Skip to main content

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

Actual fermionic kernel-volume line carries precisely the inverse q-norm action

In the question: Automated construction of operator maps and sources

Independently twice-checked actual line-representation bridge onall generators,not beta-phase match alone. EarlierεKummer-to-flat-fiber transfer andcommonU comparison corrected;cover identities retained. Character equality gives equivariant isomorphism upscalar,not functorially canonical total residue map orphysical norm. Individual legs arelinear,butclaimed individualQ/deck equivariance doesnotfollow. NoJac[2] tensor-translation/N64 equivalence;these changeh0 and differfromdeckV4. No originalP1/APS source map,selectionH0ratherthanH1,single insertion orBerezin dual choice. Whole detRΓ also containsH1 and loses uniform scalarweight sinceχ0. OldNq/theta/native module proof reused;newactual kernel-volume supplies matching linear factor,itsphysical use remains specific origintest.

Read the exact result, assumptions and evidence

Result

For actualold coefficient lift calibrated atq0,Q_kernel²=−iI3,δ=(1,−1,1),ξ=e^(−iπ/4). Q actsbyξ³ onΔ=det⊕aH0(Ta),by−ξ³ onunordered tensorZ. Independent norm test:αq0=iξ,product of exchangedq1/q2 spinmaps=βq1=+i,soQ_Nq=−ξ,Q_Nq^-1=ξ³,Q_Bq^-1=−ξ³. Orderthreec cycle acts1 onall compared lines;three nontrivial actualdeckV4 characters multiply1;spincenter−I acts−1. HenceΔ≅Nq(S0)^−1 andZ≅Bq(S0)^−1 as full line representations of group generated by these c/Q/deckV4/spincenter lifts,upnonzero scalar. Fermionic permutation sign distinguishes matching determinant line fromunordered tensor.

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

  • SOURCE-ZERO-MODE-ACTUAL-LIFT-NORM.txt lines 1–127

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SOURCE-ZERO-MODE-ACTUAL-LIFT-NORM.txt

    673abb0a6fa24cc1d989d0ae68d816acf811bbfa1ec3f8fa978e77991afde143

  • SOURCE-ZERO-MODE-NORM-INDEPENDENT.txt lines 1–126

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SOURCE-ZERO-MODE-NORM-INDEPENDENT.txt

    9c790ed53c3945d825043147fcfb31cca29753cf8212653775dd9aaaa634a39e

  • MARKED-Q-DIVISOR-CENTRAL-TWIST.txt lines 1–180

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/MARKED-Q-DIVISOR-CENTRAL-TWIST.txt

    da1f75831a46a0c0662f931486b77e6e2085126df452b009d1a90351d413d904

  • SOURCE-SELECTED-THETA-SPIN.txt lines 1–174

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SOURCE-SELECTED-THETA-SPIN.txt

    cf4478191ccd75d62a2f049a54193541009bed24877df9cbe0ed9f942d07d717

  • CLOCK-Q-PACKET-COMPATIBILITY.txt lines 1–180

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/CLOCK-Q-PACKET-COMPATIBILITY.txt

    fe37f20bbb2d959dfe678ca1bf435a69067cfcb859a3d36769294bbe9bf61c32

  • REUSE-SAME-SPIN-SEAM-AND-NEXT-OPERATOR.txt lines 1–51

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/REUSE-SAME-SPIN-SEAM-AND-NEXT-OPERATOR.txt

    e2969ebf7c654ca3498dad5143084c6c11a18d2fcd9116effbb0676d0fe10cb9

  • SAME-SPIN-REFERENCE-SIMPLIFICATION.txt lines 1–191

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/boundary_origin_20261027/uniqueness/SAME-SPIN-REFERENCE-SIMPLIFICATION.txt

    8a0586c93b371905105d33f04c1deb796c9f603c0fed09c8cc90dbb33bd64481

  • AKTUELLER-STAND.md lines 1–48

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/boundary_origin_20261027/AKTUELLER-STAND.md

    374dd640a04cfcfd4eb8edfa57a52d3e8afd89eb4c4388945550856334428db5

finding:actual-spin-kernel-determinant-has-inverse-q-norm-character