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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

Old cover winding reconstructs the local quarter current net

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

Complete operator and local-net theorem in the GIVEN original cut-cover CAR realization. Support is the two-preimage region, not a single cover arc. The later eightfold fold, cross-arc CAR transporters and original P1 support/Theta/collar/reference map do not follow from this scalar current-net theorem alone. No time interpretation of product parameters or physical gate closure.

Read the exact result, assumptions and evidence

Result

The old stress formula gives J_n=2(L_n^(3/4)−L_n^(1/4)) on the same CAR generators for every n including0. The comparison within the existing cut-cover source is not free: u_cov W0=W1 and u_cov W1=W0 u_base give U=[[0,u_base],[I,0]],rank[C,U]1 and phase-independent adjoint Fock transport AdGamma(U). The first arrow preserves factor seas and Wick ordering. Hence on factor0 J(f)=2(AdGamma(U)^−1 T_(3/4)(f)−T_(1/4)(f)). Existing self-adjointness/energy bounds and the stable unitary Trotter sequence show that this transported stress pair generates exactly the local U1 current net on every base interval. The full winding remains charged and is not globally vacuum-preserving because of the second arrow.

Required assumptions

  • Existing full cut-cover CAR source with actual winding and sea

    The already constructed NS double-cover source Hcov=W0K⊕W1K is given, with common negative sea m<0 and original winding U=[[0,u_base],[I,0]], u_base e_m=e_(m+1). Quarter stress fields retain their original CAR coefficients and Wick ordering. Base intervals carry two cover preimages. This assumes the mathematical source realization and does not derive its physical P1 field map or descent into a fixed Pin collar domain.

  • 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.

  • 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

  • QUARTER-STRESS-CURRENT-RECOVERY.txt lines 1–162

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/QUARTER-STRESS-CURRENT-RECOVERY.txt

    5861c8516e38bd1ed303622e019c7bef182d9312a25142bc754456beac573141

  • QUARTER-STRESS-CURRENT-INDEPENDENT-REVIEW.txt lines 185–295

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/QUARTER-STRESS-CURRENT-INDEPENDENT-REVIEW.txt

    7cfb5a8ed59e6286e817e26733b4f9d32609825c2e093f2153c3d93d891114ef

  • MOBIUS-QUARTER-OPERATOR-DICTIONARY.txt lines 171–276

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/canonical-seam-fermionization-20261025/MOBIUS-QUARTER-OPERATOR-DICTIONARY.txt

    0b5f5cb8a4e47bedc3c6febb00666893da1797335644d0fb058072379589bd59

  • ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt lines 33–65

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt

    62a9eeb4519b59d4514445f9d4dd5d2059e29179956a4c97ec94b7bae9ae3094

  • check_quarter_stress_current.py lines 32–181

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/check_quarter_stress_current.py

    9e0378b16674598c99b08c19e633cc3108c84ba33c1ae14d5235f695f1544007

finding:old-cover-winding-reconstructs-local-quarter-current-net