Byoungwoo Lee

Weak Tensor Transfers, Finite Tensor Closure, and Coherence from Restricted Triple Products

Description We construct a finite-exception weak tensor operation for fixed automorphic representations of general linear groups by combining restricted triple-product harmonic analysis with converse-theorem methods. The analytic construction uses the proved affine-$\Psi$ Fourier...

Weak Tensor Transfers, Finite Tensor Closure, and Coherence from Restricted Triple Products

We construct a finite-exception weak tensor operation for fixed automorphic representations of general linear groups by combining restricted triple-product harmonic analysis with a converse-theorem argument. The analytic construction uses the proved affine-$\Psi$ Fourier–Poisson...

Dilation-Orbit Detection of the Generalized Riemann Hypothesis: Exact Arithmetic Growth, Moment Spectra, Polar Renormalization, and Filter Rigidity

We study dilation-orbit restrictions of the Weil quadratic form for reflection-Hermitian $L$-data with real logarithmic-derivative coefficients. Fix a nonzero real finite-step master profile $h$ with exact support hull $[\theta, 1]$, $0 < \theta < 1$, and allow only positive dila...

First-Hit Energy and Logarithmic Viscous Memory: A Continuation Criterion for the Three-Dimensional Navier–Stokes Equations

Version v1.0 This work develops first-hit continuation criteria for the classical three-dimensional incompressible Navier–Stokes equations near a hypothetical first singular time. The construction begins at the first time a high dyadic shell reaches the scale-invariant dissipatio...

Dilation-Orbit Detection of the Generalized Riemann Hypothesis: Exact Arithmetic Growth, Moment Spectra, Polar Renormalization, and Filter Rigidity

We study dilation-orbit restrictions of the Weil quadratic form for reflection-Hermitian $L$-data with real logarithmic-derivative coefficients. Fix a nonzero real finite-step master profile $h$ with exact support hull $[\theta, 1]$, $0 < \theta < 1$, and allow only positive dila...

A Calculus of Mellin-Residue Neutralization: Finite-Rank Scattering Geometry and Potential-Theoretic Spectral Filters

We develop a Mellin-residue calculus for removing finite-dimensional polar obstructions from multiplicatively localized observables. For \[ \mathcal M_X[K;\psi] = \int_0^\infty K(t)\psi(Xt)\,\frac{dt}{t}, \] Mellin inversion gives the exact factorization \[ \mathcal M_X[K;\psi] =...

Vanishing-Scale Sobolev Equidistribution for Rankin–Selberg-Weighted Satake Measures

We study the local Satake parameters at a fixed split prime $p$ in a prime-level family of holomorphic newforms, equipped with Petersson harmonic weights further tilted by the central Rankin–Selberg values $L(1/2, f \times g)$, where $g$ is a fixed self-dual dihedral cusp form as...

Calibration-Ready Josephson–SQUID Diagnostics for Weak Josephson-Energy Perturbations: Two-Junction Identifiability, Experimental Design, and Ramsey Closure

This work develops a device-parameterized, calibration-ready synthetic framework for detecting and discriminating weak Josephson-energy perturbations in an asymmetric split-junction superconducting circuit. The study is motivated by the broader Residual Clock–Energy program, but...

An Automorphic Scattering Realization of the Triple Symmetric-Cube L-Function

We construct a higher-rank automorphic scattering realization of the degree-64 triple symmetric-cube \(L\)-function attached to three pairwise geometrically non-isogenous non-CM elliptic curves over \(\mathbb{Q}\). Starting from two prior inputs—an intrinsic all-place completed \...

Boundary Completion and Coherent Finite Tensor Closure for Weak Automorphic Transfers

This paper completes the remaining rank-two boundary in a fixed-rank weak tensor-transfer construction for general linear groups and derives a coherent finite tensor-closure principle. The new argument treats the boundary case \(q=2\) by decomposing the isobaric first factor acco...

Boundary Completion and Coherent Finite Tensor Closure for Weak Automorphic Transfers

This paper completes the remaining rank-two boundary in a fixed-rank weak tensor-transfer construction for general linear groups and derives a coherent finite tensor-closure principle. The new argument treats the boundary case \(q=2\) by decomposing the isobaric first factor acco...

A Restricted-Poisson Converse Construction of Symmetric-Power Lifts for Non-CM Elliptic Curves

Version 2.1 is the version submitted to the Journal of the London Mathematical Society on 22 September 2026. Relative to Version 2.0, this release incorporates the final journal-facing revisions, including further clarification of the fixed-rank restricted-Poisson construction, l...

Hybrid Restricted Triple-Product Functional Equations and Weak Tensor Transfers for Fixed Symmetric-Power Pairs

Version 1.2 is a notation- and exposition-hardened revision of Version 1.1. The main theorems, mathematical scope, and proof architecture are unchanged. The principal revisions are as follows: the spherical Satake parameter and the spherical Satake isomorphism are now notationall...

A Unconditional Weak $\mathrm{GL}(12)$ Transfer for the $(2,3)$ Symmetric-Power Tensor (v3.1)

We construct a weak automorphic realization on $\mathrm{GL}_{12}(\mathbb A_{\mathbb Q})$ of the tensor parameter $$\operatorname{Sym}^2(\pi_i) \otimes \operatorname{Sym}^3(\pi_j),$$ where $\pi_i$ and $\pi_j$ arise from two non-CM elliptic curves over $\mathbb Q$. More precisely,...

A Unconditional Weak $\mathrm{GL}(12)$ Transfer for the $(2,3)$ Symmetric-Power Tensor (v3.1)

We construct a weak automorphic realization on $\mathrm{GL}_{12}(\mathbb A_{\mathbb Q})$ of the tensor parameter $$\operatorname{Sym}^2(\pi_i) \otimes \operatorname{Sym}^3(\pi_j),$$ where $\pi_i$ and $\pi_j$ arise from two non-CM elliptic curves over $\mathbb Q$. More precisely,...

A Conditional Weak $\mathrm{GL}(12)$ Transfer for the $(2,3)$ Symmetric-Power Tensor (v2.0)

We construct a conditional weak automorphic realization on $\mathrm{GL}_{12}(\mathbb A_{\mathbb Q})$ of the tensor parameter $$\operatorname{Sym}^2(\pi_i) \otimes \operatorname{Sym}^3(\pi_j),$$ where $\pi_i$ and $\pi_j$ arise from non-CM elliptic curves over $\mathbb Q$. The argu...

A Unconditional Weak $\mathrm{GL}(12)$ Transfer for the $(2,3)$ Symmetric-Power Tensor (v3.0)

We construct a weak automorphic realization on $\mathrm{GL}_{12}(\mathbb A_{\mathbb Q})$ of the tensor parameter $$\operatorname{Sym}^2(\pi_i) \otimes \operatorname{Sym}^3(\pi_j),$$ where $\pi_i$ and $\pi_j$ arise from two non-CM elliptic curves over $\mathbb Q$. More precisely,...

Depth-Three Sato-Tate Harmonics for Three Non-CM Elliptic Curves: Analytic Closure of the Final Triple-Cubic Mode

This paper studies the final triple-cubic mode in the finite depth-three Sato–Tate harmonic packet attached to three non-CM elliptic curves over $\mathbb{Q}$. Let $\pi_i$ denote the unitary cuspidal automorphic representation of $\mathrm{GL}_2(\mathbb{A}_{\mathbb{Q}})$ associated...

Localized Weil Positivity Beyond the Prime-7 Threshold: Relative Coupling and Finite-Rank Tail Reduction at $X = 7.01$

We study the bottom $\lambda_a$ of the spectrum associated with the closed localization $Q_W^a$ of the Weil quadratic form in the Connes–Consani–Suzuki operator-theoretic framework. At $$X = 7.01, \qquad a = \frac{1}{2}\log(7.01),$$ we prove, by a rigorous computer-assisted argum...

Field-Theoretic Residual Clock Response and the Criterion for a Common Operational Time

Version v1.0. This work develops an explicit field-theoretic realization of a residual-induced clock-rate response and separates it from the stronger requirement of a common operational time. Starting from a broken-$U(1)$ parent theory with gauge-invariant phase mismatch $$\alpha...