The positive solution of the alpha equation
Original ledger classification: Numerical
Recorded statement: alpha^-1 = 137.035 999 216 8 unique root of F_U1=0 (existence + uniqueness + interval-arithmetic + ablation)
Statement, assumptions and sources
Paper context: TFPT — Introduction and reading guide
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EM.FP.01
Original ledger classification: Numerical
Original claim text
alpha^-1 = 137.0359992168 unique root of F_U1=0 (existence + uniqueness + interval-arithmetic + ablation)
Original classification detail
Numerical
Dependencies as recorded
AX.P1.01; EM.BUDGET.01
Open the original ledger source, row 11Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
Sections that explicitly cite this claim
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- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Is the entire Standard Model thereby derived?Standard Model and flavor structure
- Front matter / supportTFPT — Introduction and reading guide
- Is the entire Standard Model thereby derived?tfpt 2 standard model
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.
- 2. −1,138 ist eine echte bessere VariationsgrenzeTFPT Universalraum Spinlift Hauptdokument 2026-09-15 v1.6.10
- What This Note Is Aboutnote carrier rigidity lean4
- A. Ein tatsächlich neuer Rechenwert trägt eine stärkere SchrankeTFPT Universalraum Spinlift Hauptdokument 2026-09-15 v1.6.10
- Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)tfpt research contracts
- B. Die einfache Darstellung vermischt zwei NäherungszuständeTFPT Universalraum Quellkomposition Konsolidierung 2026-09-15 v1.6.9
- B. Die einfache Darstellung vermischt zwei NäherungszuständeTFPT Universalraum Spinlift Hauptdokument 2026-09-15 v1.6.10
- Zusätzliche Primärliteraturmain
- Originale Herleitungs- und AusschlussorteTFPT Gesamtsynthese 2026-09-28
All 62 linked sections
- -1.2cm TFPT — Origin Theory\\[2mm] The seam as a horizon, the cyclic compiler hull,\\ and the self-reproducing parameter-free fixed point\\[2mm] An \ structural core ( [formula in source] – [formula in source] ) with one honestly-typed \ interpretation
- Appendix: computational verification
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)
- Zusätzliche Primärliteratur
- B. Die einfache Darstellung vermischt zwei Näherungszustände
- 2026-06-23 (External-review closure: the two genuine residual targets named — v381 the all-order Epstein–Glaser/BRST contract for [formula in source] , and v382 the Quillen determinant-line variation as a tracked target)
- 2026-06-25 (No-Ambient-Dependency: no frozen readout is computed from QG.AMB.01: v423)
- -1.2cm TFPT — Origin Theory\\[2mm] The seam as a horizon, the cyclic compiler hull,\\ and the self-reproducing parameter-free fixed point\\[2mm] An \ structural core ( [formula in source] – [formula in source] ) with one honestly-typed \ interpretation
- One [formula in source] for electromagnetism, the cosmic horizon and [formula in source]
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)
- Neutrinos: Die vorhandenen Herleitungen gemeinsam lösen
- A. Ein tatsächlich neuer Rechenwert trägt eine stärkere Schranke
- Neutrinos
- Appendix: computational verification
- 2. −1,138 ist eine echte bessere Variationsgrenze
- 3. Der Text vermischt drei verschiedene Näherungszustände
- A. Ein tatsächlich neuer Rechenwert trägt eine stärkere Schranke
- Zusätzliche Primärliteratur
- Neutrinos
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)
- 2026-07-21 (XIX) ( e8-ladder-bed v2 — the 2DCS extension executed with an honest preregistered kill_2d verdict at the DETECTOR level: the known-answer map recovers [formula in source] rungs incl.\ [formula in source] via F3 difference coordinates (MC [formula in source] ), but the 2D control battery breaks (scramble [formula in source] , jitter [formula in source] at the destructive [formula in source] level) — the v1 1D results (BCVO [formula in source] , CoNb [formula in source] O [formula in source] [formula in source] ) are untouched; scorecard row updated, status/stage unchanged; experiments level only — no verification module, no gate closes, no marker moves)
- -1.2cm TFPT — Origin Theory\\[2mm] The seam as a horizon, the cyclic compiler hull,\\ and the self-reproducing parameter-free fixed point\\[2mm] An \ structural core ( [formula in source] – [formula in source] ) with one honestly-typed \ interpretation
- =150 2026-08-20 (CXI) (the externalization contracts — the two open non-RH kind-(A) external-math targets SEAM.EQUIV.01 and ALPHA.QUILLEN.EXACT.01 packaged as short, self-contained EXTERNALIZATION CONTRACTS for outside specialist mathematicians (conformal nets/VOA/AQFT for the seam; determinant lines/ [formula in source] -invariants/index theory for alpha), added as two new sections at the end of tfpt_research_contracts (before ``Certifiability and recommended order''), plus a one-sentence pointer in the head keybox; DOCUMENTATION ONLY — no module touched, no number changed, no status marker moved, no gate closed or narrowed, NO RH claim: (1) the SEAM.EQUIV.01 contract states the minimal theorem (the scaling limit of the gapped [formula in source] -equivariant CAR collar exists in local-net topology; the index-4 simple-current extension functor commutes with the limit; the OS reconstruction is the holomorphic [formula in source] lattice net) broken into the four review-named lemmata L1 (uniform energy/nuclearity bounds — honestly typed: NO uniform nuclearity estimate exists in the corpus), L2 (convergence of local algebras, the cited Osborne–Stottmeister scaling-limit theorem with the [formula in source] -equivariant structure retained), L3 (crossed product commutes with the limit; the finite index-4 Q-system is explicit, v125/ v154/ v469) and L4 (uniqueness of the holomorphic [formula in source] reconstruction; [formula in source] vs the same- [formula in source] rival [formula in source] ), with the complete typed hypothesis list (12 PROVEN-FINITE rows citing v302/ v113/ v155/ v160/ v356/ v366/ v367/ v368/ v461/ v376/ v377/ v378/ v379/ v125/ v154/ v216/ v286, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean axiom surface ( SeamScalingLimit.lean kernel-proves only the arithmetic hypotheses by decide; the analytic content is named cited axioms over opaque Props; no sorry; explicitly flagged: L1–L4 have ZERO Lean content beyond the composition audit), five must-fail controls (MF-S1: [formula in source] alone must NOT suffice — the red-team point; MF-S2: index-2 glue must yield [formula in source] ; MF-S3: the trivial [formula in source] collar must give no chiral limit; MF-S4: non-order-4 clock breaks the marks; MF-S5: the v286 import firewall) and four acceptance tests; (2) the ALPHA.QUILLEN.EXACT.01 contract states the two-step theorem T1 (gap-stable continuum limit [formula in source] under norm-resolvent convergence with the Fermi gap uniformly open over the twist torus — the Dai–Freed section has no zero; finite side computed, v472) and T2 ( [formula in source] [formula in source] Bismut–Freed curvature [formula in source] inflow response with the exact corpus coefficients [formula in source] , [formula in source] , [formula in source] , [formula in source] , exponent [formula in source] ), the two named open faces (the analytic diagonal- [formula in source] /multiplicity face v484/ v485 and the topological EM1 lemma v48/ v435), the typed hypothesis list (10 PROVEN-FINITE rows citing v3/ v48/ v341/ v382/ v434/ v470/ v435/ v342/ v367/ v472/ v484/ v485/ v391/ v433, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean statement (there is NO Lean formalisation of this target — stated plainly), four must-fail controls (MF-A1: no experimental [formula in source] anywhere in the construction; MF-A2: deck/carrier/Chern-level ablations must destroy the CODATA match; MF-A3: [formula in source] , [formula in source] ; MF-A4: the [formula in source] [formula in source] -power/metric-independence partition) and the review's three acceptance tests verbatim (no experimental [formula in source] input; unique physical fixed point [formula in source] ; ablations destroy the hit) plus one structural test; (3) the website paper mirror of tfpt_research_contracts ( papers.ts) gains one section entry covering both contracts; tfpt_research_contracts.pdf and changelog.pdf recompiled and mirrored via bash build.sh website; maps and changelog.ts regenerated via bash build.sh gen; bash build.sh audit [formula in source] AUDIT OK; manifests regenerated LAST. Both targets stay [O]; NO RH claim anywhere)
- Nachweise der erneuten Prüfung
- Outcome
- Appendix: computational verification
- Group-theoretic audits (optional)
- 2. −1,138 ist eine echte bessere Variationsgrenze
- 3. Der Text vermischt drei verschiedene Näherungszustände
- 3. Der Text vermischt drei verschiedene Näherungszustände
- Research Contract 2 — [formula in source]
- v3 — correcting overclaims
- =150 2026-08-29 (CXLII) (review wave 4 — four exploration probes graduate as v998– v1001 plus the lattice-fundamental quasilocal-family amendment, the [formula in source] closed-metrology retype, the ALPHA.QUILLEN relative-determinant note, and the master contract TFPT.TOE.COMPLETE.01; suite [formula in source] , ledger [formula in source] : two new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v997). (1) v998_ seam_ modular_ closure.py ( [formula in source] ): two-edge HS remainder bounded by [formula in source] on the frozen plateau [formula in source] ; lattice character [formula in source] EXACT four orders [formula in source] ; [formula in source] as Eisenstein series, [formula in source] -expansion match to [formula in source] orders exact (Jacobi identity; the reviewer's C7 sharpening); [formula in source] numeric transform at [formula in source] digits with [formula in source] -weight bookkeeping. Ledger notes on SEAM.EQUIV.MMST.01 and SEAM.SIMPLECURRENT.GENERATOR.01: C7 arithmetic shadow now exact; net-level C7 stays cited/open. (2) v999_ weak_ collision_ hp.py ( [formula in source] ): the continuous-time dilation leg — generator extraction Richardson [formula in source] ; [formula in source] symbolic; [formula in source] exact; GNS splitting defect [formula in source] ; locality [formula in source] ; strong-collision singularity contrast rank [formula in source] . DYN.UNITARY.DILATION.01: the finite ladder is now COMPLETE (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time); open [formula in source] the thermodynamic field limit only; contract stays . (3) v1000_ spin2_ sk_ witnesses.py ( [formula in source] ): lattice graviton — positivity exact, [formula in source] TT helicities at all [formula in source] momenta ( [formula in source] ), [formula in source] exact; SK — KMS/FDT [formula in source] , [formula in source] -dependence contrast [formula in source] vs static [formula in source] , saddle [formula in source] -fold degenerate with [formula in source] unique in the [formula in source] lift . GRAV.SPIN2.EMERGENCE.01 quadratic Hamiltonian half executed; FTRANSFER.SK.RHO0.01 mechanism executed; both contracts stay . (4) v1001_ nu_ pentagon_ chain.py ( [formula in source] ): [formula in source] inventory theorem; misalignment [formula in source] ; pentagon double hit [formula in source] frozen, all three measured angles [formula in source] (honest max pull [formula in source] ) at [formula in source] , unique LEE survivor [formula in source] ; v3 chain SHA-16 a4c28732fa687620 with [formula in source] eV, [formula in source] meV, [formula in source] meV, [formula in source] ; v270– [formula in source] tension [formula in source] TYPED; census null [formula in source] . NEW ledger row FLAV.NUSCALE.06 Candidate \ (pentagon-class misalignment; mechanism [formula in source] the [formula in source] -to-flavor operator ; kills DESI/DUNE [formula in source] vs [formula in source] /JUNO). NO seesaw closure; FLAV.NUSCALE.05 unmoved. (5) Amendments (typed; no marker moves). QFT4D.LATTICE.FUNDAMENTAL.01: a single finite box is not a world — the fundamental object is the quasilocal consistent family [formula in source] with [formula in source] ; continuum ( [formula in source] ) optional, thermodynamic limit and controlled IR universality mandatory (dated 2026-08-29). ANCHOR.VGEO.01/ .02: display retyped from open-physics/primitive phrasing to CLOSED METROLOGY STRUCTURE ( [formula in source] unit torsor; one dimensionful calibration necessary by dimensional analysis — No-Unit v153/ v725); display stays , no physical . ALPHA.QUILLEN.EXACT.01: the correct object is the relative determinant [formula in source] ; BFK [formula in source] is [formula in source] -independent at fixed cut number so [formula in source] — no physical compensation (consistent with COMPENSATION_INTERNAL). NEW master contract TFPT.TOE.COMPLETE.01 : eight gates T1–T8 with the binding separation [formula in source] vs [formula in source] AND independent holdouts; every existing [formula in source] D/dilation/detline/SK/flavor/gravity contract is a child of one gate. Surfaces: tfpt_research_contracts (executed-update paragraphs at MMST/SIMPLECURRENT, DILATION, GRAV.SPIN2, SK.RHO0; new sections TOE.COMPLETE and NUSCALE.06; lattice-fundamental amendment; ALPHA relative-det note); tfpt_4_frontier [formula in source] introduction status card / [formula in source] row; tfpt_2 (NUSCALE.06 candidate paragraph).
- Front matter / support
- Zusätzliche Primärliteratur
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- One [formula in source] for electromagnetism, the cosmic horizon and [formula in source]
- Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)
- Front matter / support
- v7 — Signature lock, predicate rename, interface discipline
- One [formula in source] for electromagnetism, the cosmic horizon and [formula in source]
- One [formula in source] for electromagnetism, the cosmic horizon and [formula in source]
- Appendix: computational verification
- Zusätzliche Primärliteratur
- Group-theoretic audits (optional)
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- 2026-06-21 (adversarial-review follow-ups: a structural anti-numerology firewall, an out-of-sample seed cross-validation, an operational data watchdog, and the Target-A holomorphy kill test: v305– v307)
- Research Contract 2 — [formula in source]
- 2026-06-22 (the heat-kernel origin of the [formula in source] terms: the Calder\'on quadratic is the Gilkey gauge-curvature coefficient; the cubic Maxwell moment stays the EM.WARD.01 residual: v342)
- Appendix: computational verification
- Full quantum gravity — induced from the boundary kernel
- Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)
- Zusätzliche Primärliteratur
Registered verification modules
- v3_em_alpha.pyRegistered verification module · em
Read the description recorded in the module registry
α⁻¹ = 137.0359992168 unique root of F_U(1)=0; ablation
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.