TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/V311-PROCESS-AMBIGUITY.txt
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | V311 TRANSFER: EXACT QUANTUM-PROCESS AMBIGUITY
000002 | 
000003 | Question. Does the whole population history of the existing three-state
000004 | transfer determine its full quantum process? No, within the extension class
000005 | constructed here. This answers an identifiability question about that reader;
000006 | it does not prove any of these extensions is the original physical TFPT source.
000007 | 
000008 | Original input: verification/v311_gap_decoupled_measure.py, transfer(). The
000009 | checker imports and compares the original numerical 3x3 matrix, and constructs
000010 | its spectral-projector expression exactly over the rationals:
000011 | 
000012 |  T = [[1651/4374, 1267/4374, 728/2187],
000013 |       [1267/4374, 1651/4374, 728/2187],
000014 |       [728/2187,  728/2187,  731/2187]].
000015 | 
000016 | Set E_ij=|i><j| and, for 0 <= e <= 731/2187,
000017 | 
000018 |  Phi_e(X) = e X + sum_ij (T_ij - e delta_ij) E_ij X E_ij^*.
000019 | 
000020 | This is a diagnostic family on an auxiliary three-dimensional Hilbert space.
000021 | The interval is sufficient for the construction; it is not claimed maximal.
000022 | Every coefficient is nonnegative, so the displayed Kraus decomposition is
000023 | completely positive. The column sums of T equal one, making Phi_e trace
000024 | preserving. The checker independently verifies the exact Choi decomposition
000025 | and its partial trace, symbolically in e. It checks the nine matrix units to
000026 | establish, for every complex input matrix X,
000027 | 
000028 |  diag(Phi_e(X)) = T diag(X),  diag(Phi_e^n(X)) = T^n diag(X).
000029 | 
000030 | Thus all e have identical population histories for all initial matrices and
000031 | all nonnegative integer times. Yet for rho=|0+1><0+1|/2 the off-diagonal
000032 | entry is e/2: values e=0, 1/5, 1/3 give 0, 1/10, 1/6 respectively.
000033 | The interval therefore contains uncountably many distinct channels with this
000034 | same population reader. This does not claim the displayed interval exhausts
000035 | all possible values or channels.
000036 | 
000037 | Additional TFPT source, E8/clock intertwiner, CAR, Higgs, locality and state
000038 | constraints are not imposed here. They may distinguish or exclude these
000039 | extensions. Identifying this qutrit with the full E8, 96-component or physical
000040 | source carrier would be an additional, unproved assumption. A classical
000041 | population history is not a complete multi-time process tensor with arbitrary
000042 | interventions; the latter could distinguish the channels.
000043 | 
000044 | Run from repository root:
000045 | 
000046 |  python3 experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_v311_process_ambiguity.py
000047 | 
000048 | Requires numpy and sympy. Exit 0 means all listed exact identities and the
000049 | comparison to the original floating-point transfer passed. This is a theory
000050 | contract diagnostic, not an empirical prediction or ledger promotion.