Fast Fourier Transform (FFT)
A radix-2 FFT guide: DFT normalization, butterfly decomposition, polynomial convolution, and the limits of floating-point integer results.
PUBLICATION
Study, research, projects, and essays.
A multidisciplinary publication organized around learning, inquiry, documented projects, and reflective writing.
Current work
I Let AI Agents Run a Nationwide CTF. The Hard Part Wasn't Solving the Challenges.
I ran an AI-agent pipeline in Japan's Ministry of Internal Affairs and Communications nationwide CTF. The official result was 26th place with 5,701 points. The bigger lesson was not model capability, but ownership, shared state, verification, and control-plane design.
26th place5,701 official points110 tracked challenges
2026-10-05PUBLICATION SECTIONS
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Notes
Study notes and explanations
Reviewed notes on mathematics, computer science, systems, AI, and software engineering.
Research
Questions, methods, evidence
A lane for research with explicit questions, methods, and evidence.
Projects
Documented systems
Project records link directly to published implementation evidence.
Essays
Long-form synthesis
Longer writing that connects engineering, research, and human practice.
EVERGREEN FROM THE ARCHIVE
Selected foundations
A short selection of mathematical and algorithmic explanations, shown with their original publication dates.
2022-05-14
Bolzano–Weierstrass Theorem
A proof that every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence, with the compactness distinction.
Floyd-Warshall Algorithm
Derive Floyd–Warshall’s all-pairs recurrence, implement it safely in C++, and interpret unreachable pairs and negative cycles.
Max-flow min-cut theorem
A proof of the max-flow min-cut theorem using residual reachability, with a concrete flow-and-cut certificate.