القائمة
Functions, categories, and information. How mathematical objects relate to each other — morphisms, entropy, signal processing.
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-mappingيبقى الأمر في سطر واحد. مرّر أفقيًا لمراجعته كاملًا قبل النسخ.
تفضّل نسخة محلية؟ نزّل الملفات المتاحة حاليًا لدى SkillsMP.
استنادا إلى تصنيف SOC المهني
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.
عرض SKILL.md
| name | mfe-mapping |
| description | Functions, categories, and information. How mathematical objects relate to each other — morphisms, entropy, signal processing. |
| user-invocable | false |
| allowed-tools | Read Grep Glob |
| metadata | {"extensions":{"gsd-skill-creator":{"version":1,"createdAt":"2026-02-26","triggers":{"intents":["function","morphism","category","functor","information","entropy","signal","probability","transform"],"contexts":["mathematical problem solving","math reasoning"]}}}} |
Mapping (Part VII: Mapping) Chapters: 22, 23, 24, 25 Plane Position: (0.2, 0.4) radius 0.4 Primitives: 42
Functions, categories, and information. How mathematical objects relate to each other — morphisms, entropy, signal processing.
Key Concepts: Category, Probability Axioms, Functor, Natural Transformation, Shannon Entropy
Category (definition): A category C consists of a collection of objects ob(C), a collection of morphisms hom(C) between objects, an identity morphism id_A for each object A, and a composition operation that is associative and respects identities.
Probability Axioms (axiom): Kolmogorov's axioms: For a sample space Omega with sigma-algebra F, a probability measure P satisfies: (1) P(A) >= 0 for all A in F, (2) P(Omega) = 1, (3) P(union A_i) = sum P(A_i) for countably many disjoint events A_i.
Functor (definition): A functor F: C -> D maps objects of C to objects of D and morphisms of C to morphisms of D, preserving identity morphisms F(id_A) = id_{F(A)} and composition F(g . f) = F(g) . F(f).
Natural Transformation (definition): A natural transformation eta: F => G between functors F, G: C -> D is a family of morphisms eta_A: F(A) -> G(A) for each object A in C, such that for every morphism f: A -> B in C, the diagram commutes: G(f) . eta_A = eta_B . F(f).
Shannon Entropy (definition): For a discrete random variable X with probability mass function P(x), the Shannon entropy is H(X) = -sum_x P(x) log_2 P(x), measuring the average information content in bits per symbol.
Fourier Transform (definition): The Fourier transform of an integrable function f: R -> C is F{f}(xi) = integral_{-inf}^{inf} f(t) e^{-2pi i xi t} dt, mapping the function from the time domain to the frequency domain.
Random Variable (definition): A random variable X: Omega -> R is a measurable function from the sample space to the real numbers, assigning a numerical value to each outcome. Its distribution is characterized by the CDF F_X(x) = P(X <= x).
Variance (definition): The variance of a random variable X is Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2, measuring the expected squared deviation from the mean. Standard deviation sigma = sqrt(Var(X)).
Probability Distributions (definition): A probability distribution assigns probabilities to events. Key distributions: Binomial B(n,p) with PMF C(n,k)p^k(1-p)^{n-k}; Poisson Poi(lambda) with PMF e^{-lambda}lambda^k/k!; Normal N(mu,sigma^2) with PDF (1/(sigma*sqrt(2pi)))exp(-(x-mu)^2/(2sigma^2)).
Joint Probability Distribution (definition): The joint distribution of random variables X, Y is P(X in A, Y in B) for all measurable sets A, B. For continuous variables, the joint density f_{X,Y}(x,y) satisfies P(X in A, Y in B) = integral_A integral_B f(x,y) dy dx.
