m ↔ m
Tier I — Equivalence CONJECTURAL
Sieve rationale
Identical tier1 key (object=rigid_body, property=Mass, context=inertial_frame, constraint=None)
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
Emergent Buckingham Π groups
Dimensionless combinations that mix parameters from both equations — only appear in the composite system.
AI review board
Unanimous APPROVE from the AI review board.
The coupling identifies the inertial mass parameter m in Newton's second law (F = ma) with the same inertial mass m appearing in the work-energy theorem (W = ½mv_f² − ½mv_i²). Both semantic descriptors specify the identical QUDT quantity kind (Mass), the same object of interest (rigid body), the same context (inertial frame), and no additional constraints, connected via an identity transfer function. This is a textbook-level tier-1 equivalence: the work-energy theorem is derived directly from Newton's second law by integrating F·ds along a path, so the mass parameter is literally the same physical quantity in both equations. The physical-constraint filter returning all not_applicable is expected, since mass is a scalar parameter rather than a bond-graph port variable, and neither equation is a linear transport law. The emergent Buckingham π groups are dimensionally consistent: F⁻¹·a·m is trivially unity by F=ma, while the groups involving v_f and v_i reflect the nondimensionalization of velocities against (F/a)^(1/2) · W^(-1/2), which is physically sensible. No spurious emergent properties are claimed. This is a well-justified, physically correct coupling.
The variables represent the same physical quantity (the rigid body’s inertial mass) in both Newton’s second law and the work–energy theorem within an inertial frame, so an identity mapping at tier-1 equivalence is appropriate. The physical-constraint checks are correctly marked not applicable because mass is a parameter, not an effort/flow variable, and this does not indicate any inconsistency. The listed dimensionless groups are reasonable (duplication aside) and do not suggest spurious emergent behavior. Overall, the coupling is physically plausible and semantically sound.
The proposed coupling is physically fundamental, as the work-energy theorem is a direct integral consequence of Newton's second law. The inertial mass 'm' is definitionally identical in both equations when applied to the same rigid body. The semantic descriptors correctly and identically capture this context. The physical constraint filter's inability to provide a positive verdict is a reflection of its current limited scope, not a flaw in the proposed coupling, as this relationship does not fit the specific forms (e.g., transport laws, bond graph ports) that the available automated checks are designed to analyze.