Established in scope
Original mixed spin products realize the positive U6 cycle
In the question: Automated construction of operator maps and sources
Constructive geometric origin of the supplied six-cycle matrix, without selecting a physical character, CP reader, field source, state or time. Keep twist lines and the harmless common orbit phase. The original physical charge assignment of triality and sheet characters still needs its actual operator map. Originals already declare rho/rho^4 as CP readouts. v233 inserts exponents 1/4 rather than evaluating the actual map J from U6^3,U6^4 to color-Casimir sector parity and family center. Geometric q/p names and the old carrier seam tau do not identify quark/lepton sectors. Clarification 30 October: the phase-free orbit basis absorbs partner phases. Raw s pullback is minus transpose, so raw antisymmetry is on the positive U6-cube sheet. Independent full q/p signs plus R have no rank-three projector; see the new complete deck test.
Read the exact result, assumptions and evidence
Result
Actual odd spin lines have nonzero global multiplication isomorphisms into the one-dimensional mixed twisted-canonical sectors. Six off-diagonal sectors form a single orbit under actual R=sc²; spin signs cancel after six steps. On the existing sixteenfold Kummer cover, intrinsic Hodge positivity and deck-character orthogonality make the orbit realization unitarily equal to the oriented v231 U6. Its rho projector has rank one although the full trace vanishes. Existing triality/sheet factors U6^4,U6^3 select rho and rho^4 joint character lines.
Required assumptions
- Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
- Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Original evidence
- MIXED-SPIN-PRODUCT-U6-SOURCE-REVIEW.txt lines 1–173
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/MIXED-SPIN-PRODUCT-U6-SOURCE-REVIEW.txt
319d9b965c909058c237b523236c2d9f4521989b8154fffbd527987d1b3ba1c8
- CLAUDE31-HEXAGONAL-RELATIONS-REVIEW.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE31-HEXAGONAL-RELATIONS-REVIEW.txt
0e1871e77a3724219d0b2ee4fae10bf9560dd15e8aaa936d09b19c6204f7c6e9
- v231_cp_mu6_phases.py lines 65–75
Source checked at this snapshot
Original location and fingerprint
verification/v231_cp_mu6_phases.py
9e3567f184de3b5ec14f21df3c969d89bf3953d69edc288c29a3b564ccad3b26
- v233_cp_triality_phase.py lines 43–88
Source checked at this snapshot
Original location and fingerprint
verification/v233_cp_triality_phase.py
43b34998aa882f2207fc1ebaa74b67cf157a5c8de977a62afa363d8f0284b94c
- ROOT-MIXED-SPIN-U6-CHECK.json lines 1–36
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-MIXED-SPIN-U6-CHECK.json
156118586394327730bf248cd6dbece42e7af4eec8ff0b1fa82a4f45d2510f36
- ORIGINAL-U6-TRIALITY-SECTOR-SELECTION-REVIEW.txt lines 1–153
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-U6-TRIALITY-SECTOR-SELECTION-REVIEW.txt
958c55a73b64fc2a35eec07d5242a497a18cefcf28d08acedb5f955b6ef7df4a
- MARKED-FIBER-K3-TRANSPORT-ADDENDUM.txt lines 1–196
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/MARKED-FIBER-K3-TRANSPORT-ADDENDUM.txt
7b2fb212bb98bb11d71361b13057cb459aa4f60f13a96f79eb35c191b4b17ef0
finding:original-mixed-spin-products-realize-positive-u6-cycle