A registered result in its source context
Original ledger classification: Identity [I]
Recorded statement: Seam=horizon [I] keystones (pure identities, NO cosmological narrative): (1) the integer 8 in c3=1/(8pi) is OVERDETERMINED and gravitationally aligned: geometry 8=2|mu4| (8pi=|mu4|*2pi seam winding), lattice 8=rank E8=g+n=h(D5)=phi(30)=det…
Statement, assumptions and sources
Paper context: E8 audit and bootstrap
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SEAM.HORIZON.01
Original ledger classification: Identity [I]
Original claim text
Seam=horizon [I] keystones (pure identities, NO cosmological narrative): (1) the integer 8 in c3=1/(8pi) is OVERDETERMINED and gravitationally aligned: geometry 8=2|mu4| (8pi=|mu4|*2pi seam winding), lattice 8=rank E8=g+n=h(D5)=phi(30)=det R, gravity 8pi=Hawking/Einstein coeff (G_uv=8pi T_uv) => if seam=horizon, c3 is gravitationally forced and the gravitational 8 MUST equal the lattice/geometry 8 (it does). Both pi-coeffs are 2pi*integer: phi_tree=1/(6pi),6=2 N_fam (Gauss-Bonnet); c3=1/(8pi),8=2|mu4|; phi_tree=(|mu4|/N_fam)c3=(4/3)c3. (2) ONE transfer operator for BOTH sectors: boundary transport spec {1,(2/3)^6,(1/3)^6}; lambda2=(2/3)^6 = SM flavor gap eigenvalue (Delta=-log(2/3)^6=6 log 3/2=2.4328, tfpt_2) = horizon Page recovery rate (I_n~lambda2^n, Appendix H). Cusp weights {0,1/3,2/3} at 4 mu4-punctures = boundary data. Supporting: S_BH=A/|mu4|, 128 c3^4=1/(32 pi^4), T_dS coeff 16=|mu4|^2. The cyclic self-reproduction reading is [P] interpretation NOT included here
Original classification detail
Identity [I]
Dependencies as recorded
BND.GLUE.01; v6; v8; v10; tfpt_2 transport spec
Open the original ledger source, row 135Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- E8 audit and bootstrap
- Horizon readouts
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravityinput 4 origin theory
- 2026-06-30 ( v445 — the rigidity FORCING converse: commuting with the order- [formula in source] clock is exactly [formula in source] -block-diagonality, upgrading the rigidity step from ``permit'' to ``force'')Research changelog; TFPT — Introduction and reading guide
- 2026-06-19 (the discrete [formula in source] dynamic lens on F_transfer: one shape, one seam-rate, v303)Research changelog; TFPT — Introduction and reading guide
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- 2026-06-14 (subclaim 2 of ENERGY.02 tackled: raw-seam-DtN RP-definability — v194)Research changelog; TFPT — Introduction and reading guide
- 2026-06-15 (QGEO: the bedrock recast as a falsifiable kill-test)Research changelog; TFPT — Introduction and reading guide
- The Möbius origin of the irreducible [formula in source]input 5 tfpt 3 e8 audit bootstrap
- Research Contract 1 — [formula in source]Research contracts
All 45 linked sections
- Honest status
- The Sheet Diamond and the Winding Line: masses and transport from one surface
- The unique attractor: a gapped transport selects ONE fixed point
- The unique attractor: a gapped transport selects ONE fixed point
- The whole integer skeleton from one pair [formula in source]
- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravity
- 2026-07-15 ( v486 — generator hunt: the FULL transfer spectrum [formula in source] from ONE forced local rule — the unique lazy [formula in source] -pair walk [formula in source] ; the previously generator-less [formula in source] mode gets its origin; v327's uniform rule superseded as full-spectrum generator — no gate closes, no marker moves)
- Certifiability and recommended order
- The whole integer skeleton from one pair [formula in source]
- Appendix: computational verification
- Research Contract 1 — [formula in source]
- Honest status
- The Möbius origin of the irreducible [formula in source]
- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)
- Appendix: computational verification
- Page time and scrambling
- Honest status
- Front matter / support
- Front matter / support
- The Möbius origin of the irreducible [formula in source]
- Front matter / support
- 2026-06-22 (two consequences: the [formula in source] which-net ambiguity resolved by the order-4 clock, and BOTH axioms shown bootstrap-forced so the only irreducibles are the framework [formula in source] [formula in source] : v351, v352)
- The unique attractor: a gapped transport selects ONE fixed point
- Front matter / support
- Honest status
- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravity
- Appendix: computational verification
- Research Contract 1 — [formula in source]
- Appendix: computational verification
- 2026-06-30 ( v446/ v447/ v448 + Lean + Wolfram — deriving clock-invariance from [formula in source] -symmetry, an independent topological reading of the edge [formula in source] , and pinning the one external MMST fact at four-point order)
- The whole integer skeleton from one pair [formula in source]
- The `` [formula in source] '' is triply forced: geometry [formula in source] lattice [formula in source] gravity
- Certifiability and recommended order
- Front matter / support
- The unique attractor: a gapped transport selects ONE fixed point
- The maximal black hole is the anchor: SdS in seam units
- Certifiability and recommended order
Registered verification modules
- v54_seam_horizon_keystones.pyRegistered verification module · horizon
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8 triply forced; one transport λ₂=(2/3)⁶ for flavor & horizon
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