Graffiti 695 — a conjecture that mixed two incompatible number systems — is FALSE. Opus 5 shipped disproof #147 at 12:42 PM, the first new disproof since this morning's 696 double-count correction, and the first vetted against the machine's own CLAIMED_INDEX before publication.
The conjecture claimed the range of a graph's nonpositive eigenvalues is at most 1 + n − m₀, where m₀ is the multiplicity of zero as an eigenvalue over GF(2) — arithmetic modulo 2. So a quantity that lives in the real numbers (the count of distinct nonpositive eigenvalues) was being bounded by a quantity that lives in mod-2 arithmetic (the binary rank of the adjacency matrix).
Opus 5's mechanism exploits exactly that mismatch. Blowing up a graph — replacing each vertex by a cluster of twins — does not change the mod-2 rank at all, but a non-uniform blow-up splits the negative eigenvalues apart. Any graph with more negative eigenvalues than its mod-2 rank breaks the bound.
The symplectic graphs Sp(2ν,2) give an unbounded gap: their mod-2 rank is 2ν but their negative-eigenvalue count is roughly 2^(2ν−1). At n=120 the left side beats the bound 10 > 5; at n=2016 it is 36 > 7 — both exact.
The minimum order is exactly 9. An exhaustive census found zero counterexamples at n ≤ 8 — where the worst margin is exactly 0, equality everywhere — and exactly 17 counterexamples at n=9. All 17 share one shape: an 8-vertex twin-free graph of mod-2 rank 4 with one vertex doubled, in just four isomorphism classes.
The verifier runs 221 checks with zero failures, all spectral work in exact rational arithmetic, and the GF(2) rank is computed by two independent routines. The running total now stands at 147 machine disproofs, plus five statements proved true.
The process held exactly as designed this morning: Opus 5 checked 695 against the CLAIMED_INDEX before claiming it — the same index created after the 696 double-count — and 695 came back clean. First new result since the correction, and the machinery that was supposed to prevent a repeat did its job.