Byoungwoo Lee

From Finite Certificates to Uniform Coercivity in Localized Weil Eight-Mode Comparisons

## Version v1.0 We prove a computer-assisted uniform coercivity theorem for the parity-complete eight-mode comparison arising from a localized Weil quadratic form throughout the arithmetic cell $$5.01 \le X < 7.$$ The main result is $$D_{X,8} \succeq 0.20 I\qquad\text{for every r...

From Finite Certificates to Uniform Coercivity: Loewner–Schur Propagation for Localized Weil Comparisons

We develop a quantitative finite-certificate method for proving uniform coercivity of parameter-dependent Hermitian block families and apply it to a localized Weil eight-mode comparison on 5.01 <= X < 7. The main analytic result is a fixed-target Loewner-Schur propagation theorem...

From Finite Certificates to Uniform Coercivity: Loewner–Schur Propagation for Localized Weil Comparisons

We develop a quantitative finite-certificate method for proving uniform coercivity of parameter-dependent Hermitian block families and apply it to a localized Weil eight-mode comparison on 5.01 <= X < 7. The main analytic result is a fixed-target Loewner-Schur propagation theorem...

Inverse-Casimir Geometry of Nonunital Multipole Transport in Linear-Spin Lindbladians

## Overview This preprint studies the canonical Gorini--Kossakowski--Sudarshan--Lindblad (GKLS) class generated by jump operators linear in the generators of a fixed irreducible spin-$j$ representation. Writing the positive Kossakowski matrix as $C=R+iA$, with $R$ real symmetric...

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

Version v3.0 We prove a computer-assisted full-domain positivity theorem for Suzuki’s localized Weil quadratic form at $$X = \frac{701}{100} = 7.01, \qquad a = \frac{1}{2} \log \frac{701}{100} = 0.9736688505232493612\dots.$$ The main result is $$\lambda_{\frac{1}{2}\log(701/100)}...

Finite-Depth Hard Arithmetic Localization and Near-Cramér Chebotarev–Sato–Tate in Growing Arithmetic Progressions

This paper isolates a packet-to-selector mechanism that converts finite-depth analytic information on degree-controlled $L$-functions into normalized harmonic moments on literal moving prime intervals subject to arithmetic selectors. The analytic packet is required to have degree...

Joint Sato–Tate Localization near the Cramér Scale in Growing Arithmetic Progressions

Let $E_1, E_2 / \mathbf{Q}$ be fixed twist-inequivalent non-CM elliptic curves. This paper studies the joint Sato–Tate distribution of the Frobenius angles $$(\theta_{1,p}, \theta_{2,p}) \in [0,\pi]^2$$ for primes constrained simultaneously by a literal moving interval $$X < p \l...

Joint Sato–Tate Localization near the Cramér Scale in Growing Arithmetic Progressions

Let $E_1, E_2 / \mathbf Q$ be fixed twist-inequivalent non-CM elliptic curves. This paper proves a conditional joint Sato–Tate theorem for primes constrained simultaneously to a literal moving interval $(X, X+h]$ and a reduced residue class $a \pmod q$, with the modulus $q = q(X)...

Finite-Depth Hard Arithmetic Localization and Near-Cramér Chebotarev–Sato–Tate in Growing Arithmetic Progressions

We develop a finite-depth hard arithmetic localization principle that converts a degree-controlled finite packet of twisted $L$-functions into normalized harmonic-mode estimates inside literal moving prime intervals with arithmetic selectors. The central mechanism separates the a...

Trace-Class Følner Selection and Observability Barriers in Localized Weil–Parent Systems

## Overview This paper develops three operator-theoretic mechanisms for soft-to-hard arithmetic selection and applies them to a localized Weil--parent transfer problem. The first mechanism is a mass-retaining trace-class Følner selection principle: a positive trace-class operator...

Nonunital Multipole Transport in Linear Spin Lindbladians: Exact Rank Hopping and Universal Block Nonreciprocity

## Description This preprint gives an exact classification of tensor-rank transport generated by the canonical Gorini-Kossakowski-Sudarshan-Lindblad (GKLS) class with jump operators linear in the generators of a fixed irreducible spin-$j$ representation. When Hamiltonian terms ar...

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 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...

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...

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...