tick_rate_bounded
plain-language theorem explainer
Recognition Science computations operate with a strictly positive minimum time quantum τ₀ per fundamental tick. This bound rules out infinite processing speed and enforces the discrete ledger dynamics that underpin the physical Church-Turing thesis. The result is obtained by direct appeal to the positivity of the tick constant already established in the computation-limits module.
Claim. The fundamental tick duration satisfies $τ_0 > 0$, where $τ_0$ is the minimum time quantum in the Recognition Science ledger.
background
The module derives the physical Church-Turing thesis from the discrete ledger structure of Recognition Science: each ledger entry is a positive real ratio, yet updates occur only at discrete 8-phase ticks with finite memory per step. The fundamental tick is introduced as the minimum time quantum $τ_0$ that any RS computation must consume. Upstream, the ComputationLimitsStructure module defines fundamental_tick := $τ_0$ and supplies the lemma tick_pos establishing its positivity (IC-002.1).
proof idea
One-line wrapper that applies the tick_pos lemma from ComputationLimitsStructure.
why it matters
The theorem supplies the discrete-time premise required by the IC-003 certificate, confirming that RS dynamics cannot perform trans-Turing operations because every step consumes at least one positive tick. It directly supports the claim that physical processes remain within BQP by enforcing the eight-tick octave and the rate bound 1/τ₀. The result closes the gap between the ledger factorization and the no-hypercomputation conclusion in the Church-Turing derivation.
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