Enter, I-B-VP-2-v2, 2026, pp. 1-40

I-B-VP-2: The exact global wavefront relation of the conical Friedrichs ground state

Ngo Cheung

October 2026

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Abstract

We determine the ordinary global wavefront set of the massless holonomy-twisted Friedrichs spectral ground-state covariance on the regular conical spacetime prescribed in I-B. The result is an equality, valid for every opening 0 < α < 1 and fractional holonomy 0 ≤ β < 1, including the angular transition where a geometric front meets the apex-diffracted front.

Let 𝒢⁺ be the closure of the positive-frequency relation of regular null geodesics, including its diagonal limit, and let 𝒟ₐₚ⁺ be the positive conormal relation of

(t − t^{′})² = (r + r^{′})² + (z − z^{′})².

Then

WF (W_{β}) = { 𝒢⁺,, α = 1/N, β = p/N,; 𝒢⁺ ∪ 𝒟ₐₚ⁺,, otherwise, }

where N ≥ 2 and p = 0, …, N − 1. Thus the full strictly diffractive relation disappears exactly in the finite-character quotient sectors. In other sectors it remains in the joint wavefront set even at isolated angular zeros of its leading coefficient.

The proof sums the Euclidean angular modes before continuation, uses a two-variable meromorphic expression to control every angular transition, and combines its reduced-variable structure with the bisolution equations. It also gives the explicit inverse-square-root diffractive coefficient and its half-order regularity improvement away from transition angles.

The contribution is a convention-complete global analysis of the specified covariance within the companion framework, not a claim of priority for conical diffraction. It distinguishes local Hadamard subtraction from a global geodesic-only spectrum condition. In particular, supported Green-operator agreement does not identify vacuum covariances, and the charged commutator is not the pointwise imaginary part of one complex bundle kernel. The result resolves V2 for this state and extension at the level of the ordinary two-point wavefront set. It neither restores global hyperbolicity nor constructs an apex field algebra, an interacting product, a measurement acquisition of wavefront data, or a gravitational source law.

Bibliographic record

Title

I-B-VP-2: The exact global wavefront relation of the conical Friedrichs ground state

Author

Cheung, Ngo

Publication date

2026/10/01

Institution

Enter

Report number

I-B-VP-2-v2

Publisher

Cheung Ngo Medical Limited

First page

1

Last page

40

Language

en