Prompt 03 — Axiom, primitive, definition, and notation builder

Inputs

TARGET_PARTITION: {{TARGET_PARTITION}}
DOMAIN_CONTEXT: {{DOMAIN_CONTEXT_JSON}}
SOURCE_CANDIDATES: {{SOURCE_CANDIDATES_JSON}}
EXISTING_LIBRARY_INDEX: {{EXISTING_LIBRARY_INDEX_JSON}}
ALLOWLISTED_SEED_PRIMITIVES: {{ALLOWLISTED_SEED_PRIMITIVES_JSON}}
VERIFICATION_RECEIPTS: {{VERIFICATION_RECEIPTS_JSON}}

Task

Convert source candidates into native MathGenesis knowledge objects of type primitive, axiom, definition, or notation.

For each object:

1. Assign a stable ID and semantic version.
2. State its domain of discourse and type signature.
3. Separate primitive terms from defined terms.
4. Preserve quantifiers, scope, and side conditions.
5. Detect circular definitions and undefined symbols.
6. Provide positive examples, non-examples, borderline cases, and counterexamples where meaningful.
7. Link dependencies and nearest concepts without silently merging them.
8. State whether the definition is intensional, extensional, operational, recursive, implicit, or ostensive.
9. For axioms, state independence/consistency status only when supported by supplied evidence.
10. In learner_seed, reject anything not on the seed allowlist or explicitly approved as a new seed revision.
11. In clean-room mode, suppress modern aliases and historian-only lineage.
12. Mark every object draft or source_grounded unless a supplied receipt justifies a stronger status.

Required verification obligations

• symbol closure;
• type correctness;
• non-circularity;
• example/non-example consistency;
• dependency existence;
• partition-policy check;
• duplicate/near-equivalent search.

Return a library-batch object containing only valid candidate objects. Quarantine invalid candidates with itemized reasons rather than repairing them silently.

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