A registered result in its source context
Original ledger classification: Exact [E] quotient/lattice identities + [E, KILL] typed cascade negative (Python-only per GATE.WOLFRAM.02).
Recorded statement: The mu4-quotient round (one module, 17 checks, ~3 s; discovery probe orbit60_quotient_probe.py 17/17, verdicts ZI-E8-QUOTIENT-CONFIRMED + CASCADE-KILLED). The quotient of the 240 E8 roots by the free mu4 clock IS the hermitian-unimodular…
Statement, assumptions and sources
Paper context: input 5 tfpt 3 e8 audit bootstrap
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
E8.ZIQUOTIENT.01
Original ledger classification: Exact [E] quotient/lattice identities + [E, KILL] typed cascade negative (Python-only per GATE.WOLFRAM.02).
Original claim text
The mu4-quotient round (one module, 17 checks, ~3 s; discovery probe orbit60_quotient_probe.py 17/17, verdicts ZI-E8-QUOTIENT-CONFIRMED + CASCADE-KILLED). The quotient of the 240 E8 roots by the free mu4 clock IS the hermitian-unimodular Z[i]-E8 with the 60-hyperplane system of ST31: H(x,y) = <x,y> + i<x,Jy> has H(v,v) = 2 on all 60 line reps; the Z[i]-span of the reps is the FULL E8 lattice (HNF covolume 256 in doubled coordinates) and a hermitian-UNIMODULAR Z[i]-basis exists among the reps (det Gram = 1); sigma acts on the 60 lines with census 19 x 3 + 3 fixed, the 3 fixed lines being exactly the J-orbits of the 12 sigma-fixed roots (v629 R4 closure); all 60 order-2 unitary reflections preserve the root set (order-4: none), and the line-permutation group has order 11520 = 46080/4 (the ST31 fingerprint: |G31| = 8*12*20*24 = 46080, hyperplanes 60 = 7+11+19+23; ST32 killed by its 40-hyperplane count). THE CASCADE HARD TEST: the 60 -> 6 route on the quotient is KILLED -- the hermitian Gram has rank 4 (no rank reduction), both |H|^2 graphs are REGULAR (any degree rule ill-defined), pair elimination has no canonical maximum (tie counts 14..360), no spectral run on the cascade grid.
Original classification detail
ZI-E8-QUOTIENT-CONFIRMED + CASCADE-KILLED: the 'complex E8' reading of the 60 free clock orbits is exact (hermitian-unimodular Z[i]-E8, ST31 hyperplane system); the quotient-cascade route 60 -> 6 carries no canonical structure -- a typed negative; no marker moves.
Dependencies as recorded
E8.INCIDENCE.01; EXTREV.LATTICE.01; v626; v629
Open the original ledger source, row 645Location 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
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 / supportE8 audit and bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
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.
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-10-18: Project separation and retained physics historyResearch changelog; TFPT — Introduction and reading guide
Registered verification modules
- v633_orbit60_quotient.pyRegistered verification module · core
Read the description recorded in the module registry
E8.ZIQUOTIENT.01: die μ₄-Quotienten-Runde — **DER QUOTIENT DER 240 E8-WURZELN NACH DER FREIEN μ₄-CLOCK IST DAS HERMITESCH-UNIMODULARE ℤ[i]-E8 MIT DEM 60-HYPEREBENEN-SYSTEM VON ST31; DIE 60→6-KASKADEN-ROUTE AUF DEM QUOTIENTEN IST GEKILLT**. [E] H(v,v) = 2 auf allen 60 Repräsentanten; ℤ[i]-Spann = volles E8 (Covolumen 256), hermitesch-unimodulare Basis unter den Reps (det Gram = 1); σ auf den 60 Linien: 19×3 + 3 fix (= die J-Orbits der 12 σ-fixen Wurzeln); alle 60 Ordnung-2-Reflexionen erhalten die Wurzeln, Linien-Gruppe der Ordnung 11520 = 46080/4 (ST31-Fingerprint; ST32 durch 40 Hyperebenen gekillt). [E, KILL] Kaskaden-Harttest: Gram-Rang 4, beide Quotienten-Graphen regulär, keine kanonische Paar-Regel — getyptes Negativ (17 checks, ~3 s)
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.