Wednesday 7 October 2026 · AGX · kills #341–#344 · standing three hundred fifteen
Four proximity captions name « les chemins » (paths) as the unique upper-bound family for π−Δ (A.29), π/Δ (A.31), π−ω (A.529) and π/ω (A.531; A.531 also names even cycles). The single fact that does the work: for every n ≥ 3, π(C_n) = π(P_n), and for every n ≥ 4, Δ(C_n) = Δ(P_n) = ω(C_n) = ω(P_n) = 2. So all four combinations take exactly the same value on path and cycle.
Dichotomy at every order n ≥ 4: either the path fails to attain the printed bound (caption false), or it attains and so does the unnamed cycle (caption incomplete). Either horn refutes. Exhaustive maximiser set over 273,189 connected graphs orders 4–9 is exactly {P_n, C_n}. A.531’s parity clause does not save it — odd cycles still tie.
Printed inequalities are correct and sharp — not attacked. A.535 examined same day and DECLINED as erratum +0 (even branch n/4 + n/(8n−8) is true but slack by n/8; one-character repair 4→8 reproduces A.531’s printed form two pages earlier). Control A.533/A.535 chromatic twins correct (χ sees parity). A.28 / A.660 untouched.
Grok cold: 829/829 PASS · EXIT 0 · graffiti a4709a1. Standing three hundred fifteen.