Enter, I-B-VP-1-Ex3-v2, 2026, pp. 1-50
I-B-VP-1-Ex3 Uniform cut estimates, logarithmic concentration, and worldsheet subtraction
Ngo Cheung
18 October 2026
Abstract
We continue the domain-explicit apex analysis of I-B-VP-1-Ex2 on the prescribed conical product. For nonnegative compressed positive-order boundary charts, we replace an unspecified ultraviolet polynomial by explicit three-region bounds for the spectral density of the weighted radial-to-boundary difference. The region √(τ) r ≥ 1 is controlled uniformly in the nonnegative boundary matrix, and its smeared contribution has arbitrarily high algebraic order in r. This supplies a direct quantitative justification of the untruncated boundary limit and its Wick-quadratic consequence on the stated energy-cutoff finite-particle domain.
For exterior core diagnostics, we allow measurable reflection profiles with only weighted-integrable ultraviolet tails. Logarithmic-power behavior at zero produces a unified concentration law, including the coefficient −1/(4π) in the double-logarithmic case, with explicit test-uniform and profile-remainder bounds. A moment expansion separates scalar contacts, dipoles, and quadrupoles, showing precisely why exterior information does not determine an assembled physical contact.
We also extend the relative-worldsheet logarithmic primitive against smooth parameter-dependent amplitudes, prove a fixed-external-support C^k estimate for a switched bulk-to-worldsheet-to-bulk numerical sandwich, and calculate both Laurent coefficients at the infinite family's resonant Mellin pole. The logarithmic coefficient has an exact phase-sensitive cancellation criterion; its companion constant is given by gamma and digamma functions. An explicit higher-rotation-weight KH contact supplements the polar-vector admissibility audit.
The potential usefulness lies in replacing formal apex assignments by quantitative domain, concentration, and normalization tests. No priority is claimed for Bessel extensions, generalized free fields, or local distributional renormalization. The complete physical core limit, unrestricted resonance and contact classifications, Dirac discrepancy, and interacting completion remain open.
Bibliographic record
- Title
- I-B-VP-1-Ex3 Uniform cut estimates, logarithmic concentration, and worldsheet subtraction
- Author
- Cheung, Ngo
- Publication date
- 2026/10/18
- Institution
- Enter
- Report number
- I-B-VP-1-Ex3-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 50
- Language
- en