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