Reuse full current functional of existing elliptic Gaussian source
The free kernel supplies current operators,state,all Weyl words and neutral native field correlations. The local neutral state witness prevents silently replacing Hardy.
For a new attempt: Derive original P1 source measure and local insertion map. Free candidate fixes four-point functions by Wick;primitive interactions must be checked against it. Do not identify source interventions with spectral-action variations.
Coupled differential contract derived and endpoint self-consistency excluded as sufficient selection. This does not determine the full physical history.
For a new attempt: Identify actual original P1 geometry/field insertion with its first response;for the fixed seam transfer retain delta g->delta q and residual/reference terms instead of choosing new free spectral profiles.
Derive conformal boundary trace before geometric four-point mixing
The positive boundary transport follows from the Dirac law and boundary density without a free trace fit. It preserves the complete Cauchy projection and existing free boundary source. Conformal factors alone produce no non-Wick correction under this identification.
For a new attempt: For the primitive P1 four-field comparison identify an original variation changing the transported covariance or an original higher fermion vertex. Preserve the unresolved full marked graph real trace/domain and the free conditional quantization premise; do not replace them by arbitrary couplings.
Derive causal geometric response of the retained seam defect
Relative source response with contact/memory and protection of the scalar factor are calculated. An originally selected geometry history does not yet follow.
For a new attempt: Compare actual admissible P1 geometry/field insertion and original residual sector variationR with measure,reference,state,time and domains to the explicit response kernel. Do not replace the complete native field action by q_min alone or this single bilinear response.
Derive the positive full projection source before an additional four-point fit
Full positive CAR projection covariance forces every word without an extra Gaussian assumption. The existing joint Cauchy graph supplies the precise target including X_A;the single mixed face marginal does not.
For a new attempt: Derive the actual original joint CAR insertion map and covariance including cross kernel from the real marked carrier. Do not infer it from a chosen purification. If the actual kernel differs from the projection target,retain it and its higher vertices.