Reviewed notes on mathematics, computer science, systems, AI, and software engineering. The collection grows as more work is reviewed.
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.
How a historical Jekyll site used GitHub Actions to validate every branch and pull request while reserving production publishing for changes merged to main.
A radix-2 FFT guide: DFT normalization, butterfly decomposition, polynomial convolution, and the limits of floating-point integer results.
A proof that every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence, with the compactness distinction.
The monotone convergence theorem for real sequences, proved from the least-upper-bound property and illustrated with examples.
The nested interval theorem: completeness gives a common point, while shrinking interval lengths make it unique.
A grouped reference to algebraic, metric, order, completeness, and limit concepts used across introductory analysis.
A compact, grouped reference to 19 foundational ideas in sets, algebraic structures, functions, and cardinality, with examples.
Why the gcd of two integers is an integer linear combination, with a least-positive-combination proof and the field-only polynomial analogue.
A proof and worked trace of the Euclidean algorithm, including its nonnegative-input C++ implementation and logarithmic step count.
Learn feasible flows, residual forward and reverse arcs, augmenting paths, cut bounds, and when Ford–Fulkerson terminates.
Derive Floyd–Warshall’s all-pairs recurrence, implement it safely in C++, and interpret unreachable pairs and negative cycles.
A proof of the max-flow min-cut theorem using residual reachability, with a concrete flow-and-cut certificate.
Understand strongly connected components and Tarjan’s index, low-link, and active-stack invariants, with a worked graph and implementation.
De Moivre's formula for positive, zero, and negative integer powers, proved with Euler's formula and illustrated by a cube calculation.
A stable least-significant-digit radix sort for nonnegative safe integers, with input validation, complexity, and edge-case behavior.