Original ledger status
SEAM.AREALAW.01
SEAM.AREALAW.01
Area-law evidence for the open Seam-Horizon step (necessary condition met, NOT a closure): (1) NUMERICAL [Python-only] - the simplest reflection-positive Gaussian system (harmonic chain) has ground-state block entanglement entropy that SATURATES to a constant when gapped (area law: 1D boundary=O(1) points) and grows ~(c/3)log L when gapless (CFT c-coefficient, c~1); demonstrated S(8)=S(16)=S(32)=0.271 gapped vs 2.197<2.409<2.602 gapless (Srednicki 1993, Bombelli-Sorkin). So an RP Calderon-type kernel GENERICALLY yields an area law - the form S=A/(4G_Sigma) needs. (2) GAP TIE: the physical sector is gapped by the SAME gap Delta=6log(3/2)>0 that makes the attractor unique (v56) => gapped => area law; one gap gives BOTH attractor and area-law structure. (3) EXACT [I]: 8=|Z2|*|mu4| (sheet x glue), c3=1/(|Z2||mu4|pi); 2pi=1/(4c3) (chaos bound/seam unit); scrambling beta/2pi=|mu4|M. HONEST: fixes the area-law FORM; the c3=1/(8pi) COEFFICIENT still needs the specific seam kernel (open [A]). Cascade D=60-2n monotone c-function-like, 60=2h(E8) [P/analogy]
Recorded status: Numerical + Identity [I] (necessary condition)
Dependencies, status detail and source
Canonical status: Numerical + Identity [I] (necessary condition)
Dependencies: SEAM.THEOREM.01; v56; v58
Scripts: v59_area_law_evidence.py
Location: origin_theory
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