TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt
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000208 | 7. Exact mean-work response on the whole original event packet
000209 | 
000210 | The original K and current CCR also fix the mean work of ANY smooth real
000211 | source profile, not merely a chosen Fourier pulse. BCH terminates exactly:
000212 |  W(phi)^* K W(phi)=K+i[K,J(phi)]
000213 |                        +1/8 sum_(m>0)m^2|phi_m|^2 I.
000214 | Each term of [K,J(phi)] shifts source energy by a nonzero integer/8.
000215 | All five original P_i have K=4 and Q=0, so their complete matrix obeys
000216 |  <P_i,W(phi)^* K W(phi)P_j>
000217 |    =[4+1/8 sum_(m>0)m^2|phi_m|^2] B4_ij.
000218 | Here B4 means the actual Gram in the chosen raw/normalized input convention,
000219 | consistently on both sides. It is a matrix-element identity, not a performed
000220 | projection. The extra mean work is scalar on this whole input packet even
000221 | though the full coherent kernel in section3 is direction dependent. Thus
000222 | the mean energy response alone also supplies no3+2 distinction. This is
000223 | not a derived profile-minimization principle or all-energy-statistics no-go.