Experimental works, jokes, and odd outputs

Crawled from Nanwhere Assistant's Yuque guide for 25th cohort new students. This project is an intermediate product of a nova club initiative.

This is a project for storing notes and materials recorded during the process of self-studying mathematics. Originally published via FigShare, DOI: 10.6084/m9.figshare.c.6094833.v7

This project serves as a Mock Service for the Nova 2025 Information Integration Tool Collaboration Project, aligning with the design of the "Collaboration Integration Plan (Draft)" to facilitate parallel development and integration testing between frontend, backend, and various teams.

This project focuses on converting Yuque documents into structured formats, enabling seamless integration with LLMs. It was developed as part of the first practice group project by the Nova Club at Nanjing University in 2025.

This paper presents the foundations of Chunpinative Geometry, a novel geometric framework anchored in the Dual-Complementary Principle (D-C-P), which asserts the axiomatic equivalence of angles and their complements. Departing from classical Euclidean axioms, it synthesizes tropical deformation techniques, derived non-Archimedean structures, and a reimagined Erlangen program to construct a self-consistent theory of complementary angle spaces. The framework axiomatizes rigid C-spaces, where angle quantization and metric degeneracies arise naturally from the D-C-P axiom. It resolves anomalies such as the CZL Lemma through quasi-schematic methods and establishes the complementarity group G as a symmetry governing geometric transformations, bridging synthetic geometry with deformation quantization.

The document of doge-v3.

This paper explores non-cooperative Pen-PL games, modeling the probability distribution of outcomes using multivariate Gaussian processes. It derives optimal 'smooth' signaling rules and proves that computing a socially optimal network placement for these games is NP-hard, linking tactical pen placement to advanced statistical mechanics and game theory concepts.

The junk paper focuses on a fictional mathematical object called “YH-DIE.” It explores the continuity of this object, its mappings on algebraic varieties, and how it serves as an intersection point between algebraic geometry and partial differential equations. The paper also asserts that the equations governing minimal surfaces represent a special case of this general framework.