A registered result in its source context
Original ledger classification: Honest [E, park] five-route adjudication with the involution-witness census and the must-fail numerology control (exact group computations; Python-only per GATE.WOLFRAM.02).
Recorded statement: The ORBIT60 census -- the 60 mu4-lines of E8 as a combinatorial object: quotient graph, sigma/clock/Coxeter dynamics on the ORBIT SPACE, and a STRICT park test for the cascade 60 -> 6 (one module, 18 checks, ~1 s; discovery probe…
Statement, assumptions and sources
Paper context: input 5 tfpt 3 e8 audit bootstrap
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E8.ORBIT60.01
Original ledger classification: Honest [E, park] five-route adjudication with the involution-witness census and the must-fail numerology control (exact group computations; Python-only per GATE.WOLFRAM.02).
Original claim text
The ORBIT60 census -- the 60 mu4-lines of E8 as a combinatorial object: quotient graph, sigma/clock/Coxeter dynamics on the ORBIT SPACE, and a STRICT park test for the cascade 60 -> 6 (one module, 18 checks, ~1 s; discovery probe orbit60_census_probe.py 18/18, verdict ORBIT60-PARKED). THE FIVE ROUTES, all adjudicated: (i) degree rules DEAD (all quotient graphs regular -- no distinguished pair sequence from incidence degrees); (ii) sigma structure DEAD (sigma-orbit sizes {3,1} on the lines, no 2-blocks); (iii) THE INVOLUTION WITNESS DOES NOT EXIST: the full involution census of the line group LG (order 11520; 375 involutions, 21 conjugacy classes) shows NO element of cycle type 2^27 1^6 (fixed-line census {0: 120, 4: 180, 12: 15, 16: 60}) -- the one-shot group-action carrier of the cascade is absent; (iv) reflection/Coxeter DEAD: W(E8) Coxeter dynamics does not descend (reflection cycle types on the lines all equal, no distinguished element with 27 disjoint 2-blocks); (v) the MUST-FAIL numerology control fires as designed: rule-free lexicographic pair removal reproduces the counting 60 - 2n in exactly 27 steps and > 10^70 equally 'successful' sequences exist -- the counting carries no structural information (v633 Q8.2 reproduced). A5 one-liner (as instructed, no expedition): order-5 elements exist (2304) but <sigma, sample order-5> has order 960 -- no visible natural A5 action attached to the compiler data. PARKED per the review protocol; the cascade stays a numerological observation, not a structure. Deterministic (fixed seed for the generating-set search only).
Original classification detail
ORBIT60-PARKED: all canonical cascade routes dead; no involution of cycle type 2^27 1^6 in the line group (order 11520; 375 involutions, 21 classes); W(E8) Coxeter does not descend; no A5 signature (order-5 elements exist but nothing natural); the must-fail numerology control fires -- parked per the review protocol.
Dependencies as recorded
E8.ST31.01; v629; v633; v634
Open the original ledger source, row 664Location recorded in the ledger
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- E8 audit and bootstrap
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- 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
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- 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
- v700_orbit60_census.pyRegistered verification module · core
Read the description recorded in the module registry
E8.ORBIT60.01: der ORBIT60-Census — die 60 μ4-Linien von E8 als kombinatorisches Objekt: Quotientengraph, σ/Uhr/Coxeter-Dynamik auf dem ORBIT-RAUM und ein STRIKTER Park-Test für die Kaskade 60 → 6 — **alle fünf Routen adjudiziert: (i) Grad-Regeln TOT (alle Quotientengraphen regulär); (ii) σ-Struktur TOT (Orbitgrößen {3,1}, keine 2-Blöcke); (iii) INVOLUTIONS-ZEUGE EXISTIERT NICHT: der volle Involutions-Census der Liniengruppe LG (Ordnung 11520; 375 Involutionen, 21 Klassen) zeigt KEIN Element vom Zykeltyp 2²⁷1⁶ (Fixlinien-Census {0:120, 4:180, 12:15, 16:60}); (iv) W(E8)-Coxeter steigt nicht ab; (v) MUST-FAIL-Numerologie-Kontrolle feuert: regelfreies lexikographisches Paar-Entfernen reproduziert 60−2n in exakt 27 Schritten, > 10⁷⁰ gleich-erfolgreiche Sequenzen — die Zählung trägt keine Struktur**; A5-Einzeiler: Ordnung-5-Elemente existieren (2304), aber keine sichtbare natürliche A5-Aktion (⟨σ, Ordnung-5⟩ hat Ordnung 960); GEPARKT per Review-Protokoll; deterministisch (18 Checks, ~1 s)
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