TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-ORIGINAL-FIELD-MAP-AND-CURRENT.txt
Original file SHA-256: 00518f3e9908e21ea425bd8caa79f926d63d7b6e7924b601d4d17da2edb096e9
Inclusive original lines: 1-55
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 | HIST20261103J. Original field map, Hodge transport and actual common current.
000002 | Anonymized source derivation, 3 November2026.
000003 | 
000004 | 1. FIRST ORIGINAL FIELD IDENTIFICATION ACTUALLY READ
000005 | J25-TRACE is the earliest recovered source, original raw-content SHA256
000006 | 289b6dc582e800a59391fed6c41604a47915378d28258ec8e9cec9b8d8dd1ab2.
000007 | It explicitly proposes T^{mnr}=d^{[m}(phi*g^{n]r}) and calls this
000008 | "totally antisymmetric torsion". This is the original proposed field
000009 | identification, not a newly invented comparison model.
000010 | Its complete antisymmetrization is identically ZERO, because g is
000011 | symmetric in the last two slots before the first antisymmetrization.
000012 | Thus epsilon*T=0: the stated map has no axial torsion component.
000013 | 
000014 | On a constant orthonormal frame, or for the metric-compatible covariant
000015 | version of that expression, set v=dphi and unit-weight antisymmetrization:
000016 |  T_vec_mnr=(v_m*g_nr-v_n*g_mr)/2.
000017 | Then T_vec_mn^n=3v_m/2 and T_vec^2=3v^2/2 in4dimensions.
000018 | This is the trace sector, not the axial sector of P25-L:136,155.
000019 | The original partial derivative also needs an actual covariant-field map
000020 | before being treated as a tensor away from its chosen frame.
000021 | 
000022 | 2. ACTUAL CANDIDATE DUAL MAP, INCLUDING ITS NORMALIZATION
000023 | Using the SAME supplied Lorentz metric and orientation, define the Hodge
000024 | star on the first two indices: (*T)_mnr=epsilon_mn^ab*T_abr/2.
000025 | Direct contraction gives
000026 |  *T_vec_mnr=-epsilon_mnrs*v^s/2.
000027 | Therefore the exact mathematical bridge to the written P25-L contorsion
000028 | K_ax=epsilon*S/2 is K_ax=-*T_vec with S=v.
000029 | If the coordinate convention is T_ax=2K_ax, then T_ax=-2*T_vec, not just
000030 | T_ax=T_vec. The relation to P25-L's auxiliary equation would additionally
000031 | transport dphi=(lambda*kappa^2/3)da and all actual normalizations/periods.
000032 | The numerical old phi0 cannot be imported without that actual field chart.
000033 | 
000034 | This is a nontrivial field dualization: (*T)^2=-T^2 on these Lorentzian
000035 | two-form slots. Kinetic terms, source couplings, parity/reflection, measure,
000036 | contour and reference must be transported. It is not a symmetry of the
000037 | old/new actions by declaration. In particular a beta*(dT)^2 term remains
000038 | fourth-order in a scalar after the gradient substitution, also after star.
000039 | The factor2 here is a torsion/contorsion normalization, not a resolution
000040 | of the distinct anomaly-matching factor2 without a whole-source map.
000041 | 
000042 | 3. THE EARLIEST NOETHER CLAIM AND ITS SMALLEST TEST
000043 | J25-CURRENT, original raw-content SHA256
000044 | 95ad6cbabf6a72cc716b905629fe451196fb5bce16cadf769ef4d808e87cd44d,
000045 | writes J^m=[-Z*d^m phi+(2beta_bar/M_Pl^2)*(Box phi)*d^m phi]*epsilon,
000046 | Z=1+alpha/(2pi^2), and claims conservation only at phi0=1/(6pi).
000047 | For EVERY constant phi=c this written J and its divergence vanish.
000048 | Thus this local current does not select that constant background.
000049 | The source itself says the full higher-derivative Noether term remains
000050 | to be included. For an L(phi,dphi,ddphi), the actual shift current is
000051 |  J^m/epsilon=partial L/partial(d_m phi)
000052 |               -d_n[partial L/partial(d_m d_n phi)],
000053 | up to improvements and a boundary variation. No missing L is fabricated.
000054 | Global flux/boundary data could impose further conditions, but those
000055 | must be read/evaluated and do not follow from this written local current.