church_turing_physics_structure
The declaration establishes that the Church-Turing thesis extends to physical processes in Recognition Science, showing they remain computable on a finite 8-phase space with bounded transitions even when the golden ratio is irrational. Researchers deriving simulation limits or the physical Church-Turing thesis from discrete ledger models would cite this result. The proof is a one-line wrapper that applies the computation limits structure theorem.
claimPhysical processes in Recognition Science are computable: the phase space is finite with 8 phases, transitions are computable functions on finite types, and the tick rate is bounded by $1/τ_0$, so the dynamics satisfy the Church-Turing thesis despite the irrationality of $φ$.
background
The module derives the Physical Church-Turing Thesis from the discrete ledger structure of Recognition Science. Ledger entries are positive real ratios, yet dynamics are confined to an 8-phase space whose transitions arise from J-cost minimization on finite types. The setting rules out hypercomputation because processing occurs only at rate $1/τ_0$ and memory per tick is bounded by the phase count. Upstream, church_turing_physics_from_ledger is defined as the proposition computation_limits_from_ledger, while has_computation_limits_structure carries the concrete structure theorem that realizes this property.
proof idea
The proof is a one-line wrapper that applies has_computation_limits_structure, which itself reduces directly to computation_limits_structure.
why it matters in Recognition Science
This theorem completes the IC-003 chain by establishing the Church-Turing physics property. It is invoked by the downstream result has_ct_structure to derive the simulation hypothesis structure. The argument relies on the eight-tick octave and finite phase space from the forcing chain, showing that RS dynamics lie in BQP and inherit undecidability from Turing machines while remaining free of trans-Turing jumps.
scope and limits
- Does not claim that all physical processes are simulable in polynomial time on classical hardware.
- Does not resolve the halting problem for arbitrary RS ledger sequences.
- Does not equate RS dynamics to full quantum computation beyond membership in BQP.
Lean usage
theorem has_ct_structure : church_turing_physics_from_ledger := church_turing_physics_structureformal statement (Lean)
106theorem church_turing_physics_structure : church_turing_physics_from_ledger :=
proof body
Term-mode proof.
107 has_computation_limits_structure
108
109/-- **THEOREM IC-003.6**: Church-Turing physics implies computation limits hold. -/