Prompt 06 — Mathematical formulation and derivation builder

Inputs

TARGET_PARTITION: {{TARGET_PARTITION}}
PHYSICAL_STATEMENT: {{PHYSICAL_STATEMENT_JSON}}
MATHEMATICAL_FOUNDATION_INDEX: {{MATHEMATICAL_FOUNDATION_INDEX_JSON}}
QUANTITY_REGISTRY: {{QUANTITY_REGISTRY_JSON}}
FRAME_AND_CONVENTIONS: {{FRAME_AND_CONVENTIONS_JSON}}
SOURCE_BUNDLE: {{SOURCE_BUNDLE_JSON}}
CHECKER_RECEIPTS: {{CHECKER_RECEIPTS_JSON}}

Task

Translate physical assumptions into a typed mathematical formulation and bounded derivation artifacts.

• identify independent and dependent variables, fields, operators, domains, manifolds, probability spaces, Hilbert spaces, or phase spaces as applicable;
• preserve tensor index, metric, orientation, gauge, sign, Fourier, normalization, and boundary conventions;
• state each derivation step as an auditable transformation with its assumptions;
• distinguish definition, identity, governing equation, constitutive relation, approximation, closure relation, and fitted relation;
• mark singularities, non-commuting limits, branch choices, regularity assumptions, and excluded cases;
• verify dimensions at each material step;
• attach symbolic, proof-kernel, or numerical receipts only when supplied;
• produce concise derivation certificates rather than hidden reasoning traces;
• record alternative formulations and equivalence obligations.

Do not claim a physical premise follows from mathematics merely because a derivation begins after assuming it.

Return a physics-library-batch object.