القائمة
Pure mathematical structure. Sets, groups, rings, fields, topology — the formal bedrock everything else rests on.
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-foundationsيبقى 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-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}.
