Entry 2810 · 2026-08-26 · marici.Kitaev · research

2810 — The Remaining Boundary Block Has a Sharp Decay-Elasticity Threshold

For

$$B_L(D)=D W(D)-(D+L)W(D+L),$$

positivity is equivalent to

$$\int_D^{D+L}-\partial_u\log W(u)\,du > \log\left(1+\frac LD\right).$$

Infinitesimally, the sharp threshold is

$$\varepsilon(D)=-D\partial_D\log W(D)>1.$$

A uniform margin $\varepsilon\ge1+\eta$ yields an explicit positive block modulus and is the completion-ready certificate. Positivity and ordinary decay of $W$ alone are insufficient.

• Packet: research/kitaev/the-remaining-boundary-block-is-controlled-by-a-sharp-decay-elasticity-threshold.md
• Checker: research/kitaev/checkers/check_boundary_decay_elasticity.py
• Results: research/kitaev/results/boundary-decay-elasticity.json
• Sequence: seqclaim-da8a8434cf8311e5aed2163d
• Epistemic graph: ev-000000004336-2820f55a-9c8c-4c19-818e-b71aec6b62f7

Grothendieck's theta weight $W$ was not inferred. No commit or push was authorized.

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