a ↔ I
Tier II — Similarity EMPIRICAL
Sieve rationale
Structural equation-level identity (sign=+1): the canonical forms of EQ-NEWTON-II and EQ-OHM are syntactically equal under rename, and a maps to I under the discovered bijection
Physical constraint filter
Both variables are bond-graph flows but pint dimensions differ ([length] / [time] ** 2 vs [current]); accepted as a STRUCTURAL flow-analogy (e.g., force ↔ voltage: both occupy the effort slot in their respective bond graphs but are not dimensionally equal). Any downstream composite that needs a numerical identity must supply a transducer coefficient.
Onsager reciprocity applies only to pairs of linear transport laws; at least one equation is not a linear PDE.
Energy conservation check is narrowly targeted at the Newton+Hooke → SHO composite in Medium m2; other composites require the Phase 7 Lyapunov/Noether machinery (not yet built).
Emergent properties
AI review board
1 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
This coupling represents a well-known structural analogy between Newton's second law (F = ma, so a = F/m) and Ohm's law (V = IR, so I = V/R). Both equations share the same algebraic form (response = driving quantity / resistance parameter), and the mapping of acceleration to current is consistent with the standard mechanical–electrical analogy where both serve as 'flow' variables in their respective bond-graph domains. The transfer function is labeled 'identity,' which is appropriate at the structural/syntactic level — the sieve correctly identifies this as a rename-level isomorphism. The physical constraint filter appropriately notes that dimensions differ and flags the need for a transducer coefficient in any numerical application, which is honest and correct. The Buckingham π groups are legitimate dimensionless groupings from each equation. No spurious emergent properties are claimed. This is a textbook-quality cross-domain analogy and is suitable for the discovery ledger as a tier-2 structural similarity.
The proposed identity mapping a ↔ I is not physically or semantically sound: in bond-graph terms the mechanical flow variable is velocity, not acceleration (which is a time-derivative of flow), whereas current is a flow. Newton’s second law (F = m a = m dv/dt) corresponds to an inertial element (analogous to an inductor), not to a resistive law (V = R I). A valid Ohm-like mechanical analog would be viscous damping F = b v with v ↔ I (mobility analogy), not a ↔ I. The semantic descriptors (Acceleration vs ElectricCurrent) do not represent the same quantity nor a named transform, yet an identity transfer is claimed. The physical-constraint filter’s Tellegen check misclassifies acceleration as a flow and overlooks the dimensional mismatch; accepting it as a “structural flow-analogy” is inconsistent with standard cross-domain analogies. The listed π-groups are merely tautologies of the individual laws, not emergent cross-domain properties.
This coupling correctly identifies the well-established force-voltage (or mobility) analogy between mechanical and electrical systems. The mapping of acceleration ('a') to electric current ('I') is valid within this framework, as both serve as 'flow' variables in their respective domains. The semantic descriptors honestly represent the distinct physical quantities, and the physical constraint filter's reasoning is sound, correctly classifying this as a structural analogy where dimensional differences are expected. The emergent property analysis is consistent with a direct structural mapping, reinforcing the validity of this Tier 2 similarity.