TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/W8-ORIGINAL-STRESS-RECONSTRUCTION.txt
Original file SHA-256: e6d33823484092c52b709ff16ddf6aa166e0614c4d599248dc3f2a588933bd90
Inclusive original lines: 130-184
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.

000130 | 5. Full separated response and source-state reconstruction
000131 | ----------------------------------------------------------
000132 | Equation(5) applies separately to EVERY v_ell, since each is neutral and
000133 | has original grade8ell. Therefore the existing positive-semigroup smoothing
000134 | 
000135 |  Psi_epsilon=sum_ell exp(-epsilon ell)v_ell, epsilon>0,
000136 | 
000137 | belongs to the closed ORIGINAL stress cycle. Its norm is finite by the
000138 | already proved full W8 two-point function. It lies outside the smaller
000139 | folded cycle by(6), and inside the original cycle by(5). These are compatible.
000140 | 
000141 | This is an all-level theorem. The grade8 computation is its smallest direct
000142 | W8 certificate, not a claim that finitely many levels prove all the others.
000143 | The weight8 homogeneous W8 source state is at original grade64; it too lies
000144 | in the original stress span, by(5), without a million-dimensional scan.
000145 | No finite approximation is presented as the whole infinite source.
000146 | 
000147 | 6. Consequence for the actual P1 problem
000148 | ---------------------------------------
000149 | The existing original source already has the global neutral state space
000150 | needed by W8. A new oscillator, source, ground-state choice, or additional
000151 | nonstress generator is not forced by the folded obstruction. This removes
000152 | an artificial extra requirement from the route.
000153 | 
000154 | A second, conditional economy follows. If the original P1 data yield the
000155 | SAME c1 Virasoro representation with h1/32, state, adjoints and positive
000156 | time, their cyclic stress-sector isometry is fixed on every descendant.
000157 | It then transports these state vectors and their time exactly on that
000158 | cyclic image. This sufficient conditional map has not been derived from
000159 | the original P1 boundary kernel by this theorem.
000160 | 
000161 | GLOBAL cyclicity does not identify the proper-interval local algebras.
000162 | It does not prove that a transported operator is the actual P1 W8 insertion
000163 | with the original eight-arc supports, point splitting and collar/reflection
000164 | domains. It does not provide a single unitary pulse preparing a pure W8
000165 | state. The local P1 image, charged seam map and full source action/measure
000166 | remain separate obligations. In particular, P1 is not redefined as this
000167 | already available CAR representative.
000168 | 
000169 | The next original calculation should use the already existing full stress
000170 | and geometric source jet, with the phase/current part retained, to construct
000171 | the local field image. Repeating the folded-only selection scan or the old
000172 | microscopic neutral-field construction is unnecessary. The charged E8
000173 | spinor extension is not a prerequisite for this neutral current composite.
000174 | 
000175 | Sources
000176 | -------
000177 | paper-source-reconstruction-20261025/ORIGINAL-CAR-WARD-IDENTIFICATION.txt:9-100.
000178 | native-octic-seam-origin-20261025/native_folded_octic_origin.py:115-133.
000179 | v16-operator-pullback-20261014/fold-results.json: actual M.
000180 | original-admissible-source-closure-20261025/quantum-octic-completion-results.json.
000181 | original-admissible-source-closure-20261025/w8-source-twopoint-results.json.
000182 | https://arxiv.org/abs/hep-th/9108023, section2, equations2.2-2.8.
000183 | 
000184 | All local source paths above are under experiments/theory-contracts/.