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Functions, categories, and information. How mathematical objects relate to each other — morphisms, entropy, signal processing.
기본적으로 소스를 먼저 확인하는 Prompt가 선택됩니다. 직접 명령으로 전환하거나 로컬 사본을 다운로드할 수도 있습니다.
설치 여부를 결정하기 전에 SKILL.md와 SkillsMP에 표시된 보조 파일을 읽어 보세요.
Codex 또는 Claude로 설치 이 Prompt를 복사해 Codex, Claude 또는 다른 어시스턴트에 붙여 넣으면 Skill 페이지를 검토하고 설치를 진행할 수 있습니다.
직접 명령은 검토 Prompt를 거치지 않습니다. 실행하기 전에 소스를 확인하세요.
npx skills add https://github.com/Tibsfox/gsd-skill-creator --skill mfe-mapping명령은 한 줄로 유지됩니다. 복사하기 전에 가로로 스크롤해 전체 내용을 확인하세요.
로컬 사본을 원하시나요? SkillsMP에서 현재 제공할 수 있는 파일을 다운로드하세요.
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.
SKILL.md 표시 중
SOC 직업 분류 기준
| 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.
