Enter, I-B-VP-5-Ex1-B-v2, 2026, pp. 1-49
I-B-VP-5-Ex1-B Audited running, uniform core finite parts, and equal-radius non-universality
Ngo Cheung
18 October 2026
Abstract
We analyze renormalized free scalar observables on smooth rotational curvature cores with a prescribed conical exterior. The heat-coefficient normalization is audited directly from the real-scalar determinant, inverse-metric variation, and Wick rotation. A lapse calculation and a constant-curvature spectral calculation agree on the stress running. An explicit all-order derivative bound supplies a bookkeeping table for longitudinal, radial, angular, and mixed exterior mode sums, including orders below one in the twisted sector.
The main additional analytical result is uniform boundedness and continuity of the complete scalar and conformal stress finite constants on a specified uniformly regular profile class. The proof combines a uniform local heat parametrix, a profile-uniform infrared estimate, and the exterior logarithmic tails. This continuity gives a stronger universality verdict than the nominal-radius argument alone: for every fixed core-adapted scale, finite-part universality also fails among smooth profiles whose minimal curvature-support radius is exactly the same. The proof uses smooth endpoint-anchored approximations and does not require unexecuted numerical comparisons of interior stresses.
For a supplied smooth magnetic flux, the complex-determinant normalization is independently checked against the constant-field heat spectrum. We distinguish physical lowering from auxiliary Cartesian lowering and obtain the corresponding current-moment conversion factor explicitly. We also construct the trace sector of the conformal thin-core expansion through its finite second-derivative contact; this exhibits a power-divergent trace-bearing contact that projected stress moments cannot see.
The potential contribution is a controlled passage from exterior scattering bounds to stable interior finite parts, together with an equal-minimal-radius non-universality theorem. No priority is claimed for heat-kernel renormalization, cosmic-string core effects, or flux regularization. The complete stress-tensor limit, finite charged-current contact, interacting products, and gravitational response remain separate tasks. Enter supplies a finite record–residual interface, not a continuum acquisition or source law.
Bibliographic record
- Title
- I-B-VP-5-Ex1-B Audited running, uniform core finite parts, and equal-radius non-universality
- Author
- Cheung, Ngo
- Publication date
- 2026/10/18
- Institution
- Enter
- Report number
- I-B-VP-5-Ex1-B-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 49
- Language
- en