arXiv subjects

Jaehwan Kim

Publications and source records attributed to Jaehwan Kim.

5 recordsLinked to original sources

arXiv2026

Closure Atlases and Local-to-Global Obstructions in Finite Closure Systems

This paper studies finite closure operators on overlapping finite universes and gives an exact local-to-global obstruction criterion for conservative globalization. Given a finite family of local closure systems, its atlas-generated closure is obtained by repeatedly applying the local closure operators to the parts visible in each chart. This closure is the least global closure operator extending all chart closures. A chart-visible obstruction is a consequence produced by this global propagation that lies inside a chart but is not validated by that chart's own closure operator. The main theorem proves that a finite closure atlas has a global conservative realization exactly when no such obstruction occurs; in that case the atlas-generated closure itself is the conservative realization. The obstruction condition is finite and directly computable. The paper also records the indexed representation layer motivating the terminology. For a finite closure system, an indexed truth space selects closed theories as contexts and represents each element by the region of selected closed theories containing it. Closure consequence is always sound for region inclusion, and the full indexed space of all closed theories recovers the original closure consequence exactly; reduced indexed spaces can therefore create spurious region consequences by deleting separating closed theories. A formal opposite gives a four-region membership decomposition - only one, only the other, both, and neither - unless additional separation assumptions are imposed. Finally, overlap-compatible local closed theories glue by canonical union under the atlas-generated closure. The framework is finite, structural, and closure-theoretic; the logical terminology is used only as an interpretation of the underlying closure data.

cs.LO↗

arXiv2026

Residue Constraints in the Rank-Three Lifting Problem for Projective-Plane Incidence Matrices

We study the rank-three lifting problem for incidence matrices of finite projective planes through residue-level determinant constraints invisible to tropical valuations alone. In residue characteristic $\neq 3$, any rank-$\le 3$ lift of the incidence matrix of a projective plane of order $q \ge 3$ forces $\Omega(q^8)$ distinct admissible $2 \times 2$ zero rectangles with nontrivial residue cross-ratio. We further prove that for $q \ge 6$ no monomial rank-$\le 3$ lift exists; in particular, any putative low-rank lift must already involve nontrivial first-order corrections on valuation-0 entries. These results arise from a local analysis of $4 \times 4$ identity-pattern minors, where we derive the leading derangement equation together with its first-order companion and show that every vanished identity-pattern minor contains a cross-ratio-defective admissible rectangle. The unresolved part of the problem is therefore genuinely global: one must decide whether a rank-3 residue model, together with a compatible first-order deformation, can satisfy the full overlapping system of local residue constraints.

math.RA↗

arXiv2026

Three-Sign Cancellation Hypernumber Systems and Associator Curvature

We introduce and study a three-sign cancellation hypernumber system $H$ which extends the real field by adjoining a third sign $\Lambda$. The underlying set is $H=\{0\}\cup\{+,-,\Lambda\}\times\mathbb{R}_{>0}$, with a single-valued multiplication and a hyperaddition $\boxplus$ designed to encode cancellation phenomena between positive and negative reals. The classical real line embeds as a genuine subfield $\mathbb{R}_{\mathrm{cl}}\subset H$, and all field operations agree with the usual ones on $\mathbb{R}$. The additive structure of $H$ is almost associative but not a canonical hypergroup. We give an explicit description of where associativity fails and compute, for triples of the form $(+,a),(-,b),(\Lambda,c)$, a closed formula for the associativity defect $\kappa(a,b,c)=2\min(a,b)=a+b-|a-b|$, which coincides with the loss of absolute value when adding $a$ and $-b$ in $\mathbb{R}$. To explain this behaviour, we construct an ambient ''cancellation monoid'' $(K,\oplus)$ on $\mathbb{R}\times\mathbb{R}_{\ge 0}$ which is strictly associative and records both real sums and accumulated cancellation mass. We prove that $H$ cannot be recovered from $K$ by any simple projection, and formulate an ambient reconstruction problem. In addition, scalar multiplication by real numbers (defined via the embedded copy of $\mathbb{R}$) distributes over $\boxplus$, and the sign-layer admits a canonical hypergroup envelope governing the possible signs of hypersums. The results provide a controlled example of a nonassociative hyperaddition sitting over the real field and suggest several directions for multisign generalizations and connections with hyperfields and tropical geometry.

math.RA↗

arXiv2024

Type-I Blowup Solutions for Yang-Mills Flow

In this paper, we construct an infinite-dimensional family of solutions for the Yang-Mills flow on $\mathbb{R}^n \times SO(n)$ for $5 \leq n \leq 9$, which converge to $SO(n)$-equivariant homothetically shrinking solitons, modulo the gauge group. As a corollary, we prove the existence of asymmetric Type-I blowup solutions for the Yang-Mills flow.

math.DG↗

arXiv2023

PITS: Variational Pitch Inference without Fundamental Frequency for End-to-End Pitch-controllable TTS

Previous pitch-controllable text-to-speech (TTS) models rely on directly modeling fundamental frequency, leading to low variance in synthesized speech. To address this issue, we propose PITS, an end-to-end pitch-controllable TTS model that utilizes variational inference to model pitch. Based on VITS, PITS incorporates the Yingram encoder, the Yingram decoder, and adversarial training of pitch-shifted synthesis to achieve pitch-controllability. Experiments demonstrate that PITS generates high-quality speech that is indistinguishable from ground truth speech and has high pitch-controllability without quality degradation. Code, audio samples, and demo are available at https://github.com/anonymous-pits/pits.

eess.AS↗