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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 root and sign lines have minimal common degree48 cover

In the question: Common clock sectors, quartic geometry and operational reconstruction

Minimal common holomorphic carrier of expressly given root coordinates and flat coefficient lines. No new physical worldsheet,CAR state or full compiler field map. Geometric clock here inverts deck generator;it is not separate commuting compiler order12 clock.

Read the exact result, assumptions and evidence

Result

For D:H¹²=f(z),w=H⁴,g=H³ and actual unramified V4 cover Yq/C,function fields are linearly disjoint over C. D/C is totally C4 ramified at four points and has no nontrivial unramified intermediate. X=Norm(D times_C Yq) has degree16 over C,degree48 over z,group C12 times_C3 A4 isomorphic A4 times C4,genus41. Minimality holds among all connected common covers:g and w determine H=w/g;trivializing three lines forces Yq. Common C3 quotient is identified once. Accepted quarter lifts combine diagonally with order4.

Required assumptions

  • Existing C2 group with untwisted raw flat spin pullbacks

    On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.

  • Ramified holomorphic half-form trace of the given C2 spin line

    Retain actual E:y²=x⁴−1, its already supplied Q fixed nontrivial NS NS spin-line class alpha and normalized Szego kernel. Holomorphic trace includes sqrt(dz/dx), while ordinary flat coefficient p_*alpha remains separate. No extra Q linearization phase, positive equal-time CAR covariance or smooth circle domain is assumed.

  • Original P2 order-three cusp class and stable bundle anchor

    Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.

  • 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.

  • 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.

  • 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

  • COMMON-COVER-COMPOSITUM.txt lines 1–180

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/COMMON-COVER-COMPOSITUM.txt

    c92e9aff9717118a4b78fc4cf582dedf75921aad114a4147d08557445735ac04

  • COMMON-COVER-COMPOSITUM.txt lines 181–292

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/COMMON-COVER-COMPOSITUM.txt

    c92e9aff9717118a4b78fc4cf582dedf75921aad114a4147d08557445735ac04

  • COMMON-COVER-INDEPENDENT-REVIEW.txt lines 1–180

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/COMMON-COVER-INDEPENDENT-REVIEW.txt

    2c9c79ddc4e4a8c97ab39b07d2562c0f13362a7a90b6e673c0693997711b11cd

  • COMMON-COVER-INDEPENDENT-REVIEW.txt lines 181–209

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/COMMON-COVER-INDEPENDENT-REVIEW.txt

    2c9c79ddc4e4a8c97ab39b07d2562c0f13362a7a90b6e673c0693997711b11cd

  • check_common_cover_compositum.py lines 1–164

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/check_common_cover_compositum.py

    7b8d14d0db28ab2cce0819ff306007aa4ba17d3673a88cbc0e5e6118343b3fb2

  • common-cover-compositum-results.json lines 1–25

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/common-cover-compositum-results.json

    83862510fea40be29d64d9f8beb5bdc8b03472b25f00b3dc208828394bd359c0

finding:original-root-and-sign-lines-have-minimal-degree48-common-cover