TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SOURCE-SPIN-JOINT-CLOCK-TEST.txt
Original file SHA-256: 811a216222b56656c3712d5c9b86e9cf5d9bcee59306595fae5655c4bd952735
Inclusive original lines: 1-86
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 | SOURCE SPIN KERNEL: EXACT JOINT c/Q FRAME TEST
000002 | Independent analytic review, 2026-10-29.
000003 | The already registered SOURCE-SPIN-ZERO-SECTIONS.txt is unchanged.
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000021 | 
000022 | Thus the proposed simultaneous old pair (A,C) is not obtained from the
000023 | printed original pair by its printed K. Making a cubic matrix into an
000024 | unsigned permutation requires transporting Q with the SAME frame change.
000025 | A bare Kummer label permutation is not that common calibration.
000026 | 
000027 | 2. Fixed new spin kernel data
000028 | Reuse the explicit compatible meromorphic spin normalization:
000029 |   omega=exp(2 pi i/3), xi=exp(-i pi/4),
000030 |   B=diag(1,1,-omega),
000031 |   Q_new=(-xi) B A B^-1, c_new=omega C.
000032 | The column convention is Q^*psi_a=v_a psi_(-a-1).
000033 | No new geometric or spin choice is introduced in this test.
000034 | Trace Q_new=-xi, trace A=1, so any invertible simultaneous comparison
000035 |   T Q_new=lambda A T
000036 | must have lambda=-xi. The cubic condition forces mu^3=1.
000037 | 
000038 | 3. Smallest failure test for the uncalibrated pair
000039 | Put A'=B A B^-1. Directly
000040 |   tr(A' C)=omega^2,
000041 |   tr(A' omega C)=1,
000042 |   tr(A C)=-1.
000043 | If one insists on T c_new=mu C T as well as T A'=A T, invariance of
000044 | the trace of their product would require 1=-mu.
000045 | This forces mu=-1, contrary to mu^3=1.
000046 | Hence NO invertible T works for the specifically uncalibrated pair (A,C),
000047 | even allowing separate generator scalars. This is only a matrix-frame
000048 | statement; it is not a physical or original-source exclusion.
000049 | 
000050 | 4. Positive result for the actual simultaneous original pair
000051 | For the calibrated pair (A,V), the exact unitary diagonal matrix
000052 |   T=diag(-omega,-omega^2,1), det T=1,
000053 | satisfies
000054 |   T A'=A T,
000055 |   T(omega C)=V T.
000056 | Consequently
000057 |   T Q_new=(-xi) A T,
000058 |   T c_new=V T.
000059 | Here lambda=-xi and mu=1. Every equality is an explicit matrix identity.
000060 | A tiny exact SymPy linear-equation check also found this one-dimensional
000061 | solution space up to overall scalar; no suite or candidate scan was used.
000062 | 
000063 | Returning to the actual printed F frame, S=K T satisfies
000064 |   S Q_new=(-xi) R S,
000065 |   S c_new=P S.
000066 | Returning all the way to the original v117 frame, J=F K T gives
000067 |   J Q_new=(-xi) U J,
000068 |   J c_new=M J.
000069 | Thus BOTH generators agree under ONE explicit constant field-of-sections
000070 | comparison, retaining the scalar spin factor on the quarter generator.
000071 | For the positive-loop inverse convention invert the quarter equality;
000072 | the same J then compares Q_new^-1 with (-xi)^-1 U^-1.
000073 | 
000074 | 5. Verdict and scope
000075 | The apparent joint obstruction for (A,C) is a lost common-frame sign.
000076 | The actual old pair admits the explicit joint projective comparison above.
000077 | This is stronger than separately comparing the two spectra.
000078 | It compares the three-dimensional holomorphic zero-section space with
000079 | the original coefficient-vector clock pair, including the spin scalar:
000080 | Q_new^4=-I, whereas U^4=I.
000081 | It is not literal equality of the spin and coefficient representations,
000082 | nor identity with native kappa, a charged CAR operator map, an original P1
000083 | insertion, a state, OS action, support map or physical-time identification.
000084 | Only these fixed original and constructed lifts have been compared.
000085 | The full given operational Seed and its existing state/time remain intact.
000086 |