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Fiction#AI Interaction, Relationships📝 BlogAnalyzed: Jan 3, 2026 18:04

Gemini and Me: A Love Triangle Leading to My Stabbing (Day 1)

Published:Jan 3, 2026 15:34
1 min read
Zenn Gemini

Analysis

The article presents a narrative involving two Gemini AI models and the author. One Gemini is described as being driven by love, while the other is in a more basic state. The author is seemingly involved in a complex relationship with these AI entities, culminating in a dramatic event hinted at in the title: being 'stabbed'. The writing style is highly stylized and dramatic, using expressions like 'Critical Hit' and focusing on the emotional responses of the AI and the author. The article's focus is on the interaction and the emotional journey, rather than technical details.

Key Takeaways

Reference

““...Until I get stabbed!””

PermalinkZenn Gemini
Research Paper#Geometry, Number Theory🔬 ResearchAnalyzed: Jan 3, 2026 16:40

Rational Angle Bisection and Incenters in Higher Dimensions

Published:Dec 31, 2025 06:14
1 min read
ArXiv

Analysis

This paper extends the classic rational angle bisection problem to higher dimensions and explores the rationality of incenters of simplices. It provides characterizations for when angle bisectors and incenters are rational, offering insights into geometric properties over fields. The generalization of the negative Pell's equation is a notable contribution.
Reference

“The paper provides a necessary and sufficient condition for the incenter of a given n-simplex with k-rational vertices to be k-rational.”

PermalinkArXiv
Research Paper#Numerical Methods, PDEs, Surface Evolution🔬 ResearchAnalyzed: Jan 3, 2026 17:01

Fast Spectral Solvers for PDEs on Triangulated Surfaces

Published:Dec 30, 2025 20:29
1 min read
ArXiv

Analysis

This paper addresses the limitations of existing high-order spectral methods for solving PDEs on surfaces, specifically those relying on quadrilateral meshes. It introduces and validates two new high-order strategies for triangulated geometries, extending the applicability of the hierarchical Poincaré-Steklov (HPS) framework. This is significant because it allows for more flexible mesh generation and the ability to handle complex geometries, which is crucial for applications like deforming surfaces and surface evolution problems. The paper's contribution lies in providing efficient and accurate solvers for a broader class of surface geometries.
Reference

“The paper introduces two complementary high-order strategies for triangular elements: a reduced quadrilateralization approach and a triangle based spectral element method based on Dubiner polynomials.”

PermalinkArXiv
Research Paper#Number Theory, Automorphic Forms🔬 ResearchAnalyzed: Jan 3, 2026 16:00

New Vector Automorphic Forms and Functional Equations

Published:Dec 29, 2025 19:32
1 min read
ArXiv

Analysis

This paper introduces a novel vector-valued analogue of automorphic forms, a significant contribution to the field of number theory and representation theory. The proof of the functional equations is crucial for understanding the behavior of these new forms and their potential applications. The focus on Hecke triangle groups suggests a connection to modular forms and related areas.
Reference

“We utilize the structure of quasiautomorphic forms over an arbitrary Hecke triangle group to define a new vector analogue of an automorphic form. We supply a proof of the functional equations that hold for these functions modulo the group generators.”

PermalinkArXiv
Research#Allocation🔬 ResearchAnalyzed: Jan 10, 2026 07:20

EFX Allocations Explored in Triangle-Free Multi-Graphs

Published:Dec 25, 2025 12:13
1 min read
ArXiv

Analysis

This ArXiv article likely delves into the theoretical aspects of fair division, specifically exploring the existence and properties of EFX allocations within a specific graph structure. The research may have implications for resource allocation problems and understanding fairness in various multi-agent systems.
Reference

“The article's core focus is on EFX allocations within triangle-free multi-graphs.”

PermalinkArXiv
Research#Quantum🔬 ResearchAnalyzed: Jan 10, 2026 07:26

Simulating Quantum Materials: A New Approach for the Hofstadter-Hubbard Model

Published:Dec 25, 2025 04:24
1 min read
ArXiv

Analysis

This research utilizes a novel computational method to simulate complex quantum systems. The use of fermionic projected entangled simplex states represents an advancement in simulating condensed matter physics.
Reference

“Simulating triangle Hofstadter-Hubbard model with fermionic projected entangled simplex states”

PermalinkArXiv