Enter, I-B-G-S-B-v2, 2026, pp. 1-44
I-B-G-S-B Positive tensor-core selection and validated conical-kernel error bounds
Ngo Cheung
18 October 2026
Abstract
We study two proposed extensions of the prescribed-cone spin-1/spin-2 construction of I-B-G-S: smooth-core selection and irrational-angle validation. An essential correction is that a smooth metric and its holonomy do not specify a gravitational perturbation operator.
For an explicitly declared class of nonnegative tensor connection forms, including the Riemannian Lichnerowicz Laplacian on the smoothed conical product, we prove profile-uniform Mosco and strong-resolvent selection of the componentwise Friedrichs realization. The tensor spin connection is calculated rather than replaced by independent scalar fluxes. In the neutral exceptional spin-2 channels, this excludes the singular curvature-regular realization used by the idealized source-test Ward construction. We obtain exact signed power-law matching data and localized resolvent bounds, including a separate logarithmic treatment at order zero. Thus a natural positive tensor smoothing and an idealized gauge-compatible boundary criterion need not select the same domain. This is a class-relative operator theorem, not a selection theorem for a coupled matter–gravity core.
For kernel validation we give explicit angular-tail bounds, a uniform complex-neighborhood bound for the subtracted kernels, a multidimensional Cauchy-coefficient error estimate, and a rounding-error contract for interval evaluation. Exact rational enclosures are supplied for the analytic target coefficients at two irrational opening ratios. These are analytical enclosures, not an independently executed full-kernel comparison. The predecessor's code, raw outputs, and error certificates were not supplied as executable artifacts; its numerical reports therefore cannot honestly be promoted to certified runs in this release.
The potential contribution is the positive-core exclusion theorem and a reproducible validation interface that separates kernel truncation, differentiation, input, and arithmetic errors. No priority is claimed for conical Green functions, inverse-square extensions, or interval arithmetic. Physical gravitational core selection and the independent irrational-angle execution remain open. No state transfer, one-point contact normalization, interacting quantum coefficient, or source law follows.
Bibliographic record
- Title
- I-B-G-S-B Positive tensor-core selection and validated conical-kernel error bounds
- Author
- Cheung, Ngo
- Publication date
- 2026/10/18
- Institution
- Enter
- Report number
- I-B-G-S-B-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 44
- Language
- en