TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-QVT-VARIATION.txt
Original file SHA-256: e54fb6e7daafeb96e997302fb4d7666cca933632643d2edef4b16c0a5415ede8
Inclusive original lines: 1-111
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | HIST20261103Q. Literal historical QVT source and decisive variation check.
000002 | Anonymized authored mathematical transcription. No private metadata.
000003 | 
000004 | Original attachment Q25, 3 pages, content SHA256:
000005 | 192b0c09f233f143028aeb4f21c46f419b3961032c753d098f38980aae4f2665.
000006 | All three pages read; equations S1-S9 visually checked on original pages.
000007 | Notation A,B,C are spacetime indices. The original displays in S1:
000008 | S_struct[g_AB,K^A_BC,alpha,a]=integral d4x sqrt(-g) [
000009 | (1/(2 khat^2)) (R-nabla_C K^C_AB+K_ACD K_B^CD)
000010 | -F_AB F^AB/4+U(alpha,L;c3,b1)-g_agamma*a*F_AB Ftilde^AB/4].
000011 | There is no displayed g^AB contraction of the last two geometric terms.
000012 | Original S2:
000013 | U=(alpha^3-2 c3^3 alpha^2-8 b1 c3^6 L)/3,
000014 | L=ln[1/phi0(alpha)],c3=1/(8pi),b1=41/10,khat^2=8pi.
000015 | Original S3 claims dU/dalpha=0 implies
000016 | I=alpha^3-2 c3^3 alpha^2-8 b1 c3^6 L=0.
000017 | Original S4 correctly differentiates I=0 at independent L:
000018 | dalpha/dL=8 b1 c3^6/(3alpha^2-4c3^3 alpha),
000019 | but calls its zero a fixed point at alpha^-1=137.0360.
000020 | Original S5 claims K variation gives
000021 | nabla_C K^C_AB-K_ACD K_B^CD=khat^2 S_AB,
000022 | S_AB=g_agamma*a*F_AB/2.
000023 | Original S6 claims metric variation gives
000024 | Q_AB=R_AB-nabla_C K^C_AB+K_ACD K_B^CD
000025 | =khat^2 (T^a_AB+T^EM_AB).
000026 | Original S7 sets V_AB=Q_AB^TF+g_AB I.
000027 | Original S8 claims V=0 reproduces CFE and UFE via Q^TF=0.
000028 | Original S9 claims nabla^A V_AB=0 from diffeomorphism invariance.
000029 | Original S10 calls Q_AB-g_AB I=0 the same compact equation.
000030 | 
000031 | Direct decisive checks of these SAME written clauses:
000032 | 1. S1 as printed mixes scalar R with rank-two terms with free A,B.
000033 | It is not a defined covariant scalar action without an extra contraction.
000034 | Its unspecified repair cannot count as original variational derivation.
000035 | 2. At fixed independent L, partial_alpha U=alpha^2-(4/3)c3^3 alpha,
000036 | not I. With L(alpha), total derivative adds -(8/3)b1 c3^6 L'(alpha),
000037 | still not the written I. No omitted kinetic term rescues that algebra.
000038 | 3. For fixed nonzero c3,b1, numerator of S4 is strictly nonzero.
000039 | No finite regular zero dalpha/dL=0 exists. At denominator zero it is
000040 | singular, not a zero. This is structural flow, not physical time.
000041 | 4. At K=0, S6 lacks the -g_AB R/2 Einstein term. For a Maxwell field
000042 | with trace zero this can coincide on shell when R=0 under further
000043 | conditions, but it is not the displayed metric variation in general.
000044 | The a F Ftilde density is metric independent at fixed differential forms;
000045 | S1 supplies no local kinetic term for a. It cannot silently give an
000046 | independent canonical axion stress tensor as written.
000047 | 5. S7 trace is 4I in four dimensions. V=0 also requires Q^TF=0.
000048 | S6 with matter instead requires Q^TF=khat^2 T^TF, generally nonzero.
000049 | A nonzero null Maxwell wave is a direct traceless-stress counterexample.
000050 | This is a test of asserted equivalence, not an invented comparison model.
000051 | 6. S10 trace is Q^A_A-4I=0, different from S7 trace 4I=0.
000052 | They agree only with extra conditions, not identically.
000053 | 7. In K=0 limit Q=Ricci, contracted Bianchi gives
000054 | nabla^A Q_AB^TF=(1/4)partial_B R. Hence div V=(1/4)dR+dI,
000055 | not an off-shell identity. Actual Noether identities include all field
000056 | Euler derivatives; they are not an arbitrary divergence-free declaration.
000057 | 8. A precise S5 variation cannot be certified from rank-mismatched S1.
000058 | For Maxwell F=dA, the density a F wedge F has no independent K variation.
000059 | The stated a F_AB source cannot be imported without an actual K coupling.
000060 | 
000061 | These checks exclude the literal Q25 closure as a valid derivation.
000062 | They do not exclude all TFPT, QVT as a future correctly derived object,
000063 | propagating torsion generally, or the distinct actual P25-L action.
000064 | The existing polynomial invariants, compiler/E8/clocks/flavor/alpha and
000065 | full96 results retain their own scopes. No replacement action is chosen.
000066 | A quartic antiderivative of I at fixed L is a mathematical reconstruction,
000067 | not a microscopic derivation or a proof of original full S_adm.
000068 | 
000069 | 9. Do not infer K=0 from a contracted repair without specifying whether R
000070 | is LC or contains K: Q25 supplies Gamma={ }+K but does not explicitly
000071 | state the torsionless-hat convention of P25-L. Such a repair is not used.
000072 | Even where a repaired metric trace relates R and I, I=0 needs an additional
000073 | R=0 condition for traceless matter and does not remove alpha variation.
000074 | At fixed L>0, c3,b1>0, the two stationary roots of U are alpha=0 and
000075 | alpha=4c3^3/3. Their I values are respectively -8b1c3^6 L and
000076 | -32c3^9/27-8b1c3^6 L, both strictly negative. The metric-trace reinterpretation
000077 | therefore does not close the simultaneous written stationarity claim.
000078 | 
000079 | S25. Earlier recovered stationarity manuscript, 6 pages.
000080 | Original content SHA256 e36849baa2d1dd5f0c1d1c479b8f5605ee1049bd9254d0c108d77f2f6f86954e.
000081 | Original section3 and section4 actually write the quartic potential
000082 | U4=A alpha^4/4-(2/3)A c3^3 alpha^3-A[8b1c3^6 L]alpha.
000083 | At fixed L its derivative is A I. This algebra is correct. It differs
000084 | from the later Q25 U=I/3. Restoring provenance is not a new chosen action.
000085 | If L=L(alpha), the derivative also includes -8A b1c3^6 alpha L'(alpha);
000086 | the independent-variable variation and subsequent feedback must be stated.
000087 | 
000088 | S25 Appendix C.2 writes the zero-external-momentum photon bubble as
000089 | Pi(0) proportional c3^2 integral d4p/(2pi)^4
000090 |  (epsilon_mnrs p^r (-p)^s)(epsilon^mnab (-p)_a p_b)/p^4.
000091 | Each parenthesis is identically zero, by antisymmetry against p^r p^s.
000092 | Thus this exact printed integrand cannot yield the claimed nonzero
000093 | coefficient 2*c3^3*alpha^3 of a potential. A correct epsilon contraction
000094 | identity by itself is insufficient; the actual momentum insertion matters.
000095 | The same manuscript explicitly says alpha is a dynamical scalar/expectation
000096 | value, but the displayed axion-photon vertex alone does not give the actual
000097 | alpha-field embedding or a nonzero constant-alpha potential derivation.
000098 | This excludes this particular printed diagram derivation, not the later
000099 | scoped E8/seam identities or the existing positive-root theorem.
000100 | 
000101 | The next historical stress-test source (4 pages), content SHA256
000102 | 90a7c8c462c36d90524800ac343ebe0c255084e7b5ddbc3c5c0832abe9930df6,
000103 | reports a box-count disagreement 8 versus12. No full enumerator or precise
000104 | physical diagram equivalence classes were supplied in that PDF. Its12
000105 | is a reported objection, not an independently established replacement
000106 | coefficient. No 8-to12 change is made to the original/current TFPT function.
000107 | 
000108 | Review discipline: exact old source equations and direct algebra decide.
000109 | External-model agreement is independent review, not physical validation.
000110 | All private provenance stays outside Atlas and Skill. The source objects
000111 | are retained privately; this authored note contains no personal identifiers.