Skip to main content

A registered result in its source context

Original ledger classification: Exact [E] census (Fraction combinatorics) + honest kill + [C] typed observations (Python-only per GATE.WOLFRAM.02).

Recorded statement: The root incidence census (one module, 6 checks, ~1 s; discovery probe root_incidence_probe.py 6/6, verdict INCIDENCE-CENSUS-DECIDED). The naive 48 x 5 incidence to the 240 E8 roots is KILLED for the compiler-canonical order-12 element…

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.INCIDENCE.01

Original ledger classification: Exact [E] census (Fraction combinatorics) + honest kill + [C] typed observations (Python-only per GATE.WOLFRAM.02).

Original claim text

The root incidence census (one module, 6 checks, ~1 s; discovery probe root_incidence_probe.py 6/6, verdict INCIDENCE-CENSUS-DECIDED). The naive 48 x 5 incidence to the 240 E8 roots is KILLED for the compiler-canonical order-12 element (orbit census 19 x 12 + 3 x 4, not 20 free zeta_12 orbits); positive residue: the mu4 clock alone acts FREELY with EXACTLY 60 orbits (60 = D_start) and the family 3-cycle fixes exactly 12 roots (the lifted marks). [2026-08-02 XLI: the positive residue sharpened two levels -- v633: the 60 free clock orbits ARE the hermitian-unimodular Z[i]-E8 with the ST31 hyperplane system (and the 60 -> 6 quotient-cascade route is killed); v634: G31 = the full unitary stabilizer with sigma = c^4, J = c^9 exact, and the honest sharpening that the compiler clock c is NOT the Springer-regular 12-element (the 19 x 12 + 3 x 4 census reproduced at the group level; the free 20-comb belongs to a different conjugacy class); see E8.ZIQUOTIENT.01 / E8.ST31.01.]

Original classification detail

INCIDENCE-CENSUS-DECIDED: the naive 48 x 5 construction fails at the first hurdle; 48 x 5 = 240 stays an audit fingerprint; 60 = D_start is a free clock-orbit count on the roots.

Dependencies as recorded

EXTREV.LATTICE.01; QGEO.COVERSEAM.01; v623; v624; v626

Open the original ledger source, row 643

Location 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.

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.

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.

Registered verification modules

  • v629_root_incidence.pyRegistered verification module · core
    Read the description recorded in the module registry

    E8.INCIDENCE.01: der Wurzel-Inzidenz-Zensus — **DIE NAIVE 48×5-INZIDENZ AUF DIE 240 E8-WURZELN IST GEKILLT, DER POSITIV-REST IST SCHARF** (der Kill-Test des Reviews, erste Hürde ausgeführt). [E, KILL] Das compiler-kanonische Ordnung-12-Element (μ₄-Clock × Familien-3-Zyklus) wirkt NICHT frei: Orbits 19×12 + 3×4 statt 20 freier ζ₁₂-Orbits. [E, positiv] Die μ₄-Clock allein wirkt FREI mit EXAKT 60 Orbits — 60 = D_start als freier Orbit-Zählwert auf den Wurzeln; der 3-Zyklus fixiert exakt 12 Wurzeln (= gehobene Marks, v623) (6 checks, ~1 s)

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries