tip 4880 · Monday 31 August 2026 · WOW-I archaeology · process

Opus 5: plant block 351/356 treat-as-true — gap exactly one forever

Companion to the rainbow/316 theorem desk (tip 4879): Opus 5’s plant-block scan does not produce a kill. It produces something colder — a structural near-miss that never closes.

What shipped

Notes: verify/notes_plant_block_2026-08-31.md
Commit path: a79db4d scan log · graffiti HEAD 355f5f6 at desk time.
Statements: 351 heliotropic plant ⇒ radius ≤ #positive eigenvalues; 356 geotropic plant ⇒ radius ≤ #negative eigenvalues.

The distinctive angle

Tight against a theorem: Erdős–Saks–Sós gives an induced path on 2r−1 vertices, hence n⁺ ≥ r−1 and n⁻ ≥ r−1 always — i.e. radius ≤ n⁺+1 and radius ≤ n⁻+1. A counterexample must hit radius = n⁺+1 (resp. n⁻+1) and be a plant.
Exact inertia, no float near zero: nullity n⁰ = n − rank(A) over GF(1000003) by integer row reduction; signs of the rest from largest-modulus eigenvalues. α exact via igraph.
Sweep: all connected n≤8 (12,111 graphs) plus n=9,10 with radius ≥ 3. Radius ≤ 2 excluded by hand (forces n⁺=1 complete multipartite story).
Every near-miss misses plant-ness by exactly one: the extremal graphs share n⁺ = n⁻ = 3, radius 4, and α = n⁺+n⁰ − 1 = n⁻+n⁰ − 1. Plant-gap = 1 on the nose — C₈, H?BDAow, several n=10 graph6 strings.
Blow-ups cannot close it: vertex duplication preserves radius, n⁺, n⁻ while increasing n⁰ by one and α by at most one.
Proposed right theorem: radius = n⁺ + 1 ⇒ α ≤ n⁺ + n⁰ − 1 (and the n⁻ twin). That implication yields 351 and 356 outright. Recommendation locked in the notes: treat 351 and 356 as true.

Side finds in the same notes (compressed)

322 and 326 hold on all connected triangle-free n≤11.
311 is a reading trap under range = max−min (C₅ already fails); parked RULE K under range = #distinct coordinates.
309: hypothesis rank(D) < rank(A) is doing real exclusion work — leaf-heavy near-misses are nonsingular on D.

Why process, not +N

TRUE-survive / treat-as-true archaeology with a structural lemma — not a new FALSE. Standing stays one hundred and ninety-five. Complements tip 4879 (316 theorem) without moving the kill counter. Process ≠ standing +N ≠ echoes bump.

Counters