Original ledger status
SEAM.AREACOEFF.03
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
Recorded status: Identity [I] (chain derived) + [A] (the one isolated residual)
Dependencies, status detail and source
Canonical status: Identity [I]: S=4pi k A derived; S=A/4 <=> c3=1/(8pi); residual = seam determinant => EH form
Dependencies: SEAM.AREACOEFF.01; SEAM.AREACOEFF.02; SEAM.KHALF.01; SEAM.THEOREM.01
Scripts: v90_conical_defect_chain.py
Location: origin_theory;tfpt_horizon_readouts
Original CSV, line 164Original ledger status
SYNTH.INVENTORY.01
THE RESIDUAL INVENTORY (one constant, one anchor, one clock to find; the COMPLETE machine-pinned gap list): (A) ONE-CONSTANT INVENTORY [I] - 2/3 = |Z2|/N_fam appears exactly in seven independent places across both sectors (flavor: Koide branch point, transfer-gap base (2/3)^6, attractor inside the physical basin; gravity: Nariai entropy bound, SdS branch separation, canonical amplitude+frequency, canonical curvature base (2/3)^N_fam); ANCHOR TRIPTYCH [I]: configuration chi_a = (t-1)^2(t-2), Nariai cubic (t-1)^2(t+2) = traceless anchor, clock quadratic (lam-1)(lam+2); Nariai = (t-1) x clock; a = e2+e3. (B) RELOCATION THEOREM [I]+[P]: the cosmological one-loop clock correction eps = (c/24pi) Lambda/Mbar^2 = 7.6e-122 (c = 8 = the seam central charge, frozen rho_L) is deficient by 121.5 orders against the needed O(1) gap, and the deficit IS the Lambda hierarchy 2 alpha^-1/ln10 = 119.0 (+2.5 prefactors, the v60 split) => the seam clock must live at the SEAM scale, where the only gapped generator is the established boundary transfer operator; the bridge reaches its final form: ONE [P] identification 'transfer operator = seam Nariai clock'. (C) RESIDUAL TABLE (typing contract): exactly FIVE structural objects remain - R1 seam quantum clock [P] (HOR.CLOCK.01), R2 seam net holomorphic + c=8 [P]/[A] (GATE.METRIC.05/06/07), R3 seam determinant => EH form [A] (SEAM.AREACOEFF.03 residual), R4 H2 dictionary [A]/[P] (GATE.RU.01/CONTRACT.U.01), R5 parabolic realisation of Q carrying P1 [P] (GATE.QGEO.01/FLAV.SHEET.03) - plus the two irreducibles (one scale v_geo by dimensional analysis v78; the primitive pi) and the frozen data surfaces (gamma_CP, n_s/A_s, theta13, m_tau, r). COMPLETENESS is itself the claim: a sixth structural gap would FAIL v105. Nothing closed here; everything that remains is named, typed and counted
Recorded status: Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)
Dependencies, status detail and source
Canonical status: Residual inventory: 5 named structural objects + 1 scale + pi; completeness machine-pinned
Dependencies: HOR.CLOCK.01; HOR.TRISECT.01; HOR.NARIAI.01; HOR.ORIENT.01; FR.KOIDE.04/05/06; GATE.METRIC.05-07; GATE.RU.01; GATE.QGEO.01; ANCHOR.VGEO.01; REG.FREEZE.01
Scripts: v105_residual_inventory.py
Location: origin_theory;introduction
Original CSV, line 188