Enter, I-B-VP-9-v2, 2026, pp. 1-38
I-B-VP-9: Matrix-extension vacuum stress on a prescribed conical spacetime
Ngo Cheung
18 October 2026
Abstract
We study the massless scalar vacuum-stress correction produced by a non-diagonal, nonnegative boundary matrix in the two-deficiency-channel sector of a prescribed four-dimensional conical product. The proposed reduction to a finite Bernoulli polynomial is false: a finite boundary matrix introduces length scales, and even a positive diagonal example has a nonconstant radial crossover. More sharply, its stress coefficient is a Stieltjes transform with a continuous, nonzero density and is therefore not rational in the boundary parameter. This obstruction persists for conformal coupling, despite the vanishing regular trace.
We replace the impossible algebraic target by an exact construction. After deriving the boundary normalization, we express every moment needed for the complete regular stress tensor and charged current as a finite combination of explicitly defined, absolutely convergent three-variable Mellin–Barnes functions. The formulas apply to unequal channel orders, retain angular interference and the radial current, and extend continuously to every finite positive-semidefinite boundary matrix. Scalar conservation and the mixed-trace identity follow analytically from the smooth bisolution correction. Friedrichs, singular scale-invariant, diagonal scale-dependent, and equal-order projector limits are recovered.
The principal contribution is a convention-complete resolution of what finite boundary rank does and does not simplify: the tensor assembly is finite, but generic radial dependence is genuinely non-algebraic. The result supplies exact crossover functions and a controlled special-function representation rather than an unsupported polynomial closure. The geometry, extension, field normalization, and subtraction remain inputs. No finite Enter record extracts a continuum observable; no apex contact normalization, interacting gauge theory, Einstein dynamics, backreaction, or spacetime emergence is inferred.
Bibliographic record
- Title
- I-B-VP-9: Matrix-extension vacuum stress on a prescribed conical spacetime
- Author
- Cheung, Ngo
- Publication date
- 2026/10/18
- Institution
- Enter
- Report number
- I-B-VP-9-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 38
- Language
- en