Enter, I-B-VP-1-Ex2-v2, 2026, pp. 1-55
I-B-VP-1-Ex2 Spectral tails, exterior contact limits, and admissibility on a prescribed conical spacetime
Ngo Cheung
18 October 2026
Abstract
We continue the corrective apex analysis of I-B-VP-1-Ex1 on the prescribed conical product, without enlarging its interacting or gravitational claims. The main advance is quantitative control of the operations that precede an apex interpretation. An elementary angular Bessel estimate gives a norm rate for the Friedrichs worldsheet restriction, including its vanishing in nontrivial holonomy sectors. For every nonnegative compressed positive-order boundary chart, we prove a matrix Källén–Lehmann formula, uniform threshold and ultraviolet bounds, and an untruncated weighted boundary limit in the original spectral Fock representation. These estimates also establish radial convergence of Wick quadratics on a common dense, energy-cutoff finite-particle domain; they do not assert convergence on arbitrary finite-particle vectors.
A second result upgrades the exterior core diagnostic from a scalar asymptotic to strong distributional concentration. After subtraction of its analytic −1/(4π)log log (b/R) term, the exterior zero-mode correction converges to a worldsheet contact. A separate moment criterion states exactly when additional core contributions preserve that coefficient. An explicit shrinking-core perturbation shows why exterior data alone cannot determine the complete contact.
We also prove fixed-external-support estimates for the two independent tadpole subtractions, retain the finite contact reparametrization, exhibit an infinite family of actual boundary-chart Mellin logarithms, and classify the Killing–homothety first-jet counterexample in a specified rotation-equivariant submodule. The potential usefulness is a controlled separation between bulk-derived boundary operators, exterior concentration, and a physically normalized defect observable. No priority is claimed for generalized free fields, Bessel extensions, or codimension-two renormalization. The full core-contact problem, unrestricted resonance and contact classifications, Dirac discrepancy, and interacting completion remain open.
Bibliographic record
- Title
- I-B-VP-1-Ex2 Spectral tails, exterior contact limits, and admissibility on a prescribed conical spacetime
- Author
- Cheung, Ngo
- Publication date
- 2026/10/18
- Institution
- Enter
- Report number
- I-B-VP-1-Ex2-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 55
- Language
- en