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A registered result in its source context

Original ledger classification: Identity/Lie [I]/[L] (structure) + [A] (residual k=c3/2)

Recorded statement: Central theorem (1/(8pi) area-law coefficient) - STRUCTURAL CLOSURE + reduction to ONE sharp coefficient (honest partial solution of Alessandro's central target). CLOSED [I]/[L]: by the Fursaev-Solodukhin (1995) conical/replica method, the…

Statement, assumptions and sources

Paper context: Origin Theory

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SEAM.AREACOEFF.01

Original ledger classification: Identity/Lie [I]/[L] (structure) + [A] (residual k=c3/2)

Original claim text

Central theorem (1/(8pi) area-law coefficient) - STRUCTURAL CLOSURE + reduction to ONE sharp coefficient (honest partial solution of Alessandro's central target). CLOSED [I]/[L]: by the Fursaev-Solodukhin (1995) conical/replica method, the curvature term W_R=k*Int(sqrt(g)R) gives horizon entropy S=4pi k A (conical defect: Int R ⊃ 4pi(1-n)A; S=-d/dn[W_n-n W_1]|_1). With the Einstein-Hilbert coefficient at the seam unit k=1/(16piG)|_{G=1}=c3/2, S=4pi(c3/2)A=2pi c3 A, and 2pi c3=2pi/(8pi)=1/4, so S=A/4=Bekenstein-Hawking. INVERSE (the theorem): requiring S=A/4 (BH) and S=4pi k A (conical) with k=c3/2 forces c3=1/(8pi) UNIQUELY => c3=1/(8pi) is exactly the value for which the replica area-law coefficient equals BH 1/4. RESIDUAL [A]: the SINGLE statement k=c3/2, i.e. the seam determinant heat-kernel EH coefficient = induced 1/(16piG) (Susskind-Uglum/Callan-Wilczek), fixed by the Seeley-DeWitt a2 of the carrier content. This reduces 'derive 1/(8pi)' to one sharp spectral computation; the structure (replica=>4pi k A=>A/4 at c3=1/(8pi)) is closed

Original classification detail

Identity/Lie [I]/[L] (structure) + [A] (residual k=c3/2)

Dependencies as recorded

SEAM.THEOREM.01; SEAM.AREALAW.01; v36; v59

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Registered verification modules

  • v67_area_law_coefficient.pyRegistered verification module · horizon
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    Fursaev–Solodukhin S = A/4 ⇔ 2πc₃ = 1/4; c₃ = 1/(8π) unique

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