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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

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