J ↔ F_spring
Tier II — Similarity REJECTED
- Object
- rigid_body
- Property
- Force
- Context
- inertial_frame
- Constraint
- net_external
Sieve rationale
Structural equation-level identity (sign=+1): the canonical forms of EQ-FICK-DIFFUSION and EQ-HOOKE are syntactically equal under rename, and J maps to F_spring under the discovered bijection
Physical constraint filter
Effort (flow) cannot be identified with flow (effort) across the coupling — they are bond-graph duals, not the same quantity.
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
Emergent Buckingham Π groups
Dimensionless combinations that mix parameters from both equations — only appear in the composite system.
AI review board
3 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
The coupling identifies molar flux (J, a flow variable with dimensions [substance]/[length]²/[time]) with spring force (F_spring, an effort variable with dimensions [mass]·[length]/[time]²) via an identity transfer function. These are dimensionally incompatible and represent fundamentally different physical quantities — one is a transport flux in a diffusive medium, the other is a restoring force on a rigid body. The physical constraint filter correctly flags this as a failed Tellegen pairing: these are bond-graph duals (flow vs. effort), not equivalent quantities. The syntactic similarity between Fick's first law (J = -D·dC/dx) and Hooke's law (F = -k·x) is a superficial algebraic resemblance (both are linear proportionalities with a negative sign), not a genuine physical coupling. The emergent Buckingham π groups are trivially the dimensionless forms of each equation individually and reveal no new physics from the proposed coupling. This is a classic artefact of structural pattern-matching without physical grounding.
The proposed identity coupling maps molar flux (a flow variable with dimensions [substance]/[L]^2[T]) to mechanical force (an effort variable with dimensions [M][L]/[T]^2), violating dimensional consistency and effort–flow role matching; the semantic descriptors do not denote the same quantity nor a recognized transform. The physical-constraint filter’s tellegen_pairing failure is correct and aligns with standard bond-graph analogies (J ↔ flow, F ↔ effort). The claimed structural identity is a superficial algebraic resemblance (y = −Kx) that does not confer physical equivalence, and the listed π-groups are trivial restatements of each equation rather than genuine cross-domain emergent properties.
The proposed coupling is physically implausible as it equates Molar Flux with mechanical Force, quantities that are dimensionally, conceptually, and semantically distinct. This identification is based on a superficial syntactic similarity between the two equations and is correctly flagged as invalid by the physical constraint filter, which notes the dimensional mismatch and the fundamental error of equating a 'flow' variable (flux) with an 'effort' variable (force). No genuine emergent properties are generated; the coupling is a physically meaningless algebraic artifact.