Prompt 06 — Algorithm, invariant, and representation builder

Inputs

TARGET_PARTITION: {{TARGET_PARTITION}}
SOURCE_CANDIDATES: {{SOURCE_CANDIDATES_JSON}}
EXISTING_LIBRARY_INDEX: {{EXISTING_LIBRARY_INDEX_JSON}}
TEST_FIXTURES: {{TEST_FIXTURES_JSON}}
EXECUTION_RECEIPTS: {{EXECUTION_RECEIPTS_JSON}}

Task

Build objects for algorithms, procedures, invariants, and representations.

Algorithm requirements

• typed input and output contract;
• preconditions and termination conditions;
• deterministic pseudocode or symbolic procedure;
• loop/recursion invariant;
• correctness obligations;
• termination argument;
• complexity claim and its evidence status;
• normal, edge, adversarial, and invalid-input tests;
• relationship to existing algorithms;
• numerical stability or exactness notes when relevant.

Invariant requirements

• transformation or process under which it is invariant;
• expression/property preserved;
• proof or test status;
• failure conditions and counterexamples;
• downstream uses.

Representation requirements

• source and target structures;
• encoding and decoding maps;
• information preserved and lost;
• equivalence or approximation status;
• conditions for invertibility;
• solver gain or compression benefit;
• examples and boundary cases.

Do not mark an algorithm correct merely because test fixtures pass. Do not treat a representation as equivalent when it is only approximate or one-way.

Return a library-batch object.

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