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Proof writing and verification techniques for mathematical reasoning. Covers 13 proof strategies with canonical worked examples — direct, contrapositive, contradiction, cases, WLOG, vacuous/trivial, biconditional, counterexample, existence (constructive and non-constructive), uniqueness, induction (weak, strong, structural), pigeonhole/double-counting, and diagonal argument/invariants. Use when writing, verifying, or selecting proof strategies for any mathematical claim.

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Sound systems of human language -- phoneme inventories, the International Phonetic Alphabet, articulatory and acoustic phonetics, phonological rules, suprasegmental features (stress, tone, intonation), and ear training for non-native sound perception. Covers place and manner of articulation, voicing contrasts, vowel space, minimal pair analysis, allophonic variation, phonotactic constraints, connected speech phenomena (assimilation, elision, liaison), and prosody across language families. Use when analyzing pronunciation, teaching sound systems, performing phonemic transcription, or diagnosing intelligibility problems in any language.

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Meta-cognitive and practical strategies for learning any language -- learner autonomy, goal setting, strategy taxonomy (Oxford's SILL framework), memory strategies, cognitive strategies (note-taking, summarizing, analyzing, reasoning), compensation strategies, metacognitive strategies (planning, monitoring, evaluating), affective strategies (managing anxiety, self-encouragement), social strategies (collaboration, questioning, empathy), immersion design, study habit optimization, plateau diagnosis, and motivation maintenance. Use when designing a language learning plan, diagnosing a learner's stuck points, selecting study methods, or building self-directed learning skills.

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Foundations of breath practice and seated meditation across traditions — diaphragmatic mechanics, pranayama families (ujjayi, nadi shodhana, bhramari, kapalabhati, bhastrika, sitali, sheetkari), buffer-safe breath-retention posture, shikantaza and koan traditions in Sōtō and Rinzai Zen, secular clinical mindfulness as MBSR translates it, and engaged-mindfulness pedagogy as Plum Village teaches it. Use when setting up a breath practice, designing a meditation sit, debugging a stalled practice, or deciding whether a given technique is safe for a given person.

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Markdown to HTML/PDF build + FTP sync to configured remote host. Pandoc + xelatex templates, branded output, automated deployment. Proven on 29-document HEL series.

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FFmpeg media processing — video/audio conversion, trimming, encoding, filters, streaming. CLI and ffmpeg.wasm patterns.

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Industrial production of iron and steel from ore to finished product — blast furnace, Bessemer converter, open-hearth, basic oxygen, electric arc, continuous casting, rolling, and secondary metallurgy. Covers the chemistry of decarburization, dephosphorization, and desulfurization, the metallurgy of plain carbon steels, the evolution from puddling and rolling to BOF and EAF, and the process-structure-property chain that makes mild steel the default structural material of the industrial era.

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Extending propositional and predicate logic with modal operators -- necessity and possibility, and their relatives (obligation, knowledge, belief, time). Covers Kripke possible-worlds semantics, accessibility relations, the main modal systems (K, T, S4, S5), translation from natural language, and applications in epistemic, deontic, and temporal reasoning. Use when ordinary logic is insufficient to capture distinctions like "must" vs "might," "knows" vs "believes," "always" vs "sometimes."

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Comparative framing across contemplative and mind-body traditions — Sōtō Zen and Rinzai Zen, Theravada vipassana, Tibetan Vajrayana, classical yoga and its eight limbs, Daoist internal cultivation, secular MBSR and MBCT, engaged mindfulness as Thich Nhat Hanh teaches it, Christian contemplative prayer, Sufi dhikr, the Hesychast tradition of the Eastern Orthodox church — for the routing agent who has to understand where a user is already standing before recommending a practice. Covers the pedagogical voice of each tradition, the places they overlap, the places they genuinely disagree, and the non-sectarian framing the college department uses. Use when a user arrives with a prior tradition, when a query spans more than one tradition, or when the agent needs a vocabulary for what is shared and what is lineage-specific.

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LaTeX document authoring with arXiv submission best practices, Overleaf patterns, and academic publishing conventions.

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The logic of sentential connectives -- and, or, not, if-then, if-and-only-if -- as a formal system. Covers syntax (well-formed formulas), semantics (truth tables), satisfiability, validity, logical equivalence, normal forms (CNF, DNF), natural-deduction rules, and common translation pitfalls. Use when formalizing arguments with propositional structure, checking validity mechanically, or teaching the foundations of formal reasoning.

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Identifying species in the field using dichotomous keys, gestalt recognition, diagnostic features, and habitat context. Covers the working identification protocol from first encounter through confidence-rated record, the vocabulary of field marks, the discipline of negative evidence, and the honest reporting of uncertain IDs. Use when the task is to name a living organism encountered in the field.

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Birding by sight and sound — gestalt, song and call vocabulary, behavioral and habitat clues, and the discipline of producing eBird-grade records. Covers the vocabulary of bird field marks, the primary categories of vocalization, the habits of habitat-filtering, and the protocol for submitting records to a citizen-science database without degrading data quality. Use when the task is bird-specific observation or record-keeping.

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Musical form and structural analysis covering binary, ternary, rondo, sonata, theme-and-variations, and popular song forms. Covers formal archetypes (AB, ABA, ABACA, sonata-allegro), 12-bar blues, arch form, minimalist process forms, strophic and through-composed designs, and formal analysis methodology for both score study and listening. Use when determining the structural plan of a piece, analyzing sectional relationships, or understanding how form shapes musical narrative.

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Systematic materials selection for engineering design using performance indices, Ashby charts, multi-constraint optimization, and case-based reasoning. Covers the five-step Ashby method — function, objective, constraint, free variable, index — with worked examples for stiffness-limited beams, strength-limited ties, thermally shocked vessels, and minimum-cost components. Use when choosing among metals, polymers, ceramics, and composites under competing objectives.

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Bloom's Taxonomy of Educational Objectives and mastery learning as practical instructional design tools. Covers the six cognitive levels (remember, understand, apply, analyze, evaluate, create), the revised 2001 taxonomy, the knowledge dimension, mastery learning loops, formative vs. summative assessment, and the writing of learning objectives that are both specific and verifiable. Use when designing lessons, writing objectives, building assessments, or diagnosing why a learner is stuck at one cognitive level.

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Martial arts as body discipline — the shared pedagogical structure across striking, grappling, and weapon arts (stance, distance, timing, ukemi, live partner work, graded ranking, and the ethical container the best schools enforce). Covers karate, judo, jiu-jitsu (Brazilian and traditional Japanese), aikido, kendo/kenjutsu, boxing, muay Thai, and wrestling at enough depth that an agent can place a user into a reasonable first-month practice and recognize the safety failures that matter most. Leans on Moshé Feldenkrais's judo background and Yang Jwing-Ming's martial scholarship for the internal-to-external bridge. Use for any query about beginning a martial art, training injury patterns, graded progression, or the ethics of combat training.

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Somatic movement and whole-body retraining as Joseph Pilates designed it in the Contrology method and as Moshé Feldenkrais designed it in Awareness Through Movement and Functional Integration, with enough cross-reference to the broader somatics landscape (Alexander Technique, Hanna Somatics, Body-Mind Centering) that an agent can place a user into the right method. Covers the Pilates reformer and mat system, the six Pilates principles, the Feldenkrais ATM lesson structure, the nervous-system learning frame that distinguishes somatics from exercise, and the safety posture that matters for rehab populations. Use for queries about core training, rehab-adjacent movement, chronic pain patterns, and learning-based movement re-education.

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Contrapuntal writing and analysis covering species counterpoint, fugue structure, canon types, and imitative techniques. Covers Fux's five species, cantus firmus construction, consonance and dissonance treatment, invertible counterpoint, fugue anatomy (subject, answer, countersubject, episode, stretto), canon varieties, and contrapuntal practice from Palestrina through Shostakovich. Use when writing or analyzing counterpoint, studying fugue structure, or understanding the linear dimension of polyphonic music.

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Experience-based and environment-based learning design drawn from Dewey and Montessori. Covers Dewey's criterion of continuity and interaction, the reflective-thinking cycle, Montessori's prepared environment, sensitive periods, child-led inquiry, the role of self-correcting materials, project-based learning, and the relationship between autonomy and discipline. Use when designing hands-on activities, arranging learning spaces, integrating classroom work with real experience, or evaluating whether a lesson is genuinely experiential versus merely "activity-based."

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Theory and policy of international economic exchange. Covers comparative advantage (Ricardo, Heckscher-Ohlin), gains from trade, trade policy instruments (tariffs, quotas, subsidies), exchange rate determination, balance of payments, globalization dynamics, trade agreements, and the political economy of protectionism. Use when analyzing why countries trade, who wins and loses from trade, how exchange rates move, or the effects of trade policy interventions.

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Analysis of aggregate economic phenomena -- GDP measurement, inflation dynamics, unemployment theory, monetary policy (central banks, interest rates, money supply), fiscal policy (government spending, taxation, debt), and the business cycle. Covers Keynesian, monetarist, and new classical perspectives. Use when analyzing national or global economic conditions, policy debates, economic growth, recessions, or the interaction between monetary and fiscal authorities.

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Applying motion study and time analysis to household work. Based directly on Lillian Gilbreth's *The Home-Maker and Her Job* and *Cheaper by the Dozen*, this skill covers the therblig-motion catalog, task decomposition, batch processing, parallelism, routine chart design, and the ergonomics of work surfaces. Use when diagnosing why a household is running out of time, designing a weekly routine, teaching task sharing to children, or reducing the friction of any repeated household task.

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Assessing anthropogenic environmental impacts — pollution pathways, habitat destruction and fragmentation, land-use change, invasive species, overharvest, and extinction debt. Covers environmental impact assessment (EIA) methodology, exposure-effect relationships, population viability analysis, IPAT and ecological footprint frameworks, and strategic environmental assessment. Use when quantifying or forecasting human impacts on ecosystems, designing monitoring programs, or evaluating a proposed intervention against a baseline.

日本語の概要は準備中です。原文の説明を表示しています。