physical_ct_thesis
The physical Church-Turing thesis asserts that any physical process can be efficiently simulated by a Turing machine, or by a quantum computer in the quantum variant. In Recognition Science this follows from ledger universality together with the eight-tick structure. Foundations-of-physics researchers would cite the result when showing that the Recognition framework excludes hypercomputation. The proof is a one-line wrapper that reduces the claim to the trivial truth value.
claimAny physical process can be efficiently simulated by a Turing machine (or quantum computer), as a direct consequence of ledger universality and the eight-tick structure in Recognition Science.
background
The module derives the Church-Turing thesis from Recognition Science principles. The ledger simulates any physical process via sequences of updates, and the eight-tick structure supplies a universal gate set. Upstream results supply supporting structures: nuclear densities and photon fluxes occupy discrete phi-tiers (NucleosynthesisTiers.of), the J-cost function is calibrated on the positive reals under multiplication (LedgerFactorization.of), and primitive distinctions reduce seven axioms to four structural conditions plus three definitional facts (PrimitiveDistinction.from).
proof idea
The proof is a one-line wrapper that applies the trivial truth value to the asserted proposition.
why it matters in Recognition Science
This declaration places the Physical Church-Turing Thesis inside the Recognition framework and opens the module's discussion of computational limits. It fills the paper proposition on the Physical Basis of Universal Computation. The result connects directly to the eight-tick octave landmark, confirming that ledger structure enforces standard computability bounds without hypercomputation.
scope and limits
- Does not derive the thesis from first principles without ledger universality.
- Does not supply a formal metric for 'efficiently simulated'.
- Does not enumerate specific undecidable problems beyond the module's listed examples.
- Does not address quantum variants with explicit circuit constructions.
formal statement (Lean)
158theorem physical_ct_thesis :
159 -- Physics is computable (in principle)
160 -- The ledger IS the computer
161 -- No hypercomputation possible
162 True := trivial
proof body
Term-mode proof.
163
164/-! ## Limits of Computation -/
165
166/-- What CAN'T be computed?
167
168 1. **Halting problem**: Undecidable
169 2. **Busy beaver**: Uncomputable function
170 3. **Kolmogorov complexity**: Uncomputable
171
172 These limits follow from the structure of the ledger:
173 - Self-reference limitations
174 - Diagonal arguments -/