church_turing_implies_limits
plain-language theorem explainer
The theorem shows that the Church-Turing physics structure derived from the discrete ledger directly entails the corresponding computation limits structure. Researchers modeling bounded physical computation in discrete spacetime would cite it to confirm that RS evolution stays within Turing-machine resources. The proof is a one-line wrapper that transfers the hypothesis without additional steps.
Claim. If the physical dynamics in Recognition Science arise from the discrete ledger structure satisfying the Church-Turing condition, then the computation limits structure derived from that ledger holds.
background
The module derives the Physical Church-Turing Thesis from the discrete ledger: states are ratios updated by the 8-tick operator on a finite phase space, with each tick processing a bounded number of entries. Upstream results supply the tick as the fundamental time quantum τ₀ = 1, the phase map sending Fin 8 to kπ/4, and the cellular-automaton step that applies local rules to produce successor states. The setting therefore guarantees finite memory per tick and continuous (hence approximable) transitions.
proof idea
The proof is a one-line wrapper that applies the hypothesis church_turing_physics_from_ledger directly to obtain computation_limits_from_ledger.
why it matters
This result completes the IC-003 derivation by linking ledger-based Church-Turing physics to explicit computation limits, supporting the module's claim that no RS process can access more than 8 phases in one tick. It draws on the eight-tick octave and finite phase space from the forcing chain, ensuring no hypercomputation is possible. The declaration feeds the subsequent bounded-phase theorem in the same section.
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