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Functions, categories, and information. How mathematical objects relate to each other — morphisms, entropy, signal processing.
デフォルトでは、最初にソースを確認する Prompt が選択されています。直接コマンドに切り替えるか、ローカルコピーをダウンロードすることもできます。
インストールを決める前に、SKILL.md と SkillsMP に表示されている付属ファイルをお読みください。
Codex または Claude でインストール この Prompt をコピーして Codex、Claude、または他のアシスタントに貼り付けると、Skill ページを確認してインストールできます。
直接コマンドでは確認用 Prompt が省略されます。実行前にソースを確認してください。
npx skills add https://github.com/Tibsfox/gsd-skill-creator --skill mfe-mappingコマンドは1行のまま表示されます。コピー前に横へスクロールして全体を確認してください。
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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.
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SOC 職業分類に基づく
| 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.
