Established within the stated premises
Free projection sewing requires maximal coherence and linear half-modular field action
finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law
For arbitrary faithful even rho,the actual canonical cross coherencemj=Tr(sqrt(rho)aj*sqrt(rho)aj) obeys0<=mj<=sqrt(cj(1−cj)). Equality holds exactly when sqrt(rho)aj=qj aj sqrt(rho),qj=sqrt((1−cj)/cj). On full finite CAR,saturation for all modes in a covariance eigenbasis is equivalent to a quasifree product density. On the existing normal all-mode HS carrier,actual all-mode saturation givesMij=qjCij,then full projection covariance and quasifreeness without uncontrolled density inverses. The already given H_int control has both deficits14745600/82945²>0 and half-modular factors2/32 and8/128 depending on spectator occupation. Positive standard doubling and its quarter clock remain,but projection coherence fails. The original property still to be tested is therefore a linear half-modular action on the actual odd fields,not merely existence of positive doubling.
Scope: Analytic finite saturation theorem plus separate all-mode theorem inside the explicit normal HS class. Finite checks do not prove all-mode saturation. The old interaction control is only an algebraic countercheck,not an admitted P1 coupling or new model study. No primitive law or physical odd-field/clock/reflection map is derived or freely chosen. For an actually nonlinear P1 half action,retain its operator contributions instead of forcing free saturation.
Required premises and original source excerpts
- Normal even sea CAR source with canonical graded HS doubling
For the algebraic source test use the already given sea Fock/CAR carrier,with faithful even normalized traceclass density rho and its standard HS space,Omega=sqrt(rho),L_A X=AX,R_A X=XA,Gamma X=Pi X Pi. Gamma is the canonical GNS implementer of source parity fixing Omega. Partner fields are represented in the fixed mode-index chart by b_j=−Gamma R_aj;this assumes no physical second P1 boundary. The finite saturation theorem covers arbitrary faithful even finite densities;the separate all-mode route requires the actual normal HS carrier,a complete covariance eigenbasis and saturation in every mode. For the free elliptic connection,rho is the already derived original thermal density,not a newly chosen geometry or temperature. TomitaJ,OSTheta,classical doubling and physical time remain distinct until actually mapped.
premise:normal-even-sea-car-source-and-canonical-graded-hs-double - 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.
premise:typed-source-structures
- experiments/theory-contracts/native-arc-charge-source-interface-20261026/HALF-PERIOD-GNS-SEWING.txt, lines 1–170
Source SHA256: 7236ecc67bbae4ff477fe5a761a1b1068b6b75418aa6651b8ee00d2f7d87e3b1
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/native-arc-charge-source-interface-20261026/check_half_period_gns_sewing.py, lines 1–136
Source SHA256: c26c50125ef471e5f6f48675fc96c8a4971e97aebb5893e5086f063de4904215
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/native-arc-charge-source-interface-20261026/half_period_gns_sewing_results.json, lines 1–43
Source SHA256: 529fc875d0aa3352592a38eabca41b770f9bda9f26bc0b29c214ba6d396cb856
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/native-arc-charge-source-interface-20261026/HALF-PERIOD-GNS-REVIEW.txt, lines 1–73
Source SHA256: 3b8e6e7430e88f13ca12cc68ead3f9d677a418863688e95ed2d7bbfcb74c333b
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/ELLIPTIC-GREEN-RP.txt, lines 33–146
Source SHA256: d8799f04851a9bd539b05b4d013b38eb00de9bec07dddde6438023aaf1facd80
bounded-excerpt · current-at-snapshot