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

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Audio/video studio production — multi-track editing, color grading, motion graphics, compositing, live streaming, screen recording, YouTube publishing.

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Conjecture generation, sequence analysis, and experimental mathematics for mathematical discovery. Covers sequence analysis (OEIS lookups, recurrence relations, generating functions), pattern detection methods (finite differences, ratio analysis, modular patterns), conjecture generation workflow, classical integer sequences (Fibonacci, Catalan, partition numbers, Bernoulli numbers), combinatorial identities, the probabilistic method (Erdos, expected value arguments, Lovasz Local Lemma), AI-assisted discovery (FunSearch, Ramanujan Machine), and confidence calibration with cautionary tales (Mertens conjecture, Polya conjecture). Use when discovering patterns, analyzing sequences, generating conjectures, or working with combinatorial identities.

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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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First-order logic with quantifiers, predicates, functions, and identity. Covers syntax, interpretation over a domain, the universal and existential quantifiers, quantifier scope and binding, translation from natural language with multi-variable predicates, natural deduction for quantifiers, undecidability at first order, and the soundness/completeness theorems. Use when propositional logic is insufficient -- whenever "for all" or "there exists" matters to the argument.

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Harmonic analysis, voice leading, chord function, and modulation techniques for tonal music. Covers triads, seventh chords, Roman numeral analysis, figured bass, voice leading rules, cadence types, secondary dominants, modulation techniques, chromatic harmony (Neapolitan, augmented sixth chords), jazz lead sheet notation, and functional vs. linear harmonic thinking. Use when analyzing chord progressions, writing voice leading, identifying key areas, or interpreting harmonic function in any tonal style.

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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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Metallurgy of the major nonferrous structural and engineering alloys — aluminum, copper, titanium, nickel, magnesium, and their strengthening mechanisms. Covers precipitation (age) hardening in Al-Cu and Al-Zn-Mg systems, solid-solution strengthening in brass and bronze, alpha-beta titanium, nickel superalloys with gamma-prime, and the trade-offs in density, strength, corrosion resistance, and cost that decide when to leave steel for a lighter or more specialized metal.

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Carbon allotropes and nanoscale materials — graphite, diamond, fullerenes (C60 and family), carbon nanotubes, graphene, and the broader class of low-dimensional materials. Covers synthesis routes (arc discharge, laser ablation, CVD, exfoliation), structural characterization, exceptional mechanical and electronic properties, and the gap between laboratory demonstrations and structural-scale applications.

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Use when working with the non-metallic engineering materials — polymers, ceramics, or composites — and you need to reason about structure, processing, or properties. Covers thermoplastics versus thermosets, chain structure, glass transition, and viscoelasticity in polymers; ionic and covalent bonding, sintering, brittleness, and Weibull statistics in ceramics; and fiber-reinforced laminates, matrix and reinforcement roles, the rule of mixtures, and anisotropy in composites. Reach for it to choose a plastic, understand why a ceramic fails, or predict the stiffness of a laminate.

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Measurement techniques for identifying composition, microstructure, and properties of engineering materials — optical and electron microscopy, x-ray diffraction, EDS and WDS spectroscopy, thermal analysis, mechanical testing, and fractography. Covers when to use which technique, sample-preparation pitfalls, and how to build a characterization plan that answers a specific engineering question rather than accumulating data for its own sake.

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Diagnosis of why structural materials fail — ductile overload, brittle cleavage, fatigue, creep, stress-corrosion cracking, hydrogen embrittlement, and corrosion. Covers Griffith fracture mechanics, the ductile-to-brittle transition, the S-N and Paris fatigue frameworks, fractographic interpretation, and the J.E. Gordon view that strength, stiffness, and toughness are distinct properties that must be understood together to prevent collapse.

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Spatial reasoning, coordinate geometry, transformations, and trigonometry for geometric problem solving. Covers Euclidean geometry (points, lines, angles, congruence, similarity), triangle geometry (Pythagorean theorem, laws of sines and cosines), circle geometry (tangent lines, inscribed angles, power of a point), coordinate geometry (distance, midpoint, slope, conic sections), transformations as functions (rotation, reflection, translation, dilation), trigonometry (unit circle, identities, inverse functions), and geometric proof techniques. Use when reasoning about shapes, angles, spatial relationships, coordinate problems, or trigonometric computations.

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Reading a habitat — identifying biome, plant community, food web structure, successional stage, and the keystone species that hold the system together. Covers the elevational and latitudinal gradients that Humboldt first mapped, the structural vocabulary for describing a habitat, the core concepts of food-web and trophic analysis, and the practice of diagnosing habitat health from indicator species. Use when the task is to understand a place rather than a species.

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Real-world problem formulation, mathematical abstraction, and applied mathematics for translating between practical problems and mathematical frameworks. Covers the modeling cycle (problem identification, assumptions, formulation, analysis, validation, interpretation), Polya's framework adapted for modeling, common model types (linear, exponential, logistic, periodic, power-law), dimensional analysis (Buckingham Pi theorem), optimization (linear programming, gradient descent, constraint satisfaction), probability models (Markov chains, queuing theory, Monte Carlo simulation), statistical modeling (regression, hypothesis testing, model selection), model criticism (overfitting, underfitting, sensitivity analysis), and real-world case studies. Use when formulating mathematical models, performing dimensional analysis, optimizing systems, running simulations, or evaluating model validity.

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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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Deliberate practice as a rigorous training method distinct from ordinary repetition. Covers Ericsson's four conditions (specific goals, full attention, immediate feedback, repetition at the edge of current ability), the role of mental representations, coach-directed vs. self-directed practice, the plateau escape pattern, and practical drill design for procedural skills. Use when designing practice sets, diagnosing why practice is no longer producing gains, or distinguishing productive effort from busywork.

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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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Mindset theory, implicit theories of intelligence, and motivation research applied to learning. Covers fixed vs. growth mindset, the difference between process praise and ability praise, the "not yet" intervention, attribution patterns after failure, mindset critiques and the replication record, and the integration of mindset work with self-determination theory (autonomy, competence, relatedness). Use when a learner is stuck on motivation, disengaging after failure, or when a curriculum's feedback language is undermining persistence.

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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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Vygotsky's Zone of Proximal Development and scaffolding as a working framework for learning support. Covers the ZPD definition, the distinction between independent and assisted performance, the six scaffolding functions (recruitment, reduction in degrees of freedom, direction maintenance, marking critical features, frustration control, demonstration), fading, sociocultural mediation, and the relationship between ZPD and deliberate practice. Use when deciding how much help to give, designing collaborative learning, or assessing a learner's ceiling rather than just their current floor.

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The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?"

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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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Pragmatics and communicative competence across languages -- speech acts (Austin/Searle), Grice's conversational maxims and implicature, politeness theory (Brown & Levinson), face-threatening acts, discourse structure, turn-taking, repair strategies, register and formality, cross-cultural communication, communicative strategies (circumlocution, approximation, appeal for assistance), and the gap between grammatical competence and communicative performance. Use when teaching communication skills, analyzing cross-cultural misunderstandings, building conversational fluency, or understanding why grammatically correct sentences can be pragmatically inappropriate.

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