TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ACTUAL-PH-CAR-AND-ADJOINT-REPLAY.json
Original file SHA-256: 6a447cc73b9614db46492350373e8cbbd478c9c7a26d709cc788308f4c15ab19
Inclusive original lines: 1-25
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.

000001 | {
000002 |   "scope": "Actual canonical finite E/Eh summand, one Pgamma+ carrier. Ordinary full retained trace multiplies by16 and (2/pi)^2. Not the whole unsmoothed Z response or a full JF-real observable.",
000003 |   "checks": {
000004 |     "exact_CAR": true,
000005 |     "filled_defect_Pauli": true,
000006 |     "FF_unadjointed": true,
000007 |     "NN_unadjointed": true,
000008 |     "FN_connected": true,
000009 |     "NF_connected": true,
000010 |     "positive_F_adjoint": true,
000011 |     "positive_N_adjoint": true,
000012 |     "positive_FN_cross_orthogonal": true,
000013 |     "four_selfadjoint_quadratures": true,
000014 |     "positive_covariance_polynomial": true
000015 |   },
000016 |   "passed": true,
000017 |   "directed_FN_trace": "a*b*(-1 + sqrt(3)*I)",
000018 |   "hermitian_covariance_without_common_factor": "Matrix([[a**2 + b**2, 0, -a*b, sqrt(3)*a*b], [0, a**2 + b**2, sqrt(3)*a*b, a*b], [-a*b, sqrt(3)*a*b, a**2 + b**2, 0], [sqrt(3)*a*b, a*b, 0, a**2 + b**2]])",
000019 |   "covariance_eigenvalues_without_common_factor": [
000020 |     "(abs(a)+abs(b))**2, multiplicity2",
000021 |     "(abs(a)-abs(b))**2, multiplicity2"
000022 |   ],
000023 |   "finite_CAR_dimension": 64,
000024 |   "face_parameters": "symbolic sech and tanh; all expectations verified before substituting ell_NS"
000025 | }