Read the result in its research context.

Result

In sameoriginalP takeU=rightL2(I),E=wholeleftplusrightIcomplement. Bf=(Xiota_If,Q_ICiota_If),B*B=C_I(1−C_I)=A². ZeroendpointkernelsgiveuniquepolarisometryB=TAonallU,noboundedAinverseassumed. DT=T(1−C_I)yieldsactualreducingU⊕TUwithcovariance[[C_I,A],[A,1−C_I]]. WholemixedCARwordsfollowinsameoriginalstate. ContractiveT_eps=B(A²+eps)^−1/2convergestrongly;onu=Agerror≤sqrt(eps)||g||,fixedwordsconvergenorm. Explicit single supportedprobeu=sqrt2 1Ihasdistinctsubsystemcutandpartnert=(Xu/a,(Cu−cu)/a),c=<u,Cu>,a²=c(1−c). Wholeoccupiedsea1/4analytic,actualchargedcrosswords/fourfieldwordevaluatedforbothquarters.

Required assumptions

• Actual elliptic two-face projection with genuine regional supports

  Given originalfree ellipticquarterCAR source c_r=(1+exp(4pi(r+alpha)))^-1,alpha1/4 or3/4,X=sqrt(C(1−C)),fullprojectionP=[[1−C,X],[X,C]] inalreadyprovedpositive transportedtwofacechart. PreserveoriginalGreen/RP/gradedHS dictionary. Regionalembeddings areactualextensionbyzero fortwononemptypropercircleintervals withopencomplements. Partnercomparison retainsgivensourcestate/linearCAR embedding. No primitiveP1measureidentification,newpurification,geometrychoice orGaussianizationafterHiggsintegration. Fullintervalsubalgebra andsingle supportedprobe aredistinctsubsystemcuts.

• 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.

• 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.

Original evidence

• REGIONAL-SOURCE-PARTNER-PROOF.txt lines 1–184

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/REGIONAL-SOURCE-PARTNER-PROOF.txt

  08ce8ea751041c7541d12c4af105f056d87eae6dab013ef42f87394bb1ab3cf9

• check_regional_source_partner.py lines 1–90

  Source checked at this snapshot

  Original location and fingerprint

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

  0d4b4979b85c955c9363839950d6209905f8107a7bc800d6e424f29cb1d45b00

• REGIONAL-SOURCE-PARTNER.json lines 1–200

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/REGIONAL-SOURCE-PARTNER.json

  2c9abd57a5bff49032518e034859b04cfd4d0c89deaeef5519fab562345bf793

• REGIONAL-SOURCE-PARTNER.json lines 201–283

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/REGIONAL-SOURCE-PARTNER.json

  2c9abd57a5bff49032518e034859b04cfd4d0c89deaeef5519fab562345bf793

• 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

• ELLIPTIC-GREEN-RP.txt lines 1–196

  Source checked at this snapshot

  Original location and fingerprint

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

  d8799f04851a9bd539b05b4d013b38eb00de9bec07dddde6438023aaf1facd80

• 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

• HIGGS-MIXTURE-WICK-PROOF.txt lines 1–150

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/HIGGS-MIXTURE-WICK-PROOF.txt

  1264ad59c4b8de007156b50e4fd0b352a868db1d82bfeafebb50e5173f99ec73

• PROJECTOR-STATE-RIGIDITY.txt lines 1–173

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/native-arc-charge-source-interface-20261026/PROJECTOR-STATE-RIGIDITY.txt

  2e14e8875c263d71bd6bda61d005461cb718bdf30fdf34a6312db53167cd80c6

finding:actual-elliptic-whole-environment-fixes-regional-car-partner