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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

Geometric exterior Schur response transfers relative arc charge but is not a local native current

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

Transfer is necessary structure for the existing native arc-charge test,not sufficient quartic/P1 identification. Second spectral Schur response is not new physical time or Hessian;full fields/composites,domains and profile/history selection remain needed.

Read the exact result, assumptions and evidence

Result

Exact second geometric Schur response at z0 contains R_h(k)=k/8 sum_m h_m²(pi*m)²/[k²+(pi*m)²]. Between actual disjoint quarter preimages I=(1/32,3/32),J=I+1/2,every nonzero cosine coefficient contributes a strictly positive multiple of(1-i). Thus transfer is nonzero for every nonconstant smooth real even profile. Concrete probe gives.001720549637597(1-i)as epsilon² coefficient;independent Fourier error7.09e-12. R_h(k)->0 is compact and cannot itself be a nonzero local folded multiplication current.

Required assumptions

  • Given flat Moebius Dirac boundary family and its full sea

    The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.

  • 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.

  • Controlled conformal normal geometry of the given Pin Dirac source

    For the authorized source study,the same given Dirac comparison D0 on its fixed(c,b)Pin/boundary domain is varied by smooth real even profiles h:g_e=exp(2e h)g0,D_e=exp(-e h/2)D0 exp(-e h/2)after unitary density transport. Profiles/amplitude are explicitly chosen diagnostic interventions,not a P1-selected history. Original pure D0 sea remains initial state;thermal Green quantization stays separate.

Original evidence

  • GEOMETRIC-ARC-TRANSFER.txt lines 1–74

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/GEOMETRIC-ARC-TRANSFER.txt

    eacdbe333028eab285bf703a182d4004b65a763918ccfd368c1d512e39c06517

  • check_geometric_arc_transfer.py lines 1–72

    Source checked at this snapshot

    Original location and fingerprint

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

    5e2f7c3bba8a0613f1f83a7512c024f30b93cb4034109c19591f79e554224262

finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact