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crabsatellite/README.md

Alex Li

Independent researcher in mathematics and computer science.

M.S. Computer Engineering, New York University. Based in Yokohama.

Personal Site ORCID


Selected Research

Hamilton cycles in noncrossing partition refinement graphs

Hamilton Cycles in Noncrossing Partition Refinement Graph — Submitted to The Electronic Journal of Combinatorics

A complete classification for every natural number: the graph is Hamiltonian exactly for n = 0, n = 1, or even n >= 4; it has a Hamilton path exactly for n <= 3 or even n. The manuscript, theorem map, and Lean 4 formalization are public, with the publication endpoints checked under standard axioms.

Concept DOI · Repository

Structural learnability in discrete 3D generation

Which Structural Constraints Are Learnable? A Regime Map for a Minecraft Voxel Generator — Accepted at the FDG 2026 17th PCG Workshop

A code-and-data-backed study of structural learnability in a fixed 32³ voxel-generation pipeline. Fourteen measured properties separate into nine controllable, four approachable, and one unresponsive regime; the released package includes the analysis, robustness checks, and an interactive explainer.

ACM DOI · Zenodo concept DOI · Repository

Information value under endogenous feasibility

The Blackwell Dilemma

A theoretical study of how more informative signals can reduce attainable welfare when feasibility is endogenous. The public materials include the working paper, formal claim ledger, Lean 4 development, simulations, and a preregistered prediction.

SSRN · Repository

Rado numbers

On Rado Numbers for x + by = bz: The b^k Pattern and a Threshold Conjecture

SAT- and Lean-backed work on multicolor Rado numbers, including verified artifacts for R_4(3) = 81, an explicit verified witness for R_5(3) > 296, and a clearly separated conjectural frontier.

SSRN · Zenodo concept DOI · Repository

The broader public research corpus spans mathematics, computer science, decision theory, AI governance, and philosophy of cognition. Personal site · SSRN paper list


Research Infrastructure

AEGIS Protocol — Reference implementation of a three-layer protocol for AI-agent action accountability, with tamper-evident records, independent signature verification, and 202 automated tests.


Open Source

Hot Bath — Independently developed and maintained Minecraft mod with more than one million downloads across public releases.

ModPorter — Developer-preview migration tool for deterministic Forge-to-NeoForge transformations, protected by regression tests and strict real-mod runtime gates.

Pinned Loading

  1. gray-code-evolution gray-code-evolution Public

    Hamilton Cycles in the Noncrossing Partition Refinement Graph — companion code, data, and interactive proof explorer

    Lean

  2. constraint-learnability-regime-map constraint-learnability-regime-map Public

    Code and results for 'Which Structural Constraints Are Learnable? A Regime Map for Discrete 3D Generative Models'

    Python

  3. aegis-protocol aegis-protocol Public

    Execution provenance protocol for AI agents — tamper-evident, third-party verifiable behavioral records. Hash chains (SHA-256) + Ed25519 signatures + JCS (RFC 8785). Zero dependencies, 202 tests.

    JavaScript

  4. rado-numbers-sat rado-numbers-sat Public

    SAT-based computation of multicolor Rado numbers for x + by = bz

    Lean

  5. hotBath hotBath Public

    Minecraft mod adding therapeutic bath fluids with healing, buffs, and temperature mod integrations — 1.8M+ downloads on CurseForge. Supports Forge 1.20.1 & NeoForge 1.21.1+

    Java 5

  6. modporter modporter Public

    Automated Minecraft mod migration tool — currently supports Forge 1.20.1 to NeoForge 1.21.1 via a 5-pass transformation pipeline (text, AST, structural, build, resources)

    Kotlin 8 1