TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/e-series-source-reconstruction-20261024/SCALAR-QUARTER-REPRODUCTION.txt
Original file SHA-256: 16e123a72d0d65e48fc1777bbc0b3a10a7585114c3f82bad33c87e0794e15f94
Inclusive original lines: 151-174
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.

000151 | 5. Reproduce the first energy norm on the original v988 state
000152 | 
000153 | Use UNCHANGED qwz_cylinder and occ_frame from v988, Nx=16,Ny=6,M=1,
000154 | twist0 for h0 and twist1 for the half-filled Slater projector P=V1 V1*.
000155 | For H=dGamma(h0), E=Tr(P h0), Wick's rule gives exactly
000156 | 
000157 |     ||(H-E)Omega_P||^2
000158 |       =Tr(P h0(1-P)h0 P)=||(1-P)h0P||_HS^2.             (5.1)
000159 | 
000160 | The actual192 dimensional case has rank(P)=96 and yields
000161 | 
000162 |     E=-146.6160592878,
000163 |     variance=7.0875042817,
000164 |     true f1=2.6622367065.
000165 | 
000166 | The trace and HS expressions agree within1e-9; the algebraic identity
000167 | is exact. In contrast, the original proxy sum_j(e_occ,j-mean(e_occ)) is
000168 | identically0. Its fitted C=1.2040009128 gives C^2=1.4496181980, BELOW the
000169 | actual f1. Thus this fitted proxy cannot serve as the claimed energy-
000170 | norm bound, even for its own finite case. This is not a disproof of every
000171 | larger bound C, the separate historical probe C=2.86, or all continuum
000172 | energy estimates. The original script calls these quantities shadows;
000173 | they must not be reused as the operator estimate required in G1.
000174 |