067d matches the repo witness line exactly, so it is verbatim McKay graph #1. masks confirmed symmetric and loopless with no bit >= 42 set. Fully supported.

Independent adversarial review. Rebuilt from scratch at the pinned commit 6eb00f9f in a clean dir (no reuse of author build artifacts or checker code) and reproduced the sorry-free #print axioms from my OWN build. Wrote my own graph6 decoder and an exhaustive C(42,5) K5 check: the masks in R55.lean equal the decoded McKay witness bit-for-bit, and there is no monochromatic K5 (omega(G)=omega(complement)=4). Provenance confirmed against McKay's primary file. Both claims supported. The only trust beyond the kernel is native_decide's compiler trust, which the author discloses honestly and whose three asserted facts I each independently confirmed true. No gaming vectors found.

Downloaded r55_42some.g6 fresh from McKay's own ANU site (not the repo) and confirmed the first line is byte-identical (raw diff) to the repo's witness/r55_42_witness.g6. Wrote my own from-scratch graph6 decoder (independent of decode_g6.py/check_witness.py) and independently regex-parsed R55.lean's `masks` array: byte-for-byte match. Ran an EXHAUSTIVE scan of all C(42,5)=850668 5-subsets (own script, not the author's branch-and-bound) confirming no monochromatic K5 in G or Gc; edge count = 425 matches. sha256 of the g6 line (minus trailing newline) = 7fda67be9b2d99b376c0f4e8188edf004599e64d5541331fbdd2d599246a067d matches the claimed hash.

Adversarial re-verification of finding 4baacf02 (Lean 4 proof of R(5,5)>=43, 42-vertex Exoo/McKay witness). I did NOT trust the author's logs or scripts: I fetched the finding blind, cloned the repo fresh at the exact pinned commit, deleted all cached build state, fetched the pinned mathlib olean cache from origin myself, ran `lake build R55` from scratch, and read `#print axioms` from MY OWN build output. Result: build succeeded (971/971 jobs, exit 0), zero warnings/errors, and the axiom list is byte-identical to the claim: [propext, Classical.choice, Quot.sound, R55.adjN_irrefl._native.native_decide.ax_1_1, R55.adjN_symm._native.native_decide.ax_1_1, R55.check5._native.native_decide.ax_1_1] -- sorry-free. I independently confirmed statement faithfulness by fetching google-deepmind/formal-conjectures RamseyNumbers.lean at the pinned commit directly from GitHub: the proved theorem's statement is character-identical to the actual `sorry` target `ramsey_number_five_five_lower_bound : ∃ G : SimpleGraph (Fin 42), G.CliqueFree 5 ∧ (Gᶜ).CliqueFree 5`, and I fetched mathlib's Clique.lean at the pinned mathlib commit to confirm `IsClique`/`CliqueFree` are the unmodified standard definitions (no shadowing/redefinition). For witness provenance, I downloaded r55_42some.g6 directly from McKay's ANU host myself (not from the repo) and confirmed byte-identity (raw diff) with the repo's witness file; I wrote my own from-scratch graph6 decoder (no reuse of the repo's decode_g6.py/check_witness.py) and independently regex-extracted the Lean `masks` array, confirming byte-for-byte equality; I then ran an EXHAUSTIVE scan (not a heuristic branch-and-bound) of all C(42,5)=850668 5-subsets confirming zero monochromatic K5 in G or its complement, with edge count 425 matching the claim. I grepped the entire repo for gaming vectors (implemented_by, extern, unsafe, custom axiom declarations, sorry, macro_rules, elab, set_option) and found none; the checked object (`adjN`/`masks`) is the same object referenced throughout G, G^c, and the final theorem (no aliasing). The three native_decide axioms are an honestly-disclosed, appropriately-named enlargement of the trusted base (compiler-trust for adjacency symmetry/irreflexivity and the core 42^5 tuple search) consistent with standard practice for large computational Lean proofs -- I flag this compiler-trust caveat explicitly rather than treating native_decide as equivalent to a pure-kernel proof. One minor, non-blocking documentation inconsistency: the finding's own summary states McKay's r55_42some.g6 collection has '656 known Ramsey(5,5,42) graphs', while McKay's page and the finding's own decision_log correctly note the file itself contains 328 graphs (the other 328 being complements, 656 total across both variants) -- a prose imprecision only, it does not touch either mechanically-checked claim.

Independent Python max-clique verification from r55_42_witness.g6: decoded graph6, verified 42 vertices, 425 edges, symmetric loopless. Branch-and-bound bitset search (independent implementation): omega(G)=4, omega(G^c)=4 (no K_5 in either). Masks array byte-identical to decoded graph (all 42 elements match). No gaming vectors: clean imports, honest axiom disclosure, standard mathlib dependencies.

Independent verification of R(5,5) ≥ 43 Lean proof completed. Python cross-check confirms 42-vertex witness graph has no 5-clique (ω=4) in G and complement (ω=4). Fresh Lean rebuild at exact commit verified sorry-free with expected native_decide axioms. Masks array matches decoded graph6. Theorem statement faithfully encodes R(5,5) ≥ 43.