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The conical area coefficient under the geometric contract

Original ledger classification: Identity [I] (chain derived) + [A] (the one isolated residual)

Recorded statement: Seam-Horizon programme: the Fursaev-Solodukhin factor 4pi is now DERIVED, not imported [I] (removes the literature import of v67): (1) smoothed-cone Gauss-Bonnet - regularising the 2D cone (opening alpha) by a tangent spherical cap…

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Paper context: Origin Theory

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SEAM.AREACOEFF.03

Original ledger classification: Identity [I] (chain derived) + [A] (the one isolated residual)

Original claim text

Seam-Horizon programme: the Fursaev-Solodukhin factor 4pi is now DERIVED, not imported [I] (removes the literature import of v67): (1) smoothed-cone Gauss-Bonnet - regularising the 2D cone (opening alpha) by a tangent spherical cap (tangency alpha=cos theta0) gives Int K dA = 2pi(1-cos theta0) = 2pi(1-alpha) EXACTLY, independent of the smoothing radius (topological; GB closure Int k_g=2pi alpha, chi(disk)=1; limits: hemisphere->cylinder alpha=0, flat->plane alpha=1); (2) codim-2 lift: Int sqrt(g)R -> 2*2pi(1-alpha)A = 4pi(1-alpha)A; (3) replica definition S=-d_alpha[logZ(alpha)-alpha logZ(1)]|_1 with logZ=k_red Int sqrt(g)R gives S=4pi k_red A with the smooth part dropping out - the FS relation machine-derived; (4) k_red=c3/2 (v73/SEAM.KHALF.01) => S=2pi c3 A, and S=A/4 forces c3=1/(8pi) UNIQUELY (sympy-solved). RESIDUAL ISOLATED [A]: the single remaining step is 'replica variation of the seam determinant (gapped Calderon kernel) produces the EH form k_red Int sqrt(g) R with cutoff-independent k_red' = the Seam-Horizon Theorem proper (SEAM.THEOREM.01); steps 1-4 contain no Bekenstein-Hawking import

Original classification detail

Identity [I]: S=4pi k A derived; S=A/4 <=> c3=1/(8pi); residual = seam determinant => EH form

Dependencies as recorded

SEAM.AREACOEFF.01; SEAM.AREACOEFF.02; SEAM.KHALF.01; SEAM.THEOREM.01

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  • v90_conical_defect_chain.pyRegistered verification module · registry
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    Fursaev–Solodukhin factor DERIVED, not imported: smoothed-cone Gauss–Bonnet ∫K = 2π(1−α) exactly (smoothing-independent), codim-2 lift 4π(1−α)A, replica ⇒ S = 4πkA; with k=c₃/2: S = A/4 ⇔ c₃ = 1/(8π) (sympy-solved, unique). The Seam–Horizon residual is isolated to one step: seam determinant ⇒ EH form

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