TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/automatic_identification/EXACT-CHANNELS.txt
Original file SHA-256: 10db566daccf1333448d748590754a7bfeb40817bc5886ba4bbe90d625dda346
Inclusive original lines: 1-44
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | COMPLETE FIXED CHANNEL IDENTIFICATION IN THE GIVEN CONSTANT SOURCE
000002 | 29 October 2026. New application of existing source theorems.
000003 | 
000004 | Use the actual source h(p)=p g-i g Phi, constant Hermitian odd Phi and
000005 | fixed beta,p>0. The already proved THERMAL-RIGIDITY.txt gives
000006 |   D_p=P_+[(1+exp(beta h(p)))^-1-n_beta(p)I]P_+ >=0,
000007 |   ker(D_p|F_+)=F_+ intersect ker(Phi).
000008 | The equality follows for every unit e from strict monotonicity of
000009 | tanh(beta x/2)/x. By the existing whole source chart, every constant e
000010 | in this kernel intertwines ALL local scalar CAR words, the whole two-face
000011 | state, product reflection and SAME quarter time. If the kernel is empty,
000012 | this entire fixed-channel old-free embedding class is empty. No scan or
000013 | new target fitting is required. The infinite spatial/Fock space is not
000014 | truncated: only the genuinely finite internal channel is determined.
000015 | 
000016 | check_exact_source_channels.py imports the unchanged v252 constructor
000017 | through the already existing original_insertions exact helper. Exact
000018 | Gaussian integer conversion rejects nonintegral inputs. These controls
000019 | are GIVEN coefficient tests, not derived physical Yukawa/mass values.
000020 | 
000021 | The pre-existing diagonal control has all48 positive-grade directions
000022 | coupled: kernel0. A deliberately rank-deficient control finds2 positive
000023 | directions, one gauge neutral. Restoring only the Majorana entry removes
000024 | that neutral direction and leaves1 other positive direction. The all-word
000025 | classification follows from the theorem, not from a finite moment fit.
000026 | 
000027 | For the actual neutral positive family module nu_R^c tensor C3,
000028 |   K_neutral=ker[[MR],[entrywise_bar(Ynu)]].
000029 | This reuses the actual P2 dictionary and does not replace entrywise bar
000030 | by adjoint. A nonreal exact control rejects that erroneous substitution.
000031 | The resulting dimensions/ranks/supports are in exact-source-channels.json.
000032 | 
000033 | Universalraum interpretation: all scalar future responses agree for these
000034 | channels by the operator theorem. Different e in that kernel require no
000035 | further arbitrary choice for the scalar response alphabet. Additional
000036 | P2 or marked insertion generators must be compared if they are demanded;
000037 | the original alphabet cannot be invented by the solver.
000038 | 
000039 | This is a complete automatic recognition test in its specified class,
000040 | not an original P1 source law. A physical interacting source need not
000041 | equal the old free scalar source. Variable Phi, moving fields, general
000042 | quantum bosons, different source maps and full spacetime reconstruction
000043 | are not excluded. Old general kernel/GNS/intertwiner calibrations remain
000044 | completed and are reused, not reintroduced as new mathematical methods.