TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/P1-W8-LOCAL-MAP-AND-TWOPOINT-TEST.txt
Original file SHA-256: 072b6588666504ec4f04024e279030bbdf83b724102bac181ee3696133c1be28
Inclusive original lines: 146-173
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000146 | 6. A concrete failed candidate: replacing the shifted source by vacuum
000147 | ----------------------------------------------------------------------
000148 | For q=exp(-tau), subtract the disconnected term A0 and obtain
000149 | 
000150 |  C_conn(tau)=sum_(r=1)^8 A_r/[4sinh^2(tau/2)]^r.           (6)
000151 | 
000152 | Every A_r in this actual source is strictly positive. Its lowest spectral
000153 | coefficient is
000154 | 
000155 |  a1=A1=93237295693374937125/15629680934138150912 >0.
000156 | 
000157 | For the unshifted vacuum the exact answer is only ||W8||^2 X^8, whose
000158 | spectral coefficients at levels1 through7 vanish. Thus a map preserving
000159 | the state, the same radial generator and this W8 insertion cannot replace
000160 | the actual quarter source by that vacuum. This rejects a specific proposed
000161 | dictionary, not every original P1 seed.
000162 | 
000163 | The generator conversion is explicit:
000164 | 
000165 |  N=Lhat0-85/256=(Lcal0^alpha-1/32)/8=K_alpha,
000166 |  H0=Lcal0^alpha-1/32=8N
000167 | 
000168 | on the folded neutral sector. The lowest shifted connected response has
000169 | N-level1 and original H0-grade8. The homogeneous unshifted W8 state has
000170 | N-level8 and H0-grade64. Conformal weight, the grade of a vacuum state and
000171 | the first response on a shifted source must not be confused. Neither tau
000172 | nor the circle convention is an absolute calibration to physical seconds.
000173 |