A registered result in its source context
Original ledger classification: Identity [E] (modular 2pi=1/4c3, scalaron Wald factor, area law) + physical bridge [C] (the BH/modular identification)
Recorded statement: BLACK-HOLE THERMODYNAMICS FROM THE SEAM: modular Hawking temperature + scalaron-corrected Wald entropy (2026-06-15, archive integration of the dropped tfpt-42 stationary-horizons/compact-objects section, re-typed through the…
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Paper context: Horizon readouts
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HOR.BHTHERMO.01
Original ledger classification: Identity [E] (modular 2pi=1/4c3, scalaron Wald factor, area law) + physical bridge [C] (the BH/modular identification)
Original claim text
BLACK-HOLE THERMODYNAMICS FROM THE SEAM: modular Hawking temperature + scalaron-corrected Wald entropy (2026-06-15, archive integration of the dropped tfpt-42 stationary-horizons/compact-objects section, re-typed through the Tomita-Takesaki seam work v198/v199). (1) [E] MODULAR T_H: the modular flow Delta^{it}=e^{-2 pi t K_H} (Bisognano-Wichmann/Tomita-Takesaki) gives KMS at beta=2 pi and T_H = kappa/(2 pi); the 2 pi IS the seam unit 1/(4 c3) (1/2pi=4c3, v58), reproducing T_H=c3/M (v57); the seam<->horizon modular identification is [P] (ties to [rho,Lambda]=0, v198/v199). (2) [E] SCALARON WALD ENTROPY: with the induced f(R)=R+R^2/(6 M_s^2) (M_s=c3^{7/2} Mbar, v28), S_W=(f_R A)/(4 G)=(A/4G)(1+R_h/3M_s^2), f_R=1+R/(3M_s^2) -- leading A/4G is the c3 area law (1/4=1/|mu4|), the correction an EXACT scalaron consequence; BH application [P]. (3) [E] SdS T_H=(1/4pi r_h)(1-Lambda r_h^2), 1/4pi=2c3. (4) [E] area law S_BH=M^2/(2c3)=4 pi M^2=A/4G, same 1/(4c3)=2pi factor as the modular beta. Wolfram-mirrored (the f_R Wald identity + modular 2pi=1/4c3 are exact)
Original classification detail
Identity/bridge [E]/[C]: T_H=kappa/2pi from modular flow (2pi=1/4c3); scalaron Wald entropy S_W=(A/4G)(1+R_h/3M_s^2) exact from v28; area law S_BH=A/4G; the BH/modular identification is [C]
Dependencies as recorded
AX.P1.01; HOR.01; v57_horizon_crosslinks.py; v28_gravity_fR.py; v198_modular_commutator_reduction.py
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- Horizon readouts
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- 2026-06-15 (archive integration \#5: six dormant results revived from the old papers)Research changelog; TFPT — Introduction and reading guide
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- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravityinput 4 origin theory
- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravityinput 4 origin theory
- Schwarzschild thermodynamics in four [formula in source] -linesHorizon readouts
- The celestial and twistor continuum routeinput 5 tfpt 3 e8 audit bootstrap
- =150 2026-07-23 (VIII) (prominence pass — the v519–v529 breakthroughs lifted into the FRAME texts of the papers and the website data layer; purely editorial, NO new modules, NO marker moves — (1) tfpt_5_redteam gains the seam round Target G: the ten-test side-blind scoreboard on the alignment bit ( v512/ v521/ v525/ v529) and the first firing kill test of the programme — the interacting straddle law ( v529), documented as a named threat AND the first hard selection principle for [formula in source] , fenced at toy level; (2) the bit-reduction statements in tfpt_1, tfpt_2 and origin_theory extended from the v512 state to the current state (ten side-blind tests, the twist-class definition with gauge-robust order parameter, ``in principle interferometrically readable'', v528 — the bit stays formal input); (3) the thermal seam lifted into the origin_theory horizon chapter (new keybox: [formula in source] measured, temperature the third leg of [formula in source] , v526) and into the tfpt_horizon_readouts head keybox; (4) tfpt_3 title/keybox now carry the thirty-step story and ``the measure chain is derived'' ( v520/ v523) prominently; (5) tfpt_research_contracts title/intro keybox now show the executed stages of CELEST.SEAM.01 (M1–M3, [formula in source] -chains decided, [formula in source] derived) and WOIT.OS.TWISTOR.01 ( [formula in source] executed, [formula in source] next under the straddle constraint); both contracts stay Open)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravityorigin theory
- The celestial and twistor continuum routeinput 5 tfpt 3 e8 audit bootstrap
All 11 linked sections
- =150 2026-07-23 (IV) ( v526 — the thermal seam promoted as the ledger row SEAM.THERMAL.KMS.01: KMS of the reconstructed free OS quotient CLOSED onto the Nariai/BH temperature chain — the THIRD LEG of [formula in source] ; verdict SUCCESS; the celestial/twistor story in tfpt_3 gains Step 27 — (1) [formula in source] MEASURED [formula in source] at both levels ( [formula in source] : [formula in source] , [formula in source] ; [formula in source] : pairing exponent [formula in source] ; wrong [formula in source] excluded); (2) [formula in source] EXACT [formula in source] , [formula in source] [formula in source] Bisognano–Wichmann/Hawking normalisation ( v208) ; (3) modular Hamiltonian closed ( [formula in source] , [formula in source] ; Tomita KMS- [formula in source] on all [formula in source] pairs); (4) [formula in source] third-leg class- [formula in source] selection / (Hawking/Nariai chain; v104 cross-link); (5) entropy [formula in source] , [formula in source] , horizon fractions do NOT transfer ; (6) -5 silver [formula in source] thermal kernel ratio; non-compact [formula in source] ; NO marker moves)
- Front matter / support
- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravity
Registered verification modules
- v208_bh_thermodynamics.pyRegistered verification module · horizon
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black-hole thermodynamics from the seam: the modular Hawking temperature and the scalaron-corrected Wald entropy (archive integration of the dropped tfpt-42 stationary-horizons/compact-objects section, re-typed through the current Tomita–Takesaki seam work v198/v199). [E] MODULAR T_H: Δ^{it}=e^{−2πtK_H} (Bisognano–Wichmann) ⇒ KMS at β=2π and T_H=κ/(2π); the 2π IS the seam unit 1/(4c₃) (1/2π=4c₃, v58), reproducing T_H=c₃/M (v57); seam↔horizon identification is [P]; [E] WALD ENTROPY: with the induced f(R)=R+R²/(6M_s²) (M_s=c₃^{7/2}M̄, v28), S_W=(f_R A)/(4G)=(A/4G)(1+R_h/3M_s²) — leading A/4G is the c₃ area law (1/4=1/|μ₄|), the correction an EXACT scalaron consequence; [E] SdS T_H=(1/4πr_h)(1−Λr_h²), 1/4π=2c₃; [E] area law S_BH=M²/(2c₃)=4πM²=A/4G.
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