The explicit D₅ and A₃ lattice construction of E₈
Original ledger classification: Lattice
Recorded statement: E8 = (D5 (+) A3) + mu4 glue: explicit lattice certificate (240 roots norm^2=2; even; unimodular Gram det=1; glue index 4=|mu4|); disc=Z4; q(D5)+q(A3)=5/4+3/4=2
Statement, assumptions and sources
Paper context: Architecture, E8 and the electromagnetic fixed point
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E8.GLU.01
Original ledger classification: Lattice
Original claim text
E8 = (D5 (+) A3) + mu4 glue: explicit lattice certificate (240 roots norm^2=2; even; unimodular Gram det=1; glue index 4=|mu4|); disc=Z4; q(D5)+q(A3)=5/4+3/4=2
Original classification detail
Lattice
Dependencies as recorded
D5; A3; Z4
Open the original ledger source, row 5Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
- E8 audit and bootstrap
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- Front matter / supportTFPT — Introduction and reading guide
Navigation through a shared verification script
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- 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
- What this changes, and what stays openE8 audit and bootstrap
- The [formula in source] glue and the [formula in source] discriminant theorem (proved)tfpt 1 architecture e8
- Appendix: computational verificationtfpt 1 architecture e8
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- The [formula in source] glue and the [formula in source] discriminant theorem (proved)Architecture, E8 and the electromagnetic fixed point
- 2026-06-19 (an infinite-derivative narrowing of the Stelle-ghost attack, the double-pushout figure, and the ``constancy of [formula in source] '' framing of SEAM.EQUIV.01: v304)Research changelog; TFPT — Introduction and reading guide
All 47 linked sections
- The [formula in source] glue and the [formula in source] discriminant theorem (proved)
- The [formula in source] glue: how [formula in source] is really built
- Front matter / support
- 2. −1,138 ist eine echte bessere Variationsgrenze
- Appendix: computational verification
- Research Contract — PRED.JOINTLIKELIHOOD.01 (from hit-counting to overdetermined relations)
- Research Contract 1 — [formula in source]
- Appendix: computational verification
- 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)
- Appendix: computational verification
- Group-theoretic audits (optional)
- 2. −1,138 ist eine echte bessere Variationsgrenze
- The Einstein normaliser as a corrected tree value
- Research Contract 2 — [formula in source]
- 2026-07-20 (VIII) (E8 mass-ladder blind-recovery bed EXECUTED: verdict validated at the detector level — the Cartan–PF ladder pipeline blindly recovers the published Zamolodchikov-E8 spectra of BaCo [formula in source] V [formula in source] O [formula in source] (8/8) and CoNb [formula in source] O [formula in source] (6/8 in-window) and rejects every control class; experiments level only — confirms Zamolodchikov E8, not TFPT; no verification module, no gate closes, no marker moves)
- 2026-06-12 (version system, predictions/K5, readability pass B3)
- What this changes, and what stays open
- Appendix: computational verification
- Front matter / support
- Research Contract — PRED.JOINTLIKELIHOOD.01 (from hit-counting to overdetermined relations)
- Front matter / support
- The Einstein normaliser as a corrected tree value
- Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)
- 2026-06-07 / 2026-06-08
- What this changes, and what stays open
- Group-theoretic audits (optional)
- Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)
- 2026-06-17 (The Modular Spectral Closure: Dirac as covariance induction, the modular cutoff, the Kummer/K3 unification, and the assembly certificate, v258– v261)
- The [formula in source] compiler: [formula in source] as a closure, not an input
- The [formula in source] compiler: [formula in source] as a closure, not an input
- The Einstein normaliser as a corrected tree value
- Research Contract 1 — [formula in source]
- Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)
- Appendix: computational verification (reproducibility)
- Research Contract 2 — [formula in source]
- The [formula in source] compiler: [formula in source] as a closure, not an input
- Research Contract — PRED.JOINTLIKELIHOOD.01 (from hit-counting to overdetermined relations)
- Appendix: computational verification
- 2026-07-14 (website + figure refresh — the /verification journey views become live HTML (the stale timeline/residual-chain images replaced by interactive components wired to the in-browser reproducer), the prediction surface's empirical-audit wall of text restructured into dated, expandable rounds, and the generated timeline/residual-chain figures extended to the current suite — presentation only, no content or marker moves)
Registered verification modules
- v1_e8_glue.pyRegistered verification module · core
Read the description recorded in the module registry
E₈ glue: disc ℤ₄, q(D₅)+q(A₃)=2, 240=16·5·3, 248
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.