physicsInterpret
The definition maps each element of LogicNat, the inductive type generated by identity and successive steps, to a PhysicsState by setting its tick field to that element. Researchers constructing the carrier for a LogicRealization instance in the forcing-chain realization layer cite this embedding. The body is a one-line structure constructor that performs the direct wrapping.
claimThe function sending each logic-natural number $n$ to the physics state whose sole tick component equals $n$.
background
LogicNat is the inductive type whose constructors are identity (the zero-cost multiplicative identity) and step (one further iteration of the generator), realizing the smallest subset of the positive reals closed under multiplication by the generator and containing 1. PhysicsState is the structure whose single field is a LogicNat value, serving as the minimal recognition-state skeleton indexed by identity ticks.
proof idea
The definition is a one-line wrapper that applies the PhysicsState constructor directly to the input LogicNat value.
why it matters in Recognition Science
This definition supplies the embedding that physicsRealization uses to set Carrier := PhysicsState inside the LogicRealization record. It realizes the module's stated purpose of providing identity ticks as the step action and recognition states as the carrier for the lightweight physics hook. The construction therefore sits at the interface between the arithmetic orbit forced by the Law of Logic and the equality-cost realization of physical tick arithmetic.
scope and limits
- Does not compute costs, comparisons, or dynamics on the resulting states.
- Does not incorporate numerical values for phi, c, or other constants.
- Does not extend the construction to higher-dimensional or full forcing-chain objects.
Lean usage
def exampleState : PhysicsState := physicsInterpret LogicNat.identityformal statement (Lean)
42def physicsInterpret (n : ArithmeticFromLogic.LogicNat) : PhysicsState :=
proof body
Definition body.
43 ⟨n⟩
44
45/-- Physics realization skeleton. -/