TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/FOUR-POLAR-CONTEXT-ALGEBRA.txt
Original file SHA-256: f9bb309bae0d65b31df6a38899c526547f027b69eb89b34800497e72b4ea9bdb
Inclusive original lines: 5-25
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000005 | 
000006 | Continue the four-start result using the same actual intrinsic six-ray matrix
000007 | N, NN*=I5, N*N=I6-J6/6, central quartic OPE metric, global pair S={0,1},
000008 | original positive polar rule and original full fold-state D1 tensors. Do not
000009 | choose a new state, coupling, measurement optimization or preferred q.
000010 | The original equations are in FOUR-STARTING-POINTS-STATE-RELATIVE-EQUIVALENCE.txt
000011 | sections3--4 and check_four_starting_points.py. The independent source tensors
000012 | are in fold_response_tensors_results.json, not fitted to the present result.
000013 | 
000014 | The original technical companion explicitly supplies a CONDITIONAL instrument:
000015 | documents/archive--tfpt-45--source_extracts--technical_companion_source/
000016 | sections/007-section-yukawa-kernels-and-positivity-lemmas.tex:268--296.
000017 | It assumes a stable pointer algebra A_obs subset A_rec and a complete
000018 | orthogonal projector family {P_i}, then writes p_i=tr(rho P_i) and
000019 | M_O(rho)=sum_i P_i rho P_i tensor |i><i|. Lines347--359 supply the OPTIONAL
000020 | context Q=(rho0,O_Q,Delta_Q,t,C_Q,R_Q). This is a source rule for given
000021 | pointers/context, not a source identification of these pointers with P_q.
000022 | The original admissibility requirement also preserves H_adm under BOTH A,A*;
000023 | the finite code is not silently identified with H_adm or a closed system.
000024 | 
000025 | 2. COMPLETE FOUR-MARK ALGEBRA, WITHOUT SOURCE RESPONSE