Established in scope
Single positive process saturation fixes full Hodge channel without SU5 premise
In the question: Common clock sectors, quartic geometry and operational reconstruction
Complete mathematical selector for unread channel,not derivation of process saturation fromP1. Actual source amplitude/input-reference required;P_A state purity no substitute. No unique observed instrument/pointer register or full physicalTFPT established.
Read the exact result, assumptions and evidence
Result
For arbitrary CPTP T:End10→End10bar,T=Phi iffTr(P5 J_T/10)=1. Positivity forces Choi support inP5,henceJ=VKV*,K≥0. Actual25 identities C_m*C_n=delta_mnI-dGamma(E_nm) giveTP Choi partialtrace A(K)=trK I-dGamma(K^T)=I. Coefficientrank25,unique rational solutionK=I5/3,henceJ=2P5. Full100directions/phases/Petersen population follow without assumed group or population rule. Shorter concrete source target isTr((I-P5)J_source)=0 with actualTP insertion.
Required assumptions
- 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.
- Given five-slot exterior source with retained complement index
V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.
- Specified CPTP source process with positive P5 saturation
In fixed dual H=Lambda²C5 dictionary,T is a CPTP channel with Choi J_T,trace10. Require Tr(P5 J_T/10)=1 for rank5 projector from epsilon amplitudes. Sufficient conditional contract,not already proved P1 premise or arbitrary P_A state expectation. No assumed fullSU5 covariance,Petersen population or observed Kraus register.
Original evidence
- SINGLE-PROCESS-WARD-CRITERION.txt lines 1–126
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/single_ward_refinement/SINGLE-PROCESS-WARD-CRITERION.txt
4af9dd295fae970d03e90c224183d7ea635cc6e02f1c46587418e41eefa87a36
- check_covariant_rigidity.py lines 1–194
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/single_ward_refinement/check_covariant_rigidity.py
46a0edd1825f3e6a440f26a452fe333742dce26e40f5f87e19c2711a3bc9fce1
- covariant-rigidity-results.json lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/single_ward_refinement/covariant-rigidity-results.json
760848d95be53cf860e2a3ee0c9a48153fb85ff3b07c1bdbe74cd651ae363ec2
- covariant-rigidity-results.json lines 201–304
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/single_ward_refinement/covariant-rigidity-results.json
760848d95be53cf860e2a3ee0c9a48153fb85ff3b07c1bdbe74cd651ae363ec2
- WARD-VERIFICATION.json lines 1–8
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/single_ward_refinement/WARD-VERIFICATION.json
de21c0d7dccbf44396cfbb7853bb0dc671c97427d89f790d21a8c12e0120ca4b
- SINGLE-WARD-INDEPENDENT-REVIEW.txt lines 1–44
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/single_ward_refinement/SINGLE-WARD-INDEPENDENT-REVIEW.txt
59652d2f5abd48a0a2e66641bf933378852bf45d8a7e1a95f35dd57e267e5ea8
finding:single-positive-process-saturation-selects-full-hodge-channel