Enter, I-B-VP-5-v2, 2026, pp. 1-35
I-B-VP-5: Curvature-core selection on the prescribed conical Enter spacetime
Ngo Cheung
October 17, 2026
Abstract
We resolve a curvature-coupling selection problem in a specified untwisted sector of the prescribed conical spacetime of I-B. The additional geometric data are smooth rotational cores
q_{ε} = P_{ε}(r/ε)²dr² + α²r²dφ² + dz²,
where 0 < α < 1, each profile increases from α to 1, and the exterior is exactly conical. For every fixed ξ ≥ 0, the operators −Δ_{q_{ε}} + ξR_{ε}, after a declared unitary identification of their Hilbert spaces, converge in the strong resolvent sense to the Friedrichs cone operator. The theorem permits profiles varying with ε and requires no uniform bounds on their derivatives. Nevertheless, the curvature densities converge to the nonzero measure 4π(1 − α)δ_{𝒲}. Thus a concentrated curvature measure does not determine the limiting operator coupling by ordinary multiplication.
For a fixed profile, exact zero-energy matching gives L_eff(ε) = εexp [−1/d(P, ξ)]. Its finite-radius value depends on the profile, whereas its boundary-relation limit is Friedrichs. We give quantitative bounds, an explicit profile functional in the weak-coupling expansion, and an exterior zero-mode resolvent estimate. These distinguish finite-core fitting from a zero-thickness operator limit.
For the alternative distributional model, the ordinary positive point-evaluation energy is not closable. On a declared logarithmic maximal domain, however, a one-parameter family of well-defined renormalized curvature products realizes every finite logarithmic extension at the same curvature measure and coupling. The resulting non-selection theorem identifies the missing datum as a product prescription, not an observable contact. The contribution is a convention-complete selection criterion and obstruction within this ledger, not the discovery of two-dimensional scattering lengths. No state convergence, apex observable normalization, scalar or Einstein backreaction, or field acquisition by Enter reporting is inferred.
Bibliographic record
- Title
- I-B-VP-5: Curvature-core selection on the prescribed conical Enter spacetime
- Author
- Cheung, Ngo
- Publication date
- 2026/10/17
- Institution
- Enter
- Report number
- I-B-VP-5-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 35
- Language
- en