Theorems — Kinematics
Every theorem derives from Axiom-0. Classical results emerge as degenerate limits.
10 theorems across 1 modules
Catalog
| ID | Name | Module |
|---|---|---|
KN1-ELASTIC-CONSERVATION | All elastic collisions conserve momentum AND energy | kinematics_theorems |
KN2-ENERGY-ADDITIVITY | E_mechanical = E_kinetic + E_potential to machine precision | kinematics_theorems |
KN3-WORK-ENERGY-THEOREM | Work-energy theorem: valid when W_net = ΔKE, invalid otherwise | kinematics_theorems |
KN4-ENERGY-CONSERVATION-DETECTION | Conservation detector: constant series → conserved, decaying → not | kinematics_theorems |
KN5-OSCILLATION-CLASSIFICATION | Sinusoidal → oscillatory; linear/constant → Non_Oscillatory | kinematics_theorems |
KN6-STABILITY-ORDERING | Tighter trajectories have higher K_stability than wider ones | kinematics_theorems |
KN7-STABILITY-TREND | Monotone K series correctly classified as Degrading/Improving/Stable | kinematics_theorems |
KN8-MOTION-REGIME-CLASSIFICATION | Five regimes reachable via explicit parameter combinations | kinematics_theorems |
KN9-PHASE-SPACE-GEOMETRY | Phase trajectories have non-negative path length and enclosed area | kinematics_theorems |
KN10-CROSS-MODULE-CONSISTENCY | Full chain: kinematics → energy → phase → stability is consistent | kinematics_theorems |
Kinematics Theorems
Source: closures/kinematics/kinematics_theorems.py
KN1-ELASTIC-CONSERVATION: All elastic collisions conserve momentum AND energy
- Function:
theorem_KN1_elastic_conservation() - Module:
kinematics_theorems
KN2-ENERGY-ADDITIVITY: E_mechanical = E_kinetic + E_potential to machine precision
- Function:
theorem_KN2_energy_additivity() - Module:
kinematics_theorems
KN3-WORK-ENERGY-THEOREM: Work-energy theorem: valid when W_net = ΔKE, invalid otherwise
- Function:
theorem_KN3_work_energy_theorem() - Module:
kinematics_theorems
KN4-ENERGY-CONSERVATION-DETECTION: Conservation detector: constant series → conserved, decaying → not
- Function:
theorem_KN4_energy_conservation_detection() - Module:
kinematics_theorems
KN5-OSCILLATION-CLASSIFICATION: Sinusoidal → oscillatory; linear/constant → Non_Oscillatory
- Function:
theorem_KN5_oscillation_classification() - Module:
kinematics_theorems
KN6-STABILITY-ORDERING: Tighter trajectories have higher K_stability than wider ones
- Function:
theorem_KN6_stability_ordering() - Module:
kinematics_theorems
KN7-STABILITY-TREND: Monotone K series correctly classified as Degrading/Improving/Stable
- Function:
theorem_KN7_stability_trend() - Module:
kinematics_theorems
KN8-MOTION-REGIME-CLASSIFICATION: Five regimes reachable via explicit parameter combinations
- Function:
theorem_KN8_motion_regime_classification() - Module:
kinematics_theorems
KN9-PHASE-SPACE-GEOMETRY: Phase trajectories have non-negative path length and enclosed area
- Function:
theorem_KN9_phase_space_geometry() - Module:
kinematics_theorems
KN10-CROSS-MODULE-CONSISTENCY: Full chain: kinematics → energy → phase → stability is consistent
- Function:
theorem_KN10_cross_module_consistency() - Module:
kinematics_theorems
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