q ↔ F_spring
Tier II — Similarity REJECTED
- Object
- heat_conducting_medium
- Property
- HeatFluxDensity
- Context
- near_equilibrium
- Object
- rigid_body
- Property
- Force
- Context
- inertial_frame
- Constraint
- net_external
Sieve rationale
Structural equation-level identity (sign=+1): the canonical forms of EQ-FOURIER-HEAT and EQ-HOOKE are syntactically equal under rename, and q 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
2 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
The coupling maps heat flux density (a flow variable with dimensions [mass]/[time]³) to spring force (an effort variable with dimensions [mass]·[length]/[time]²) via an identity transfer function. The physical constraint filter correctly identifies that these are bond-graph duals, not equivalent quantities, and the Tellegen pairing check fails because their dimensions are incompatible. While Fourier's law and Hooke's law share a superficial syntactic similarity (both are linear proportionality relations between a response and a driving gradient/displacement), this structural analogy does not constitute a physically meaningful coupling. The identity transfer function is dimensionally inconsistent, the semantic descriptors identify fundamentally different physical quantities (heat flux density vs. mechanical force), and the claimed emergent pi groups are simply restating each equation's own dimensionless form rather than revealing any genuine cross-domain insight. This is an artifact of syntactic pattern matching, not a real physical coupling.
The proposed identity coupling maps heat flux density (q) to mechanical force (F) despite fundamentally different physical roles (thermal flow vs mechanical effort) and incompatible dimensions, so it is not physically plausible. The semantic descriptors identify distinct quantity kinds without a named transform linking them. The physical-constraint filter’s Tellegen pairing and dimensional checks correctly fail, aligning with standard bond-graph conjugacies (thermal: T/heat flow; mechanical: force/velocity). The listed Buckingham Pi groups are trivial rearrangements of each law individually, not genuine cross-domain emergent properties. Consequently, the coupling should not enter the discovery ledger.
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