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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

Existing elliptic half period has a canonical graded GNS intertwiner

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

Exact connection inside the already given free elliptic source and its faithful normal HS carrier. Its numerical cross kernel was not unknown;the previous cross gap still means its actual physical P1 operator/sewing identification. Geometric OSTheta is not presented as TomitaJ,nor the chiral scalar as a full Dirac vector. Domains/subtractions and previous state/time exclusions remain unchanged.

Read the exact result, assumptions and evidence

Result

The already given actual NS Green kernel gives S(W)=−S(−W)=(2cosh(WB))^-1=X_A,also as both reflected charge Grams at t=u=W/2. In the existing thermal HS GNS,aR=L_a and aL=−Gamma R_a with aL*=Gamma R_a* give full double CAR and crossMij=Tr(sqrt(rho)ai*sqrt(rho)aj). For the same free rho,M=X_A,hence complete covarianceP_A. The previous projection theorem gives all words;the cyclic isometry to the given graph-state GNS is ontoHS. No new physical state or particle carrier is introduced. Bare Euclidean evaluations a(W),a(0) are not independent CAR families:their cross anticommutator is exp(−Wlambda),not0. Using onlyL_Pi instead of canonical HS parity produces false spectator factors,detected already with2modes.

Required assumptions

  • Normal even sea CAR source with canonical graded HS doubling

    For the algebraic source test use the already given sea Fock/CAR carrier,with faithful even normalized traceclass density rho and its standard HS space,Omega=sqrt(rho),L_A X=AX,R_A X=XA,Gamma X=Pi X Pi. Gamma is the canonical GNS implementer of source parity fixing Omega. Partner fields are represented in the fixed mode-index chart by b_j=−Gamma R_aj;this assumes no physical second P1 boundary. The finite saturation theorem covers arbitrary faithful even finite densities;the separate all-mode route requires the actual normal HS carrier,a complete covariance eigenbasis and saturation in every mode. For the free elliptic connection,rho is the already derived original thermal density,not a newly chosen geometry or temperature. TomitaJ,OSTheta,classical doubling and physical time remain distinct until actually mapped.

  • 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.

  • Free chiral Cauchy quantization of the canonical elliptic annulus

    Treat the dividing half of the given square curve in its canonical flat conformal representative as a product collar. Compute the Cauchy graph of Dplus=partial_t+B_Sigma,B_Sigma=−i partial_s with NS boundary,then interpret it using the expressly free chiral CAR construction as a quasifree two-boundary state. The labelled second-face compression is the covariance;the other is complementary. This Gaussian interpretation does not derive the original relative spectral-action measure,P1 time or EM/Quillen response.

  • Original quarter CAR source with fixed fold and current dictionary

    The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.

Original evidence

  • HALF-PERIOD-GNS-SEWING.txt lines 1–170

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/native-arc-charge-source-interface-20261026/HALF-PERIOD-GNS-SEWING.txt

    7236ecc67bbae4ff477fe5a761a1b1068b6b75418aa6651b8ee00d2f7d87e3b1

  • check_half_period_gns_sewing.py lines 1–136

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/native-arc-charge-source-interface-20261026/check_half_period_gns_sewing.py

    c26c50125ef471e5f6f48675fc96c8a4971e97aebb5893e5086f063de4904215

  • half_period_gns_sewing_results.json lines 1–43

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/native-arc-charge-source-interface-20261026/half_period_gns_sewing_results.json

    529fc875d0aa3352592a38eabca41b770f9bda9f26bc0b29c214ba6d396cb856

  • HALF-PERIOD-GNS-REVIEW.txt lines 1–73

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/native-arc-charge-source-interface-20261026/HALF-PERIOD-GNS-REVIEW.txt

    3b8e6e7430e88f13ca12cc68ead3f9d677a418863688e95ed2d7bbfcb74c333b

  • ELLIPTIC-GREEN-RP.txt lines 33–146

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/ELLIPTIC-GREEN-RP.txt

    d8799f04851a9bd539b05b4d013b38eb00de9bec07dddde6438023aaf1facd80

finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner