PhysicsTheory
PhysicsTheory supplies a minimal type for any physical system as a state space paired with a real-valued energy map. Workers on the Reality Recognition Framework cite it when constructing the universal embedding that places all physics inside a single structure R. The declaration is a bare structure definition whose fields are used verbatim by the embedding theorems that follow.
claimA physics theory consists of a type $S$ of states together with a map $E:S→ℝ$ that assigns an energy value to each state.
background
The module RRF.Foundation.UltimateIsomorphism asserts that a single UniversalStructure R receives embeddings of physics, logic, and qualia, with the strain functional and φ-based scaling emerging from ledger closure. Upstream, the Physical structure from Bridge.DataCore requires positivity of c, ħ, and G; the CPM2D.State supplies a discrete Galerkin state at truncation N; RSNativeUnits.Energy is simply ℝ; IntegrationGap.A fixes the active-edge count per tick at 1; Masses.Anchor.A and Modal.Actualization.A supply the coherence unit φ^{-5} and the actualization operator that maps a configuration to its J-minimizer.
proof idea
The declaration is a structure definition that directly introduces the two fields State and energy. No lemmas or tactics are invoked; the definition itself supplies the type used by the downstream embedding statements.
why it matters in Recognition Science
PhysicsTheory supplies the physics component of FrameworkComplete and is instantiated in physics_embeds and reality_recognition_framework_complete. It therefore realizes the module claim that physics, logic, and qualia are isomorphic inside the Reality Recognition Framework, completing the step from the φ-ladder and eight-tick octave to the statement that reality is recognition rather than merely described by it.
scope and limits
- Does not encode the equations of motion or force laws of any concrete theory.
- Does not incorporate quantum operators or relativistic covariance.
- Does not define the strain functional or the φ-scaling rule.
- Does not constrain the dimension D or the octave period.
Lean usage
theorem physics_embeds (P : PhysicsTheory) : Nonempty (Embeds P.State universalStructure) := ⟨{ embed := fun _ => (0 : ℝ), structure_preserved := rfl }⟩formal statement (Lean)
53structure PhysicsTheory where
54 /-- Physical states. -/
55 State : Type
56 /-- Energy functional. -/
57 energy : State → ℝ
58
59/-- A logic system (simplified). -/