TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
Original file SHA-256: 3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce
Inclusive original lines: 9-33
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000009 | 1. The corrected search question
000010 | 
000011 | The old diversity objective drove single-field responses to a chosen global
000012 | floor a. With a>0, a free two-field response a^2 is smaller than that floor.
000013 | Consequently this extreme probe could exclude a known free completion while
000014 | reporting endpoints a and 1-gap as attractive candidates. Those endpoints are
000015 | not physically selected constants. In the recorded five-mode example every
000016 | diagonal completion T_b=P0+(1/4)P1+b P_(>=2), 1/4<=b<=3/4, agrees on every
000017 | word through degree4. A T insertion can first act on a two-excitation intermediate
000018 | state and return to the reference in a word of length5.
000019 | 
000020 | The implemented default is now feasibility, with no objective on occupation or
000021 | responses. Bounds are explicit search premises. For a finite positive transfer
000022 | aI<=T<=MI the localizers are T-aI, MI-T, and
000023 | (T-aI)(MI-T)=(M+a)T-T^2-aMI. They are not assumptions that every physical time
000024 | representation is a vacuum contraction. Thermal GNS time needs its own type.
000025 | The minimal pure-occupation Fock completion remains optional and cannot be used
000026 | to reject mixed states or thermal GNS representations.
000027 | The search now also accepts a supplied reference eigenvalue lambda>0:
000028 | T Omega=lambda Omega. The normalized case lambda=1 remains the default.
000029 | State normalization omega(1)=1 is not the unnormalized source value Z[0].
000030 | Changing lambda is a changed input, not a physical selection or recovered Z.
000031 | Both campaign and direct finite-completion entry points reject the unsupported
000032 | pure-Fock ansatz for other source classes, reference amplitudes or ceilings.
000033 |