メニュー
Pure mathematical structure. Sets, groups, rings, fields, topology — the formal bedrock everything else rests on.
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-foundations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。
ローカルで確認しますか？SkillsMP が現在取得できるファイルをダウンロードできます。
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 を表示中
SOC 職業分類に基づく
| name | mfe-foundations |
| description | Pure mathematical structure. Sets, groups, rings, fields, topology — the formal bedrock everything else rests on. |
| user-invocable | false |
| allowed-tools | Read Grep Glob |
| metadata | {"extensions":{"gsd-skill-creator":{"version":1,"createdAt":"2026-02-26","triggers":{"intents":["set","logic","proof","group","ring","field","topology","axiom","formal","abstract"],"contexts":["mathematical problem solving","math reasoning"]}}}} |
Foundations (Part VI: Defining) Chapters: 18, 19, 20, 21 Plane Position: (-0.6, 0.6) radius 0.35 Primitives: 55
Pure mathematical structure. Sets, groups, rings, fields, topology — the formal bedrock everything else rests on.
Key Concepts: Set Definition (ZFC), Topological Space, Group Definition and Axioms, Propositional Logic (Boolean Operations), Predicate Logic (Quantifiers)
Set Definition (ZFC) (axiom): A set is a well-defined collection of distinct objects (elements). Membership is denoted x in S. Two sets are equal iff they have exactly the same elements (Axiom of Extensionality). Sets are the foundational objects of mathematics under ZFC.
Topological Space (axiom): A topological space (X, tau) is a set X with a collection tau of subsets (called open sets) satisfying: (1) emptyset and X are in tau. (2) Any union of sets in tau is in tau. (3) Any finite intersection of sets in tau is in tau.
Group Definition and Axioms (axiom): A group (G, ) is a set G with a binary operation * satisfying: (1) Closure: ab in G for all a,b in G. (2) Associativity: (ab)c = a(bc). (3) Identity: exists e in G such that ea = ae = a. (4) Inverses: for each a, exists a^{-1} with a*a^{-1} = a^{-1}*a = e.
Propositional Logic (Boolean Operations) (definition): Propositional logic deals with propositions (true/false statements) combined by logical connectives: AND (conjunction, p ^ q), OR (disjunction, p v q), NOT (negation, ~p), IMPLIES (conditional, p -> q), IFF (biconditional, p <-> q).
Predicate Logic (Quantifiers) (definition): Predicate logic extends propositional logic with variables, predicates P(x), and quantifiers: universal (forall x, P(x)) meaning P holds for all x, and existential (exists x, P(x)) meaning P holds for some x. Negation: ~(forall x, P(x)) iff (exists x, ~P(x)).
Homomorphism (definition): A group homomorphism f: G -> H is a function satisfying f(a *_G b) = f(a) *_H f(b) for all a, b in G. It preserves the group operation. The kernel ker(f) = {a in G : f(a) = e_H} is a normal subgroup of G. The image im(f) is a subgroup of H.
Open Set and Closed Set (definition): In a topological space (X, tau), a set U is open if U in tau. A set C is closed if X \ C is open. The closure cl(A) is the smallest closed set containing A. The interior int(A) is the largest open set contained in A. A set can be both open and closed (clopen).
Cartesian Product (definition): The Cartesian product of A and B is A x B = {(a,b) : a in A, b in B}. For n sets: A_1 x ... x A_n = {(a_1,...,a_n) : a_i in A_i}. |A x B| = |A| * |B|. R^n = R x R x ... x R (n times).
Relation (definition): A relation R from A to B is a subset of A x B. We write aRb or (a,b) in R. Properties: reflexive (aRa), symmetric (aRb => bRa), antisymmetric (aRb and bRa => a=b), transitive (aRb and bRc => aRc).
Equivalence Relation (definition): An equivalence relation ~ on set A is a relation that is reflexive (a ~ a), symmetric (a ~ b => b ~ a), and transitive (a ~ b and b ~ c => a ~ c). It partitions A into disjoint equivalence classes [a] = {x in A : x ~ a}.
