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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

Canonical conformal boundary trace preserves the existing elliptic Cauchy state

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

Analytic smooth massless conformal Cauchy-data theorem, not a regulator-limit claim. The free state consequence uses the existing CAR quantization premise. Newly metric-defined stress, spectra, resolvents, APS projections, full marked graph traces, P1 origin and physical time are not identified; previous nonzero Schur/sea responses remain intact.

Read the exact result, assumptions and evidence

Result

The conformal Dirac law and boundary density give V_sigma=e^((d-1)sigma/2), which exactly cancels the harmonic-spinor factor:V_sigma Tr psi_sigma=Tr psi0. Thus V_sigma P_sigma V_sigma*=P0 for the orthogonal closed Cauchy-data projection. Both marked faces and regional supports are preserved. In common bulk L2 the required trace is T_sigma=e^-sigma_boundary/2 Tr for Dtilde=e^-sigma/2 D e^-sigma/2. Quarter/fold are transported afterwards. The existing labelled marginal and full free current source are identical for all compatible metrics on the same complex curve. An unweighted raw trace produces an exactly detected spurious covariance change.

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:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state