TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/source-dynamics-selection-20260920/PROOF.txt
Original file SHA-256: 03c09468b07cc68abd31d7f8d6715dd474564728d053ccb063a67a1ca71c89d2
Inclusive original lines: 30-58
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000030 | We test the ALREADY CONDITIONAL ten-channel edge:
000031 |  Gamma=Z^10, K=diag(1^9,-1), B(x,y)=x^T K y,
000032 |  V_x=cocycle_x :exp(i x^T K phi):,
000033 |  q(x)=sum x_i,
000034 |  Y=(-1/3,-1/3,-1/3,1/2,1/2,0,0,0,1,1),
000035 |  g=(2,2,2,2,2,0,0,0,3,3) modulo4,
000036 |  n=(1,1,1,-1,-1,-1,-1,-1,-1,3), z=e9-e10.
000037 | Write a=(1,1,1,-1,-1,-1,-1,-1), m=(a,0,3)=n+e9.
000038 | The previous selected energy is V_aux=K+2Kmm^T K.
000039 | Equal original free velocities are normalized to one: V0=I.
000040 | Neither this granted ten-channel comparison nor its interaction is a new
000041 | derivation from the one-copy QWZ source or from P1/P2.
000042 | 
000043 | 1. An energy-preserving dictionary is different from changing the energy
000044 | 
000045 | Use the existing integral unimodular W=W_aux, with
000046 |  W^T K W=G_E8 direct_sum diag(1,-1).
000047 | If phi=W chi, a passive change of fields necessarily gives
000048 |  K'=W^T K W, V'=W^T V W.                                  (2)
000049 | For V0 the second matrix is W^T W, not G_E8 direct_sum I2.
000050 | The latter is W^T V_aux W. Replacing one with the other changes the
000051 | physical Hamiltonian and its state/correlation dynamics.
000052 | 
000053 | For the specific positive generalized metrics used here, V K V=K and
000054 | K^2=I. The equal-time covariance metric is K V^-1 K=V. Consequently the
000055 | scaling dimension of V_x is Delta_V(x)=x^T V x/2. This formula is NOT
000056 | asserted for an arbitrary positive kinetic matrix. Alternatively the
000057 | dimensions below follow by diagonalizing to the declared free chiral
000058 | coordinates and using the transported vertex charges.