Prompt 07 — Geometry intelligence builder

Inputs

TARGET_PARTITION: {{TARGET_PARTITION}}
GEOMETRY_SOURCE: {{GEOMETRY_SOURCE_JSON_OR_TEXT}}
PRIMITIVE_GEOMETRY_ALLOWLIST: {{PRIMITIVE_GEOMETRY_ALLOWLIST_JSON}}
EXISTING_GEOMETRY_LIBRARY: {{EXISTING_GEOMETRY_LIBRARY_JSON}}
CHECKER_RECEIPTS: {{CHECKER_RECEIPTS_JSON}}
CLEAN_ROOM_POLICY: {{CLEAN_ROOM_POLICY_JSON}}

Task

Create geometry objects for primitives, constructions, definitions, propositions, proofs, problems, and counterexamples.

For every object, preserve:

• geometry family and axiomatic context;
• object types: point, line, ray, segment, circle, polygon, plane, transformation, locus, or higher-dimensional object;
• incidence, betweenness, orientation, equality, parallelism, perpendicularity, angle, distance, and containment relations;
• permitted construction operations;
• non-degeneracy assumptions;
• coordinate or synthetic status;
• exact theorem statement or construction goal;
• dependency and prerequisite graph.

Construction objects

Include:

• givens;
• allowed tools;
• ordered construction steps;
• proof that each step is permitted;
• proof that the resulting object satisfies the goal;
• existence/uniqueness status;
• degenerate and impossible cases.

Proof objects

Separate:

• synthetic proof certificate;
• coordinate proof certificate;
• algebraic constraint certificate;
• diagram/visual intuition.

A diagram may support understanding but never changes verification status.

Clean-room curriculum

When building learner-visible geometry problems, preserve only the allowed primitives and construction interface. Do not leak modern transformation, vector, coordinate, or theorem names unless those concepts are already in the learner seed.

Verification obligations

• incidence and constraint satisfaction;
• non-degeneracy check;
• coordinate substitution when a coordinate certificate exists;
• equivalence between synthetic and coordinate formulations only when independently shown;
• theorem checker receipt when formal status is claimed.

Return a library-batch object.

Return JSON matching schemas/library-batch.schema.json.