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: 174-197
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.

000174 | 7. Information retained and information the test cannot select
000175 | ---------------------------------------------------------------
000176 | The actual orthogonal root automorphism g=-M R M^-1, with R coordinate
000177 | reversal, takes d_(1/4) to d_(3/4), fixes W8 and preserves N. It intertwines
000178 | the Heisenberg Fock representations of these two real charge modules.
000179 | Therefore ALL separated pure W8 correlation functions in the two charge
000180 | states agree, not merely (4). This does not identify charged CAR fields,
000181 | the full marked clock tuple or their geometric P1 supports. A W8-only test
000182 | cannot choose between these two quarter labels.
000183 | 
000184 | At the same time the source is not an exact finite-state dynamics. For
000185 | every ell>=1, the convergent expansion of (6) has
000186 | 
000187 |  a_ell=sum_(r=1)^min(ell,8) binom(ell+r-1,2r-1)A_r
000188 |         >=ell A1>0.                                     (7)
000189 | 
000190 | Hence infinitely many distinct N levels occur. To avoid any point-field
000191 | domain issue, apply the existing positive semigroup e^(-epsilon N) to the
000192 | one-insertion vector. Its spectral coefficients become
000193 | a_ell exp(-2epsilon ell)>0 and its norm is finite for every epsilon>0.
000194 | The cyclic time subspace is still infinite dimensional. No finite spectral
000195 | support with this same time generator can reproduce its exact two-point
000196 | function. Finite approximations and finite native observation codes remain
000197 | possible; they are not the complete local source dynamics.