TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/p5-phase-range-results.json
Original file SHA-256: 33a73d1fe16bfa90a9e5e7d8d19d3b6bef2f44c4d2a05bf2039a991fc0f879af
Inclusive original lines: 1-42
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | {
000002 |   "carrier": "Lambda2(C5) in original PAIRS basis; original E8 Cm and P5",
000003 |   "family": "Phi o Ad(a P_CC + b P_CW + c P_WW), |a|=|b|=|c|=1",
000004 |   "objective": "Tr(P5 J) = |a+4b+c|^2/6 + |a+b|^2",
000005 |   "normalization": "unnormalized Choi trace 10; divide objective by 10 for normalized probability",
000006 |   "exact_min": "2/3",
000007 |   "min_phases": [
000008 |     "-1",
000009 |     "1",
000010 |     "-1"
000011 |   ],
000012 |   "exact_max": "10",
000013 |   "max_phases": [
000014 |     "1",
000015 |     "1",
000016 |     "1"
000017 |   ],
000018 |   "proof": "Gauge b=1. Put t=Re(a), s=|a+4|=sqrt(17+8t), 3<=s<=5. Minimizing over c gives (s-1)^2/6+(s^2-9)/4, strictly increasing for s>=3; hence 2/3 at s=3. Triangle bounds give 10; equal phases attain it. Continuous domain gives full interval.",
000019 |   "legacy_one_sided_control": "8/3 (normalized probability 4/15)",
000020 |   "coverage": "only this phase family, not all SM-covariant channels and not all processes",
000021 |   "source_bridge": "P5 embedding into local P1 A_adm and operational sewing rule remain unproved; none of these phase channels is thereby selected",
000022 |   "clock": "original U5 is scalar on Lambda2 C5 and cannot distinguish this family",
000023 |   "all_petersen_cptp": {
000024 |     "exact_min": "0",
000025 |     "exact_max": "10",
000026 |     "construction": "Dm flips 3 of the 6 nonzero entries of each original Cm, with all other entries unchanged. J0 = (1/3) sum |Dm>><<Dm|.",
000027 |     "controls": "Exact orthogonality to all Cm, every individual Dm effect = Cm effect, TP, unital, every one of 100 populations unchanged.",
000028 |     "interval_proof": "0<=P5<=I and Tr(J)=10. Endpoints J0 and Jphi meet bounds; all convex mixtures preserve the full population and yield the interval.",
000029 |     "scope": "All CPTP channels with full fixed Petersen population; the exhibited zero-construction is not SM-covariant.",
000030 |     "zero_candidate_sm_covariance": "fails: SU3 E01-E10 commutator of M0=3J0 has exact HS norm squared 576"
000031 |   },
000032 |   "same_p5_as_psi": {
000033 |     "phases": [
000034 |       "-1",
000035 |       "1",
000036 |       "(1+2i sqrt(2))/3"
000037 |     ],
000038 |     "P5": "2",
000039 |     "P45": "16/3",
000040 |     "psi_P45": "4 (prior exact six-mark original-source check)"
000041 |   }
000042 | }