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Foundational measurements and relationships. The axioms of the system — numbers, distance, angles, and the geometry of seeing.
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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-perception |
| description | Foundational measurements and relationships. The axioms of the system — numbers, distance, angles, and the geometry of seeing. |
| user-invocable | false |
| allowed-tools | Read Grep Glob |
| metadata | {"extensions":{"gsd-skill-creator":{"version":1,"createdAt":"2026-02-26","triggers":{"intents":["number","count","distance","magnitude","circle","trigonometric","angle","inner product","orthogonal"],"contexts":["mathematical problem solving","math reasoning"]}}}} |
Perception (Part I: Seeing) Chapters: 1, 2, 3 Plane Position: (-0.2, 0.2) radius 0.4 Primitives: 43
Foundational measurements and relationships. The axioms of the system — numbers, distance, angles, and the geometry of seeing.
Key Concepts: Sine Function, Cosine Function, Real Numbers, Unit Circle, Inner Product (Dot Product)
Sine Function (definition): The sine function sin: R -> [-1,1] is defined as the y-coordinate of the point on the unit circle at angle theta from the positive x-axis. It is periodic with period 2*pi, odd: sin(-theta) = -sin(theta).
Cosine Function (definition): The cosine function cos: R -> [-1,1] is defined as the x-coordinate of the point on the unit circle at angle theta. It is periodic with period 2*pi, even: cos(-theta) = cos(theta). cos(theta) = sin(theta + pi/2).
Real Numbers (definition): The real numbers R form a complete ordered field: closed under +, -, *, /, ordered by <, and satisfying the completeness axiom. R = Q union (R \ Q).
Unit Circle (definition): The unit circle is the set of points (x, y) in R^2 satisfying x^2 + y^2 = 1. Every point on the unit circle can be written as (cos(theta), sin(theta)) for a unique angle theta in [0, 2*pi).
Inner Product (Dot Product) (definition): The inner product (dot product) of vectors u = (u1,...,un) and v = (v1,...,vn) in R^n is u . v = sum_i u_i * v_i = |u||v|cos(theta), where theta is the angle between u and v.
Natural Numbers (axiom): The natural numbers N = {1, 2, 3, ...} satisfy the Peano axioms: there exists a first element 1, every element n has a unique successor S(n), no two elements share a successor, and the induction principle holds.
Pythagorean Theorem (theorem): In a right triangle with legs a and b and hypotenuse c: a^2 + b^2 = c^2. Conversely, if a^2 + b^2 = c^2 for a triangle with sides a, b, c, then the triangle is right-angled.
Complex Numbers (definition): The complex numbers C = {a + bi : a, b in R, i^2 = -1} form an algebraically closed field. Every complex number has modulus |z| = sqrt(a^2 + b^2) and argument arg(z) = atan2(b, a).
Absolute Value (definition): For x in R, the absolute value |x| = x if x >= 0, |x| = -x if x < 0. Equivalently, |x| = sqrt(x^2). It measures the distance from x to 0 on the number line.
Euler's Formula (identity): For all theta in R: e^(itheta) = cos(theta) + isin(theta). The special case theta = pi gives Euler's identity: e^(i*pi) + 1 = 0.
