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module module high

IndisputableMonolith.Papers.GCIC.BrainHolography

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The BrainHolography module assembles lemmas showing that any single vertex value fixes the entire field on a connected graph at exact J-minimum. Researchers modeling neural states via holographic information bounds would cite it for the core local-to-global step. The structure composes graph rigidity with the GCIC derivation from the RS forcing chain.

claimOn a connected graph $G$ with ratio energy $C_G[x]=0$, the positive field $x$ is constant, hence the value $x(v_0)$ at any vertex determines $x(v)$ for all $v$.

background

The module sits inside the GCIC paper and imports the J-cost definition, the RS time quantum $ au_0=1$, and the forcing chain results. GraphRigidity states that $C_G[x]$ vanishes on finite connected graphs if and only if $x$ is constant and positive. GCICDerivation shows that T5 J-uniqueness plus T6-T7 compact phase forces uniform $ heta$ at stationarity. ApproximateHolography supplies the near-minimum perturbation bound while BekensteinFromLedger derives the entropy bound on the $\mathbb{Z}^3$ ledger.

proof idea

This is a composition module. It imports seven supporting files, then defines lemmas such as local_determines_global by direct application of the constancy result from GraphRigidity, followed by subgraph and boundary variants. No new algebraic reduction is performed beyond the imported rigidity theorem.

why it matters in Recognition Science

The module supplies the information-theoretic core that feeds the brain holography argument and closes Gap G2 in ApproximateHolography. It rests on the GCIC derivation from the T5-T8 chain and supplies the exact J=0 case used by BekensteinFromLedger. The parent claim is the full local-to-global holography statement in the GCIC paper.

scope and limits

depends on (7)

Lean names referenced from this declaration's body.

declarations in this module (16)