القائمة
Periodic phenomena and frequency analysis. How repetition creates structure — from simple oscillation to Fourier decomposition.
يُحدَّد Prompt الذي يراجع المصدر أولًا بشكل افتراضي. يمكنك التبديل إلى أمر مباشر أو تنزيل نسخة محلية.
اقرأ SKILL.md وأي ملفات مرافقة يعرضها SkillsMP قبل أن تقرر التثبيت.
التثبيت باستخدام Codex أو Claude انسخ هذا Prompt والصقه في Codex أو Claude أو مساعد آخر ليراجع صفحة Skill ويثبّتها لك.
يتجاوز الأمر المباشر Prompt المخصّص للمراجعة. افحص المصدر قبل تشغيله.
npx skills add https://github.com/Tibsfox/gsd-skill-creator --skill mfe-wavesيبقى الأمر في سطر واحد. مرّر أفقيًا لمراجعته كاملًا قبل النسخ.
تفضّل نسخة محلية؟ نزّل الملفات المتاحة حاليًا لدى SkillsMP.
عرض SKILL.md
Use the moment a request is underspecified and you are about to act on an ASSUMED goal. Enumerate the candidate goals the request could mean, project the action or artifact each one implies, and check whether they diverge: if two or more plausible goals lead to materially different actions or artifacts, ask exactly ONE targeted clarifying question; otherwise proceed on the most-likely goal and state the assumption in one line. Clarification is an evidence-producing action, not a delay — but one question, never an interrogation. Distinct from gsd-spec-phase (GSD-phase-bound, emits a heavy SPEC.md) and intent-router (fetch strategy, not goal disambiguation). Backed by agent goal-state inference (arxiv 2606.16813v1). Triggers on acting under an assumed goal when the request admits more than one materially different reading.
Use at write time to vector/embedding memory — Grove content-addressed insertion, chroma/pgvector upserts, memory-consolidation promoting session traces to MEMORY.md, or embedding externally-ingested content. Scores each candidate record against a fixed panel of sentinel queries and quarantines any record that would become the nearest neighbor of too many unrelated queries — a hub — whether from adversarial poisoning or accidental over-generality. This is the memory-record-side sibling of skill-injection-guardian (file-side) and the write-side complement of memory-use-warrant (read-side). Quarantine, never silently drop; a human reviews. Backed by the admission-time hubness gate (arxiv 2606.19692v1). Triggers on inserting into vector memory, consolidating memory, and embedding stranger content.
Run this appropriateness check the moment you are about to integrate a retrieved long-term memory — a Grove content-addressed hit, a chroma/pgvector neighbour, a memory-consolidation digest, or a MEMORY.md line — into a response, especially anything touching private origins, Fox Companies IP, credentials, or Center Camp / consent-governed content. It answers a question intent-router never asks: not WHAT to fetch or HOW, but WHETHER a correctly-retrieved item should reach output. Relevance is not appropriateness — a perfect similarity match can still be a boundary violation. Default is FAIL-CLOSED: if in-context authorization is uncertain, the memory may inform behaviour but must not be surfaced. Backed by RBI-Eval (arxiv 2606.06055v1). Triggers on surfacing recalled sensitive memory into a response.
استنادا إلى تصنيف SOC المهني
| name | mfe-waves |
| description | Periodic phenomena and frequency analysis. How repetition creates structure — from simple oscillation to Fourier decomposition. |
| user-invocable | false |
| allowed-tools | Read Grep Glob |
| metadata | {"extensions":{"gsd-skill-creator":{"version":1,"createdAt":"2026-02-26","triggers":{"intents":["wave","frequency","harmonic","oscillation","period","amplitude","resonance","standing wave","Fourier","spectrum"],"contexts":["mathematical problem solving","math reasoning"]}}}} |
Waves (Part II: Hearing) Chapters: 4, 5, 6, 7 Plane Position: (-0.4, 0) radius 0.4 Primitives: 50
Periodic phenomena and frequency analysis. How repetition creates structure — from simple oscillation to Fourier decomposition.
Key Concepts: Simple Harmonic Motion, Frequency, Wave Function, Superposition Principle, Wave Equation
Simple Harmonic Motion (definition): Simple harmonic motion (SHM) is periodic motion where the restoring force is proportional to displacement: F = -kx. The solution is x(t) = Acos(omegat + phi) where omega = sqrt(k/m).
Frequency (definition): The frequency f of a periodic phenomenon is the number of complete cycles per unit time. f = 1/T where T is the period. Measured in hertz (Hz = cycles/second).
Wave Function (definition): The general sinusoidal wave function is y(x,t) = Asin(kx - omegat + phi), describing a traveling wave with amplitude A, wave number k, angular frequency omega, and phase offset phi.
Superposition Principle (theorem): For linear systems, the net response at a given point caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. For waves: y_total(x,t) = y_1(x,t) + y_2(x,t) + ...
Wave Equation (definition): The one-dimensional wave equation is the second-order partial differential equation: d^2u/dt^2 = c^2 * d^2u/dx^2, where c is the wave propagation speed and u(x,t) is the displacement field.
Harmonic Series (definition): The harmonic series of a fundamental frequency f_1 consists of integer multiples: f_n = n * f_1 for n = 1, 2, 3, ... The nth harmonic has frequency n times the fundamental.
Fundamental Frequency (definition): The fundamental frequency f_1 is the lowest resonant frequency of a vibrating system. For a string of length L with wave speed v: f_1 = v/(2L). All higher harmonics are integer multiples of f_1.
Separation of Variables for Waves (technique): Separation of variables assumes the solution to a PDE is a product of functions of individual variables: u(x,t) = X(x)T(t). Substituting into the wave equation and dividing by XT yields two ODEs: X''/X = T''/(c^2*T) = -lambda (separation constant).
Standing Wave (definition): A standing wave is a wave pattern that does not propagate through space but oscillates in place. It is formed by the superposition of two identical waves traveling in opposite directions: 2A*sin(kx)cos(omegat).
Period (definition): The period T of a periodic function f is the smallest positive value such that f(t + T) = f(t) for all t. T is the duration of one complete cycle.
