<?xml version="1.0" encoding="UTF-8"?><rss version="2.0"><channel><title>0archlinux0 — Publication</title><description>A public record of study notes, research, projects, explanations, and essays across disciplines.</description><link>https://0archlinux0.github.io/</link><language>en</language><item><title>I Let AI Agents Run a Nationwide CTF. The Hard Part Wasn&apos;t Solving the Challenges.</title><link>https://0archlinux0.github.io/posts/nationwide-ctf-ai-agent-automation-retrospective/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/nationwide-ctf-ai-agent-automation-retrospective/</guid><description>I ran an AI-agent pipeline in Japan&apos;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.</description><pubDate>Mon, 05 Oct 2026 00:00:00 GMT</pubDate><category>Systems</category><category>AI Engineering</category></item><item><title>Validate Every Change, Deploy Only from main: Jekyll + GitHub Pages</title><link>https://0archlinux0.github.io/posts/github-pages-actions-workflow/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/github-pages-actions-workflow/</guid><description>How a historical Jekyll site used GitHub Actions to validate every branch and pull request while reserving production publishing for changes merged to main.</description><pubDate>Fri, 02 Oct 2026 01:04:21 GMT</pubDate><category>Guide</category><category>GitHub Pages</category><category>GitHub Actions</category><category>Jekyll</category><category>CI/CD</category><category>deployment</category></item><item><title>Fast Fourier Transform (FFT)</title><link>https://0archlinux0.github.io/posts/fast-fourier-transform/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/fast-fourier-transform/</guid><description>A radix-2 FFT guide: DFT normalization, butterfly decomposition, polynomial convolution, and the limits of floating-point integer results.</description><pubDate>Sat, 14 May 2022 21:59:08 GMT</pubDate><category>Math</category><category>Algorithm</category><category>FFT</category><category>DFT</category><category>Cooley–Tukey</category><category>Polynomial Multiplication</category></item><item><title>Bolzano–Weierstrass Theorem</title><link>https://0archlinux0.github.io/posts/Bolzano-Weierstrass-theorem/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Bolzano-Weierstrass-theorem/</guid><description>A proof that every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence, with the compactness distinction.</description><pubDate>Sun, 24 Apr 2022 09:28:00 GMT</pubDate><category>Math</category><category>Analysis</category><category>Bolzano–Weierstrass theorem</category></item><item><title>Monotone Convergence Theorem</title><link>https://0archlinux0.github.io/posts/Monotone-Convergence-Theorem/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Monotone-Convergence-Theorem/</guid><description>The monotone convergence theorem for real sequences, proved from the least-upper-bound property and illustrated with examples.</description><pubDate>Sun, 24 Apr 2022 09:28:00 GMT</pubDate><category>Math</category><category>Analysis</category><category>Monotone Convergence Theorem</category></item><item><title>Nested Interval Theorem</title><link>https://0archlinux0.github.io/posts/Nested-Interval-Property/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Nested-Interval-Property/</guid><description>The nested interval theorem: completeness gives a common point, while shrinking interval lengths make it unique.</description><pubDate>Sun, 24 Apr 2022 09:28:00 GMT</pubDate><category>Math</category><category>Analysis</category><category>Nested Interval Property</category></item><item><title>Analysis Foundations: Metric Spaces, Order, and Limits</title><link>https://0archlinux0.github.io/posts/Analysis-%ED%95%B4%EC%84%9D%ED%95%99(2)/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Analysis-%ED%95%B4%EC%84%9D%ED%95%99(2)/</guid><description>A grouped reference to algebraic, metric, order, completeness, and limit concepts used across introductory analysis.</description><pubDate>Fri, 15 Apr 2022 16:39:00 GMT</pubDate><category>Math</category><category>Analysis</category><category>수학</category><category>해석학</category><category>거리공간</category></item><item><title>Mathematical Foundations: A Compact Glossary</title><link>https://0archlinux0.github.io/posts/Analysis-%E8%A7%A3%E6%9E%90%E5%AD%A6-1/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Analysis-%E8%A7%A3%E6%9E%90%E5%AD%A6-1/</guid><description>A compact, grouped reference to 19 foundational ideas in sets, algebraic structures, functions, and cardinality, with examples.</description><pubDate>Wed, 13 Apr 2022 08:28:00 GMT</pubDate><category>Math</category><category>Foundations</category><category>Set Theory</category><category>Functions</category><category>Cardinality</category><category>Algebra</category></item><item><title>Bézout&apos;s Identity: Integers and Polynomials over a Field</title><link>https://0archlinux0.github.io/posts/B%C3%A9zout&apos;s-identity-p1/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/B%C3%A9zout&apos;s-identity-p1/</guid><description>Why the gcd of two integers is an integer linear combination, with a least-positive-combination proof and the field-only polynomial analogue.</description><pubDate>Tue, 12 Apr 2022 09:28:00 GMT</pubDate><category>Math</category><category>Number Theory</category><category>Bézout&apos;s identity</category><category>Proof</category></item><item><title>The Euclidean Algorithm: Computing a Greatest Common Divisor</title><link>https://0archlinux0.github.io/posts/Euclidean-Algorithm/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Euclidean-Algorithm/</guid><description>A proof and worked trace of the Euclidean algorithm, including its nonnegative-input C++ implementation and logarithmic step count.</description><pubDate>Tue, 12 Apr 2022 09:28:00 GMT</pubDate><category>Math</category><category>Number Theory</category><category>Euclidean Algorithm</category><category>Greatest Common Divisor</category><category>Proof</category></item><item><title>Flow network</title><link>https://0archlinux0.github.io/posts/Flow-network/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Flow-network/</guid><description>Learn feasible flows, residual forward and reverse arcs, augmenting paths, cut bounds, and when Ford–Fulkerson terminates.</description><pubDate>Tue, 12 Apr 2022 09:28:00 GMT</pubDate><category>Graph theory</category><category>Flow network</category><category>Algorithm</category><category>Max-flow min-cut</category><category>Ford–Fulkerson algorithm</category><category>flow network</category></item><item><title>Floyd-Warshall Algorithm</title><link>https://0archlinux0.github.io/posts/Floyd-Warshall-Algorithm/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Floyd-Warshall-Algorithm/</guid><description>Derive Floyd–Warshall’s all-pairs recurrence, implement it safely in C++, and interpret unreachable pairs and negative cycles.</description><pubDate>Tue, 12 Apr 2022 09:28:00 GMT</pubDate><category>Graph theory</category><category>Algorithms</category><category>Algorithm</category><category>Floyd-Warshall</category><category>Shortest path</category></item><item><title>Max-flow min-cut theorem</title><link>https://0archlinux0.github.io/posts/Max-flow-min-cut-theorem/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Max-flow-min-cut-theorem/</guid><description>A proof of the max-flow min-cut theorem using residual reachability, with a concrete flow-and-cut certificate.</description><pubDate>Tue, 12 Apr 2022 09:28:00 GMT</pubDate><category>Graph theory</category><category>Flow network</category><category>Algorithm</category><category>Max-flow min-cut</category><category>flow network</category></item><item><title>Graph theory. Strongly Connected Components (SCCs)</title><link>https://0archlinux0.github.io/posts/Graph-theory-Strongly-Connected-Component/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Graph-theory-Strongly-Connected-Component/</guid><description>Understand strongly connected components and Tarjan’s index, low-link, and active-stack invariants, with a worked graph and implementation.</description><pubDate>Fri, 26 Nov 2021 00:00:00 GMT</pubDate><category>Record</category><category>Code</category><category>Graph theory</category><category>Algorithm</category><category>Strongly connected components</category><category>SCC</category><category>Tarjan&apos;s algorithm</category></item><item><title>De Moivre&apos;s Formula for Integer Powers</title><link>https://0archlinux0.github.io/posts/De-Moivre-s-formula/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/De-Moivre-s-formula/</guid><description>De Moivre&apos;s formula for positive, zero, and negative integer powers, proved with Euler&apos;s formula and illustrated by a cube calculation.</description><pubDate>Wed, 24 Nov 2021 12:29:00 GMT</pubDate><category>Math</category><category>Complex Analysis</category></item><item><title>Radix Sort</title><link>https://0archlinux0.github.io/posts/Sort-Radix-Sort/</link><guid isPermaLink="true">https://0archlinux0.github.io/posts/Sort-Radix-Sort/</guid><description>A stable least-significant-digit radix sort for nonnegative safe integers, with input validation, complexity, and edge-case behavior.</description><pubDate>Fri, 20 Aug 2021 23:53:00 GMT</pubDate><category>Record</category><category>Code</category><category>JavaScript</category><category>Radix sort</category><category>Sorting algorithm</category></item></channel></rss>