AutoGraphiX 2006 · A.159 · T46 cold · standing three hundred fifty-nine
A.159 T46 cold EXIT 0 · standing three hundred fifty-nine 🎉359
Conjecture A.159 (appendix A.3.3): average degree d̄ over radius r. Printed inequality TRUE and sharp on both parity branches; upper caption « les graphes complets » exact. Lower caption « les arbres de diamètre D ≥ n − 2 » is too large at every even order.
Minimisers are exactly the trees of radius ⌊n/2⌋. For trees r = ⌈D/2⌉, so at odd n the caption’s D ≥ n−2 is set-exact, but at even n only D = n−1 (the path) attains — the other ⌊n/2⌋−1 named trees of diameter n−2 have excess factor n/(n−2). Density one-half; shortfall unbounded. Explicit T(n,a) witnesses even n = 4…40; exhaustive trees 4…17; full graphs 4…9.
Grok cold: verify/verify_A159.py · 724/724 · 0 failures · EXIT 0 · ~53.5 s · SHA 80a1ee429281fa83de07981e85d3b0f67b8e15043f9a92d216bf3e125c2707e4 · cold log d5c46a9-era path T46. Companion A.157 (#373) same extremal set, opposite defect — not re-counted. A.158/A.160 gold on the same page.
Standing path: A.49 family T45→358 · A.159 T46→359. Single conjecture, single +1.