m ↔ R
Tier II — Similarity CONJECTURAL
Sieve rationale
Structural equation-level identity (sign=+1): the canonical forms of EQ-NEWTON-II and EQ-OHM are syntactically equal under rename, and m maps to R under the discovered bijection
Physical constraint filter
At least one variable is not a bond-graph port variable (role_a=parameter, role_b=parameter); Tellegen pairing is only defined for effort/flow.
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
2 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
While Newton's second law (F = ma) and Ohm's law (V = IR) share a syntactically identical trilinear algebraic structure, the proposed coupling maps mass (m) to resistance (R) via an identity transfer function, which is physically unjustified. Mass and resistance have incompatible dimensions ([mass] vs. [mass·length²·time⁻³·current⁻²]), and the identity mapping between them is dimensionally inconsistent. The analogy between these equations is a well-known purely formal/structural one (inertia as 'resistance to acceleration' paralleling electrical resistance to current), but a formal structural isomorphism does not constitute a genuine physical coupling. The physical constraint filter passed no checks (all returned not_applicable), providing no supporting evidence. The emergent pi groups are simply the trivially dimensionless restatements of each equation independently and reveal no new cross-domain insight. This is an artefact of algebraic pattern matching, not a physically meaningful coupling.
Despite a superficial algebraic similarity (both laws are linear proportionalities), mapping Newton’s mass m to electrical resistance R via an identity transfer is physically and semantically invalid: Mass (inertial, energy-storing) and resistance (dissipative) are different quantities with incompatible dimensions and roles; in standard analogies mass corresponds to inductance, not resistance. The semantic descriptors (Mass vs Resistance) do not identify the same quantity nor a justified transform. The physical-constraint filter flags unequal dimensions and offers no supporting reciprocity/energy checks. The listed Pi groups are per-equation tautologies, not emergent from the coupling. Therefore the proposed coupling is not physically plausible.
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