Enter, I-B-VP-5-Ex2-v2, 2026, pp. 1-39
I-B-VP-5-Ex2 Smooth flux-core selection on a prescribed cone
Ngo Cheung
18 October 2026
Abstract
We determine the zero-radius operator limits of a declared class of smooth rotational curvature and magnetic-flux cores on the prescribed conical product of spacetime Enter. The scalar and Dirac answers differ.
For the minimally coupled charged scalar with nonnegative curvature coupling, every admissible core family selects the twisted Friedrichs operator in the strong-resolvent sense, including families whose profiles vary with the core radius. The proof uses the correct magnetic form domain and does not transfer the untwisted global energy comparison. For each deficient scalar channel we obtain an exact signed zero-energy matching parameter,
(B_{ε})/(A_{ε}) = ε^{2ν}(ν − Λ_{ε})/(ν + Λ_{ε}), Λ_{ε} ≥ 0,
and an exterior localized resolvent estimate of order ε^{2ν}. Thus no singular scalar E₀ realization is selected within this positive-core class.
For the minimally coupled Dirac operator, with the spin structure that extends across the smooth disk, a separate first-order argument gives a profile-independent limit. In the window
|β − 1/2| < α/2,
the unique critical radial channel selects one explicitly stated chiral boundary condition. Its square has Friedrichs in one component and the singular nonnegative E₀ Bessel realization in the other. The proof constructs a smooth-core zero-mode continuation of the singular boundary generator, with a quantitative graph approximation; it does not infer a Dirac domain from independent scalar form limits.
The contribution is this profile-uniform cone implementation, the scalar–spinor contrast, and the normalized matching estimates. Flux regularization and Dirac/Pauli extension selection are established subjects, not priority claims of the Enter programme. The results identify which idealized domains arise from the specified cores, but do not normalize vacuum-polarization contacts, prove convergence of renormalized one-point functions, or construct an interacting state. The metric and flux remain inputs: no finite Enter record acquires a continuum operator, and no Einstein dynamics or spacetime emergence is inferred.
Bibliographic record
- Title
- I-B-VP-5-Ex2 Smooth flux-core selection on a prescribed cone
- Author
- Cheung, Ngo
- Publication date
- 2026/10/18
- Institution
- Enter
- Report number
- I-B-VP-5-Ex2-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 39
- Language
- en