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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

Averaging the conformal factor preserves the given free boundary Wick words

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

Only the given conditional free quantization and correctly transported CAR observables; no Gaussian theorem for original S_prim/P1 measure and no assertion that connected current correlations vanish. Z_ref[0] cancels in Z_rel[J]/Z_rel[0], not automatically from geometric forces. The next decisive four-field test requires an original covariance-changing variation or higher fermion vertex.

Read the exact result, assumptions and evidence

Result

After the derived boundary transport, each given conditional free CAR word on the same marked curve is independent of sigma. Its identical normalized source functional therefore factors out of any source-independent integrable total geometric weight of nonzero normalization, including determinants, reference, Jacobian and anomalies. The connected fermion four-point defect stays exactly zero, as do all higher Wick rules. No particular geometric measure is selected or discarded. Pure conformal geometry variance is therefore not evidence of an interacting boundary source. With other varying data, integrating out this factor may change their effective weight; their covariance requires a separate test.

Required assumptions

  • 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.

  • Conformal metric family of the same marked massless annulus

    Study the existing smooth midpoint-annulus source on the same complex square curve with fixed spin, cut and face markings and massless geometric chiral Dirac operator. g_sigma=exp(2sigma)g for arbitrary smooth real sigma, with canonical spin lift and bulk/boundary L2 transport derived from volume densities. On the fixed complex curve this includes all Hermitian metrics. Connection, mass and complex structure do not vary. An unchanged original reflection/clock requires invariant profiles; otherwise transport the symmetry as well. No identification with the unresolved full marked equator graph, primitive P1 measure or physical time. The averaging lemma expressly retains the given free conditional CAR quantization, source-independent integrable total weights and nonzero normalization.

Original evidence

  • CONFORMAL-TRACE-AND-WICK.txt lines 1–183

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/native-arc-charge-source-interface-20261026/CONFORMAL-TRACE-AND-WICK.txt

    77a6bffa2192b809f0264406afe7dd57d4718576f7f6632c107a7036de6ff5d1

  • check_conformal_trace_wick.py lines 1–99

    Source checked at this snapshot

    Original location and fingerprint

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

    c30f3058a971b28d17ba3af73f6cbb63fbac43d94a4640ad58d8c64fe613271d

  • conformal_trace_wick_results.json lines 1–20

    Source checked at this snapshot

    Original location and fingerprint

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

    84cbf70dba2439348d6f450a57b6852ea1779bcc0882b718e7abc2feabee8238

  • CONFORMAL-TRACE-REVIEW.txt lines 1–62

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/native-arc-charge-source-interface-20261026/CONFORMAL-TRACE-REVIEW.txt

    ac8d7282712059c7ba465a088ea9f8fdd023b3e2e31cb13fb01de271d0f80ad9

finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words