Read the result in its research context.

Result

Extensionbyzeroiota gives actualC_I=iota*C_alpha iota,endpointkernels0;modulatedsupportedprobes show0/1 spectralendpoints. Entire selfadjointk_I=log((1−C_I)/C_I) on spectraldomain,unboundedbothsides. Resolventreader integral0infinity[(C_I+s)^−1−(1−C_I+s)^−1] yieldsgivenfreeCAR modularflow sigma_t(a(u))=a(exp(−itk_I)u),antilineara. No localdensitymatrix forinfinitealgebra. Actual3mode subalgebra u_j=sqrt2exp(2ijtheta)1_I retainswholeHardysea exactly viatrigamma/digamma pluswhole exponentialthermalcorrection;independent8D Fockcalculation matchesoriginal2/4field/twonumberunitarywords andmodularsign.

Required assumptions

• Actual elliptic quarter source with supported current and interval CAR modular-time test

  Unchanged given free CAR source of original elliptic midpointannulus:occupation c_alpha(r)=(1+exp(4pi(r+alpha)))^-1,alpha1/4 or3/4,entire original theta charge law/current Weyl source. Actual sourcecircleintervalI and extensionbyzero L2(I) embedding. Compared geometricclass:realC5 pointdiffeomorphisms I ontoI,generatorcontinuous atfixed endpoints,unchanged weight1 current smearing f→f composed gamma^-1,arbitrary scalar affine current shifts. No fieldmixing,changed dictionary orprimitivephysicalmeasure identification assumed. Preserve existing constructive neutralMoebius vacuum as distinct provedstate.

• 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.

• 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.

• 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

• LOCAL-SOURCE-MODULAR-TIME-PROOF.txt lines 1–197

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/LOCAL-SOURCE-MODULAR-TIME-PROOF.txt

  befcbfd2b372d25dc947ab067481095951b3d00c06a4b7fe149b236e929f2656

• check_local_source_modular_time.py lines 1–124

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  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_local_source_modular_time.py

  6caeca452b19ea1b1cd010273b3cd7842748ee591e0b9673819fcb3078e7c7e6

• LOCAL-SOURCE-MODULAR-TIME.json lines 1–200

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  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/LOCAL-SOURCE-MODULAR-TIME.json

  48f419a5a233e91bb7a7d246e2dc6e019e323082e9ffb468194525e333a3d9c8

• LOCAL-SOURCE-MODULAR-TIME.json lines 201–400

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  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/LOCAL-SOURCE-MODULAR-TIME.json

  48f419a5a233e91bb7a7d246e2dc6e019e323082e9ffb468194525e333a3d9c8

• LOCAL-SOURCE-MODULAR-TIME.json lines 401–424

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  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/LOCAL-SOURCE-MODULAR-TIME.json

  48f419a5a233e91bb7a7d246e2dc6e019e323082e9ffb468194525e333a3d9c8

• ELLIPTIC-CURRENT-SOURCE.txt lines 1–178

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  experiments/theory-contracts/native-arc-charge-source-interface-20261026/ELLIPTIC-CURRENT-SOURCE.txt

  657b2ace6d7152c53dbb29c76d8e0daca6e6b1ce747c535da7dffb0ff38d9b48

• PROOF.txt lines 1–193

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  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/neutral_moebius_source_20261029/PROOF.txt

  d738013d8775f9769747a5cd97f60cfc6b2ff0d2122c4fbfd20b2d65ebe9f4e0

• 001-section-primitive-core-and-carrier-interface-handoff.tex lines 314–343

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  documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex

  7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79

finding:actual-elliptic-interval-car-source-produces-local-modular-generator