Layer Codes 1024 to 2047

Abstract

An interval of base-three layer codes satisfies the exact support score bound.

Theorem 1.1 (Exact layer-code interval).

$$\forall code\in \mathrm{Nat},\left(1024\le code\wedge code<2048\right)\Rightarrow \mathrm{exactRow}\left(positions8,code\right)=\mathrm{true}$$

Proof. Machine-checked in Lean as D5/S3/Combinatorics/GeneralizedPetersen/ZeroForcingThreeGapCover8G1.covers (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Arnav Krishnan (2026). A correction to the Zero Forcing Number of the Generalized Petersen Graphs P(n,3). DOI: 10.48550/arXiv.2607.19412. URL: https://arxiv.org/abs/2607.19412v1.

Commentary.

For positions8, every code from 1024 through 2047 passes exactRow. The exactChunk checks cover this interval; a decoded set of ten vertices has directScore at most twice the support length plus two.

References

• Truth anchor: D5/S3/Combinatorics/GeneralizedPetersen/ZeroForcingThreeGapCover8G1.covers
• Dependency: D5/S3/Combinatorics/GeneralizedPetersen/ZeroForcingThreeGapExact