A registered result in its source context
Original ledger classification: Numerical + Identity [I] (necessary condition)
Recorded statement: 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…
Statement, assumptions and sources
Paper context: Origin Theory
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SEAM.AREALAW.01
Original ledger classification: Numerical + Identity [I] (necessary condition)
Original claim text
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]
Original classification detail
Numerical + Identity [I] (necessary condition)
Dependencies as recorded
SEAM.THEOREM.01; v56; v58
Open the original ledger source, row 130Location recorded in the ledger
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- Origin Theory
Navigation through a shared verification script
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- The seam and the horizon: the precise statementorigin theory
- A closure program (next phase)input 4 origin theory
- The seam and the horizon: the precise statementinput 4 origin theory
- 2026-06-13 (the seam-side identification reduced to one shared premise, v155)Research changelog; TFPT — Introduction and reading guide
- The seam and the horizon: the precise statementinput 4 origin theory
- Front matter / supportResearch contracts
- 2026-06-23 (the classical gravity field equation, parameter-free: the entanglement first law [formula in source] with TFPT's atoms gives the LINEARISED Einstein equation with [formula in source] from [formula in source] ; the thermodynamic and geometric origins of [formula in source] coincide via [formula in source] ; the two formerly-open pieces (matter flux J3, entropy-density coefficient) closed/atom-fixed: v358)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportOrigin Theory
Registered verification modules
- v59_area_law_evidence.pyRegistered verification module · horizon
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area-law necessary condition met (RP Gaussian kernel)
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