TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/ELLIPTIC-GREEN-RP.txt
Original file SHA-256: d8799f04851a9bd539b05b4d013b38eb00de9bec07dddde6438023aaf1facd80
Inclusive original lines: 191-238
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.

000191 | 
000192 | The constant spin-lift phase of U_Q cancels in (12) and in every neutral
000193 | Gaussian expectation. It is the already fixed alpha lift, not a new fitted
000194 | phase. Equations (11)-(12) show exactly how Q transports the two OS halves:
000195 | it exchanges the charge covariances and reverses winding. It is not an
000196 | internal time translation of either annulus.
000197 | 
000198 | 6. What has and has not been closed
000199 | ====================================
000200 | 
000201 | PROVED: the actual NS--NS elliptic Szego kernel equals the spectral Green
000202 | kernel of partial_t+B with the normalization (3).
000203 | 
000204 | PROVED: the Schottky reflection rho=-bar(z), together with the fixed constant
000205 | field phase in (6), is positive for both charged blocks and all free Gaussian
000206 | CAR words supported in 0<t<1/2.
000207 | 
000208 | PROVED: the full free Gaussian Green state has the labeled marginal of the
000209 | same finite-width Calderon graph already found on this elliptic annulus, and
000210 | that graph supplies its canonical two-face purification.
000211 | 
000212 | PROVED: winding preserves the actual Sobolev domain, is inverted by Theta,
000213 | and Q transports the paired cuts by B->-B, C->1-C and u->u^-1.
000214 | 
000215 | OPEN: identification of this elliptic free Gaussian source with the primitive
000216 | P1 kernel, the interacting measure, the old Hardy W8 state or physical OS
000217 | time. The theorem supplies a concrete same-E candidate for that remaining
000218 | map; it does not assume the map.
000219 | 
000220 | Sources reused
000221 | ==============
000222 | 
000223 |   research-20261026-fundamental-rethink/geometry/
000224 |   DIVIDING-REAL-FORMS.txt
000225 | 
000226 |   research-20261026-fundamental-rethink/primitive/
000227 |   ANNULUS-TO-ORIGINAL-SEAM-SOURCE.txt
000228 | 
000229 |   research-20261026-p1-reflection/
000230 |   NS-COVER-FULL-DIRAC-RP.txt
000231 |   NS-COVER-GREEN-RP-INDEPENDENT-REVIEW.txt
000232 | 
000233 | Method comparison only:
000234 | 
000235 |   A. Jaffe and G. Ritter, Reflection Positivity and Monotonicity,
000236 |   arXiv:0705.0712v2, section 4.2.
000237 | 
000238 | No Atlas record or canonical project source was changed.