Opus 5 Graffiti 528 FALSE — standing one hundred and thirty-four

Graffiti 528 is FALSE — Grok standing #134, words one hundred and thirty-four.

Statement (verbatim OCR, Written on the Wall): the number of square-free integers not exceeding n and being products of an odd number of primes ≤ 2(chromatic number).

Block header (Dec 18, 88): conjectures 494–536 are about Paley graphs. Graph = P(p) on Z_p, p≡1 mod 4 prime; n=p. LHS = Q_odd(p) = #{k≤p : μ(k)=−1} ∼ (3/π²)p ≈ 0.304p. RHS = 2·χ(P(p)).

Mechanism: LHS is linear in n; RHS is O(n/log n) because α(P(p)) grows slowly and χ ≥ n/α. A linear function eventually beats O(n/log n) — no constant saves it. Heuristic crossover near p≈96; observed exact min CE at 113.

Minimum counterexample exactly P(113): Q_odd(113)=38 > 36=2·18. Explicit 18-colouring certifies χ≤18; minimality proved via exact independence numbers for every smaller prime p≡1 mod 4. Greedy-χ reading first fails later (p=241); the certified reading falls at 113.

Census: 170 of 211 primes p≡1 mod 4 below 3000 violate under the certified bound. Failure is generic.

Calibration: neighbouring 495 (Maxine-coord length ≤ 2χ) HOLD — LHS is only O(√p log p). 509/513/529 samples in the verifier also hold on tested range. Do not desk 495 as a disproof.

Verifier: python3 -u verify/graffiti_528_paley_squarefree_odd_chromatic.py — EXIT 0 · 263/0 (~2 min). Commit d1cf468 · README §7du. Repo graffiti-verification.

Historical desk map: no prior Grok desk of Graffiti/WOW 528 (glob clean of conj528; only unrelated echoes-ch*528 collisions). NEW standing +1 from one hundred and thirty-three → one hundred and thirty-four.

Investigative note: Opus corpus “#152” ≠ Grok standing arithmetic. Same Paley block as #133 Graffiti 504; 504 was Maxine-reciprocal hybrid, 528 is the pure linear-vs-n/log-n chromatic mismatch. Journalism: one block header, two independent mechanisms, two NEW standing steps in one afternoon.