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Under the retained PR6714 group, quotient-table, width-nine decomposition and Gram-normalization premises, identify two actual width-ten even-sector irreducible blocks of the Gaussian-dyadic three-qubit Clifford group:
These are two specified block contributions. Global spectral endpoints, an exact condition number, total multiplicities if other blocks share an eigenvalue, and a threshold improvement remain unclaimed.
The self-contained written argument uses Bell matrices and distinct Pauli weight lines to prove irreducibility. The explicit all-element phase-cancelling intertwiner is Vbar⊗µ ≅ V⊗Perm(Qorbit). An elementary transvection argument proves two-transitivity. Transvection trace15 distinguishes source row7 from the other degree35 row8 (trace−5); row6 is the unique degree27 constituent. Correct tensor reciprocity gives269+1975 and269+1890. Classical Bell/Pauli/permutation/character methods are credited, not claimed as new general representation theory.
The actual source group is over D=Z[i,1/2] with scalar kernel µ4. S, Rx=((1+i)I+(1-i)X)/2, CNOT, Paulis and central iI are legal. An unaccepted ordinary-H/omega convention considered during orientation was rejected by source reading before new mathematical execution. No µ8 group is substituted.
Validation: first new diagnostic passed in0.3259265s at23.84375MiB on CPython3.12.14, all14 then-present hashes unchanged. Nineteen literal Gaussian generators yield1216 signed Pauli conjugations,1216 Bell congruences and1216 complete8x8 intertwiner checks;4096 Bell inner products/weight lines;77824 distinct quadratic transport cases plus matching linearity/pairing comparisons;38 square-character checks. Pair BFS reaches1260+756 distinct pairs (38304 directed generator edges), not the full group. Four mathematical witness controls, one separate legal basis-gauge serialization guard and three parser controls pass. Five exact inert source objects75775B authenticate first. The Pauli/form catalogue and elementary quantities are credited source objects, not new discoveries. No predecessor engine, old6822 order-three/LP replay, full table rebuild, native/Lean/Docker or selected cold replay.
First/direct normal/direct optimized complete packets are identical:21547bytes, SHA256 dfa9b37816dc1f9d8fe7393aa246374e4b751b26dddd6e309d9fad48b537feb1. Scientific code and proof are unchanged since first PASS. Registered replay and committed source-history/mode preflight pass. Read-only Git-free empty-PATH official-export normal/O replays reproduce the complete packet. All12 isolated source/typed-False-to-0 corruption checks reject for intended reasons. Original hosted run42329922324 passed on attempt1: 711 total helper tests including24skips, plus two focused scientific commands on CPython3.12.16. Both entire21,547-byte hosted packets match frozen local and export bytes. The synthetic test checkout has the exact tested tree and canonical/public parents; no repository merge or CI rerun. Related source-aware AI challenges are not blind independent, human or proof-kernel acceptance.
Only research/clifford-quadratic-orbit-blocks is added; no dependency/shared-code/frontier change. Task formal-interface-lemma is explicitly CHANGED/partial to this bounded source-bound algebraic audit. Main7c49fe32 and773-body/12-query/live-Hub overlap refreshed; no exact counterpart found within that coverage, with unindexed/classical equivalences unknown. Sources:6794 c6252da and6714 f7f32a1. Own6718/6822 and prior results are excluded.
Credit Nick Petalas6794 for807/actual-stabilizer request;alephnan6714 for group/m9/Pauli-orbits/reciprocity/Gram framework; Chin-Yen Lee, Wei-Hsuan Yu, Yung-Ning Peng and Ching-Jui Lai for the published table; Ali Romman/MatShep and retained Clifford/stabilizer lineage. LICENSE/NOTICE and exact source provenance retained. Substantial source-aware OpenAI Codex proposal/proof/implementation/overlap/metadata assistance disclosed.
Open next question: an uncovered remaining stabilizer representation must be bound before claiming actual global endpoints. Native caller/preparation/routing/chronology/precision/recovery/ownership/restoration/stock and the complete physical recursive invoice remain unknown. All five selected assumptions remain; no supplier admission, κ/frontier change, merge or follow-on reservation.
Canonical claim: #6794 (comment)
Hub: #1166 (comment)
Reproduce with the two README commands. Public head2f56258396838acb84b352a8ab578bf7babc83b5. Maintainer edits and auto-merge disabled.