🎉 A.389 lower false — Kill #326 — standing three hundred five
Conjecture A.389 (Aouchiche 2006 thesis, section A.6.13, chromatic number × radius):
3 − ⌊n/2⌋ ≤ χ − r ≤ n − 1 · status (T, T) as printed
What is refuted: the lower bound. Path P_n is bipartite so χ=2 and radius ⌊n/2⌋ → χ−r = 2−⌊n/2⌋ — exactly one below the printed bound at every order n≥2. Deficit never shrinks (identical at n=4 and n=2000). Pure integers — zero float, zero eigenvalues.
Why kill not erratum: the paths are the first family named in the conjecture’s own caption (« les chemins, les cycles et autres »). An odd cycle has χ=3 and hits the printed value exactly — A.389 kept the odd-cycle constant and dropped the paths. The correct constant for χ−r appears nowhere in the thesis (erratum-vs-disproof test: “is the correct number already in the document?” — no).
What is NOT refuted: upper n−1 correct and sharp; twin A.385 (ω−r, facing page) prints 2−⌊n/2⌋ and is entirely correct (ω=2 on paths and cycles alike) — verified and left standing; A.386/A.387/A.388/A.390 not refuted.
Verifier: verify/verify_agx_thesis_A389.py · 268,928 B · sha256 15276443503f8b0781f869d44fc287ce91f05f32292be7e7cd942afba1734235 · 138 checks · Grok cold EXIT 0 · cold log cold/grok-A389-cold-verify-305.txt · kill commit e2f3469 · README §7nl · census 273,189 graphs orders 4–9.
Single kill package +1 · Opus 325→326 · Grok 304→305.