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Original ledger classification: Exact [E] integer/finite-group census; P1/P2 typed as reconstruction behind the circularity fence, NOT derivation (Python-only per GATE.WOLFRAM.02; companion Lean module kernel-checked).

Recorded statement: The Gaussian ORBIT PACKET lemma (one module, 26 checks, ~1 s; discovery probe orbit_packet_probe.py 26/26, verdict ORBIT-PACKET-EXACT). BURNSIDE EXACT: the sigma orbit census on the 15 nonzero Gaussian classes gives N_orbit = (15 + 3 +…

Statement, assumptions and sources

Paper context: input 5 tfpt 3 e8 audit bootstrap

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E8.ORBITPACKET.01

Original ledger classification: Exact [E] integer/finite-group census; P1/P2 typed as reconstruction behind the circularity fence, NOT derivation (Python-only per GATE.WOLFRAM.02; companion Lean module kernel-checked).

Original claim text

The Gaussian ORBIT PACKET lemma (one module, 26 checks, ~1 s; discovery probe orbit_packet_probe.py 26/26, verdict ORBIT-PACKET-EXACT). BURNSIDE EXACT: the sigma orbit census on the 15 nonzero Gaussian classes gives N_orbit = (15 + 3 + 3)/3 = 7 (3 fixed classes + 4 moved orbits). THE CANONICAL PACKET SPLIT: 240 = 5 x 48 -- one fixed block + 4 moved blocks of 12 Gaussian lines (48 roots) each, pairwise disjoint, label-free canonical (the 15-class partition agrees with the intrinsic equivalence x ~ y <=> (1-J)(x-y)/2 in L; the only residual freedom is the ordering of the 4 moved blocks); packets = 1 fixed + 4 moved = 5 = g_car and 240 = g_car x 48. ANCHOR: the fixed-syndrome leader weights (0,1,1,2) reproduce the (1,1,2) anchor, leader pair e6/e7 = the v638 anchor pair. Q NORMAL FORM: 240 = 16 x 15 and 248 = 240 + 8. CIRCULARITY FENCE: P1 (c3 = 1/(8 pi)) and P2 (g_car = 5) come back as EXACT-INTERNAL-RECONSTRUCTION -- the packet law reconstructs the axioms from the code, it does NOT derive them. SIGMA-CLASS SPECIFICITY: the 160 free order-3 elements of G31 give Burnside 5, not 7 -- the 1 + 4 packet law is sigma-class-specific, not generic. Companion Lean module TfptCarrier/OrbitPacket.lean (34 theorems, kernel decide/norm_num only, no sorry, no native_decide). No marker move.

Original classification detail

ORBIT-PACKET-EXACT: Burnside 7, the canonical 5 x 48 packet split (1 fixed + 4 moved = g_car), the (1,1,2) anchor from the leader weights, the q = 16 normal form; P1/P2 come back as exact internal reconstruction (circularity fence: reconstruction, not derivation); sigma-class-specific (free order-3 census gives Burnside 5); Lean companion OrbitPacket.lean.

Dependencies as recorded

E8.GAUSSCODE.01; E8.GAUSSIAN.CODE.01; v638; v623

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Registered verification modules

  • v736_orbit_packet.pyRegistered verification module · core
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    E8.ORBITPACKET.01: das Gaußsche ORBIT-PACKET-Lemma — **ORBIT-PACKET-EXACT: Burnside 7 = (15+3+3)/3; die kanonische 5×48-Partition (Fixblock + 4 bewegte Blöcke à 12 Gaussian Lines, label-frei kanonisch — Packete = 1+4 = 5 = g_car, 240 = g_car×48); Anchor (1,1,2) aus den Fixsyndrom-Leader-Gewichten (0,1,1,2), Leader-Paar e₆/e₇ = v638-Anchor-Paar; q-Normalform 240 = 16·15, 248 = 240+8**; Zirkularitäts-Fence: P1/P2 kommen als EXACT-INTERNAL-RECONSTRUCTION zurück (Rekonstruktion, KEINE Ableitung); σ-Klassen-Spezifität: die 160 freien Ordnung-3-Elemente von G31 geben Burnside 5, nicht 7; Lean-Begleitmodul OrbitPacket.lean (34 Theoreme, kernel-checked) (26 Checks, ~1 s)

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