Established in scope
Free projection sewing requires maximal coherence and linear half-modular field action
In the question: Common clock sectors, quartic geometry and operational reconstruction
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.
Read the exact result, assumptions and evidence
Result
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.
Required assumptions
- 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.
- 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.
Original evidence
- HALF-PERIOD-GNS-SEWING.txt lines 1–170
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/HALF-PERIOD-GNS-SEWING.txt
7236ecc67bbae4ff477fe5a761a1b1068b6b75418aa6651b8ee00d2f7d87e3b1
- check_half_period_gns_sewing.py lines 1–136
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/check_half_period_gns_sewing.py
c26c50125ef471e5f6f48675fc96c8a4971e97aebb5893e5086f063de4904215
- half_period_gns_sewing_results.json lines 1–43
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/half_period_gns_sewing_results.json
529fc875d0aa3352592a38eabca41b770f9bda9f26bc0b29c214ba6d396cb856
- HALF-PERIOD-GNS-REVIEW.txt lines 1–73
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/HALF-PERIOD-GNS-REVIEW.txt
3b8e6e7430e88f13ca12cc68ead3f9d677a418863688e95ed2d7bbfcb74c333b
- ELLIPTIC-GREEN-RP.txt lines 33–146
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/ELLIPTIC-GREEN-RP.txt
d8799f04851a9bd539b05b4d013b38eb00de9bec07dddde6438023aaf1facd80
finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law