Byoungwoo Lee

A Certified Lower Bound for the Localized Weil Positivity Frontier Across the Prime-7 Threshol

Version v2.0 We prove a computer-assisted full-domain positivity theorem for Suzuki’s localized Weil quadratic form at $$X = \frac{701}{100} = 7.01, \qquada = \frac{1}{2}\log\frac{701}{100}= 0.9736688505232493612\dots.$$ At this endpoint the active von Mangoldt ledger is $\{2,3,4...

A Certified Lower Bound for the Localized Weil Positivity Frontier Across the Prime-7 Threshol

Version v2.0 We prove a computer-assisted full-domain positivity theorem for Suzuki’s localized Weil quadratic form at $$X = \frac{701}{100} = 7.01, \qquada = \frac{1}{2}\log\frac{701}{100}= 0.9736688505232493612\dots.$$ At this endpoint the active von Mangoldt ledger is $\{2,3,4...

Macroscopic Core Rigidity and Endpoint-Amplified Non-Parseval Defects in Bandwidth-One Weil-Certificate Sources

This paper studies the surviving common-depth branch of a bandwidth-one Weil-certificate source model after Stein normalization and weighted-exponential provenance have been imposed. The analysis develops a structural rigidity chain from deep-source order growth and fixed-scale f...

Finite-R Poisson Transfer for Mellin-Neutralized Incomplete Eisenstein Observables I: Effective Aggregate Sarnak–Zhao Identification and Logarithmic Persistence

This paper provides the technical proof carrier for the finite-$R$ reconstruction of harmonic quantum variance for a Mellin-neutralized moving family of incomplete Eisenstein observables on the modular surface. Starting from the exact parity-complete Kuznetsov decomposition $$S_R...

Primal–Dual Mellin Neutralization for Arithmetic Quantum Observables: Incomplete-Eisenstein Matrix Elements, Unconditional Logarithmic Persistence, and Noncommuting Limits

This work develops a theorem-level arithmetic-quantum application of primal–dual Mellin neutralization on the modular surface. The basic observables are incomplete Eisenstein series built from compact logarithmic windows, and the analysis combines exact Rankin–Selberg unfolding,...

Generic and Robust Schmidt Structure of Weighted Phase Networks: Matching Laws, Parameter Geometry, Higher-Order Obstructions, and Gauge-Centered Stability

This work develops a fixed-bipartition theory of Schmidt-rank capacity, parameter accessibility, higher-order algebraic obstruction, and quantitative Schmidt-spectrum stability for diagonal weighted phase networks acting on full-support product states. For a bipartition $V=P\sqcu...

Generic Schmidt-Rank Width of Fixed Weighted Phase Networks: Maximum-Matching Width, Template Diversity, and Single-Parameter Global Saturation

This work studies the global multipartite entanglement width generated by fixed pairwise weighted-phase networks acting on full-support product inputs. It develops the global-width consequences of the fixed-cut weighted-phase theory established in the preceding study, Schmidt-Ran...

Generic Schmidt-Rank Width of Fixed Weighted Phase Networks: Maximum-Matching Width, Template Diversity, and Single-Parameter Global Saturation

This work studies the global multipartite entanglement width generated by fixed pairwise weighted-phase networks acting on full-support product inputs. It develops the global-width consequences of the fixed-cut weighted-phase theory established in the preceding study, Schmidt-Ran...

Primal–Dual Mellin Neutralization for Arithmetic Quantum Observables: Incomplete-Eisenstein Matrix Elements, Exact Harmonic Variance, and Noncommuting Limits

This paper develops a theorem-level application of primal–dual Mellin neutralization to arithmetic quantum observables on the modular surface $$\operatorname{PSL}_2(\mathbb Z)\backslash\mathbb H.$$ Starting from compactly supported logarithmic profiles, we construct a common fami...

Boundary-Heat Pair Reconstruction for Ramanujan's Third-Order Mock-Theta Completion: Sesquilinear Spectral Packets and a Mellin Regulator Obstruction

This paper develops a boundary-heat and spectral reconstruction theory for a positive quadratic observable derived from the positive-frequency Fourier coefficients of Zwegers’ vector-valued completion of Ramanujan’s third-order mock theta functions. For a damping parameter $\sigm...

How Much Arithmetic Can Zero Data Recover? Localized Explicit Formulas, Bandwidth Obstructions, and a Spectral Inverse Program for L-Data

## Overview This preprint develops a deterministic spectral inverse framework for Booker's distributional $L$-data. Its central question is: > Which arithmetic coefficients can be recovered from specified observations of the zero distribution, and with what stability? The analysi...

How Much Arithmetic Can Zero Data Recover? Localized Explicit Formulas, Bandwidth Obstructions, and a Spectral Inverse Program for L-Data

## Overview This preprint develops a deterministic spectral inverse framework for Booker's distributional $L$-data. Its central question is: > Which arithmetic coefficients can be recovered from specified observations of the zero distribution, and with what stability? The analysi...