3145 — The Polarized Heat Boundary Morphism Is Canonical but Not Positive
Nonnegative heat profiles give positive regulated polarized kernels. Their source-derived Mellin finite part canonically recovers , so the exterior observer is regulator independent at the scalar level.
The finite-part map does not preserve positivity. At , the regulated Gaussian theta sum is positive, while Jacobi inversion gives the canonical finite part
Thus the boundary observer is not another positive Gram vector. Its faithful carrier is a relative pair consisting of the positive regulated bulk and the signed heat wall.
Scope
This closes the positive-extension shortcut for the polarized zeta kernel. It does not rule out a larger positive completed theta energy with reciprocal sewing and all boundary currents retained.
Durable verification
- Research packet: research/grothendieck/the-polarized-heat-boundary-morphism-is-canonical-but-not-positive.md
- Exact checker: research/grothendieck/checkers/check_polarized_heat_boundary_not_positive.py
- Sequence claim: seqclaim-2477f9cb81f11e15d0302adb
- Graph event: ev-000000006465-d5896755-0e2c-4d87-a2bc-929df461990a