Enter, I-B-VP-1-Ex1-v2, 2026, pp. 1-51
I-B-VP-1-Ex1 Worldsheet domains, core diagnostics, and first-order apex dependence
Ngo Cheung
18 October 2026
Abstract
We strengthen and qualify the apex constructions of I-B-VP-1 on a prescribed conical product, without changing its background, state-selection inputs, or standing interaction boundaries. The principal results concern domains rather than formal apex values. For the Friedrichs scalar field, we construct the timelike-worldsheet restriction as a strong limit on the finite-particle domain, identify its one-particle range and exact two-point function, and prove that the restriction is zero in nontrivial holonomy sectors. For deficient modes, weighted boundary values have an explicit positive matrix Källén–Lehmann representation; their Wick squares exist as worldsheet-smeared operators, but are not themselves generalized free fields. A second result supplies an analytic −1/(4π) double-logarithmic coefficient for an explicitly normalized exterior core diagnostic, and proves negative-coupling instability directly on the core geometry, avoiding an unjustified transfer of a Euclidean weak-binding theorem. At first order in λφ⁴, two disjoint local subtractions define the tadpole, its finite constant is absorbed by an explicit contact-coordinate change, and the off-apex response to the free contact is calculated exactly. Finally, a Mellin criterion makes the U(2) resonance exclusion precise, an explicit boundary-chart example develops a logarithm, and a supported tensor counterexample shows why the previously stated broad Killing–homothety uniqueness conclusion requires an additional normalization condition. The potential significance is a sharper distinction between bulk-derived boundary operators, observable contact limits, and spatial operator limits. No interacting apex algebra, universal core selection, resonant classification, or all-orders interaction is claimed.
Bibliographic record
- Title
- I-B-VP-1-Ex1 Worldsheet domains, core diagnostics, and first-order apex dependence
- Author
- Cheung, Ngo
- Publication date
- 2026/10/18
- Institution
- Enter
- Report number
- I-B-VP-1-Ex1-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 51
- Language
- en