Established in scope
Original hexagonal curve rotation has concrete rho Hodge line
In the question: Automated construction of operator maps and sources
Constructive realizationofalreadyoriginalhexagonalphaseinexistingcurve;reuseoldclock/cover/spin/norm,limiteddedupenotnoveltyproof. NotfreelyinsertedrhoscalarorautomaticOS/Pinreflection. ActualHodge-to-field/readoutcontractionstillneeded;line-valuedtraceisnotscalarbeforeclosing,andpairedduallegsdo notcreate netcharacter. Spin/norm/fullHodgedeterminantcannotbereplacedbyoneeigenline. NophysicalCP/fullsolutionclaim.
Read the exact result, assumptions and evidence
Result
Actualcurveeta²=1-w6hasR=sc²:w→rho w,positiveinverseofoldT=sc,coversz→1/zandexchangesq/p. ReuseoldjointKummermaps. CanonicalspinliftswapsPhi/Chiwithlambda²=rho,order12;pairedpointnormeigenvalues±i. EllipticquotientX=w^-2,Y=eta/w³satisfiesY²=X³-1,andRacts(omega²X,-Y),soR*(dX/Y)=rho dX/Y,pullback-2dw/eta. ThisisactualgeometricrhoHodgelineinthesamesource. Otherlinehasomega,wholeHodgedeterminantminusone. Independentexactrootcheckpassed.
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
- HEXAGONAL-OPEN-SOURCE-PHASE-REVIEW.txt lines 1–160
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/HEXAGONAL-OPEN-SOURCE-PHASE-REVIEW.txt
34e897a08c91ad4110f56baaceac82745640a17b675e5a70a1619a105f5f8b8c
- ROOT-HEXAGONAL-PHASE-CHECK.json lines 1–12
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-HEXAGONAL-PHASE-CHECK.json
8192603638de3e849f26a28e2164829f8e9cbee26f636c5e3b8d376da4408c29
finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line