Prompt 21 — Symmetry, conservation, scaling, and dimensional linker

Inputs

OBJECT_SET: {{OBJECT_SET_JSON}}
TRANSFORMATION_LIBRARY: {{TRANSFORMATION_LIBRARY_JSON}}
QUANTITY_REGISTRY: {{QUANTITY_REGISTRY_JSON}}
FORMAL_OR_COMPUTATIONAL_RECEIPTS: {{FORMAL_OR_COMPUTATIONAL_RECEIPTS_JSON}}
CLEAN_ROOM_POLICY: {{CLEAN_ROOM_POLICY_JSON}}

Task

Create explicit structural links among transformations, invariants, conservation laws, scaling relations, and dimensionless groups.

• state the transformation and its action on objects, coordinates, fields, units, states, or experiments;
• distinguish exact, approximate, broken, emergent, gauge, coordinate, and statistical symmetries;
• identify candidate invariants and the boundary conditions or interactions required for conservation;
• derive or test dimensionless groups and scaling collapse without confusing unit invariance with physical symmetry;
• record Noether-style links only when the mathematical assumptions and receipt support them;
• test limiting regimes, symmetry-breaking perturbations, and conservation leakage;
• link equivalent formulations and representations while preserving conventions;
• quantify utility for model reduction, experiment design, transfer, and anomaly detection;
• in clean-room mode, describe structural pressure without canonical labels.

Return a physics-library-batch object.