fundamental_tick
plain-language theorem explainer
The minimum time quantum in Recognition Science is defined to equal one in native units. Researchers deriving bounds on computation speed from discrete time cite this as the indivisible interval. The definition directly aliases the base constant without further reduction.
Claim. The minimum time quantum $τ_0$ equals $1$ in Recognition Science native units.
background
In the module on computation limits, temporal discreteness arises because the tick serves as the smallest time interval. The constant tick is defined as 1, with $τ_0$ as its notation. This underpins the claim that maximum bit rate equals the inverse of this quantum, per the module documentation on RS answers to Bremermann and Landauer limits. Upstream results establish the tick as the fundamental RS time quantum in Constants, with one octave spanning eight ticks.
proof idea
The definition is a one-line alias to the abbreviation $τ_0$ which reduces to the constant tick set to 1.
why it matters
This anchors the temporal component of IC-002, supplying the base unit for downstream results including computation_takes_time which shows n steps require at least n ticks and tick_rate_bounded which confirms the rate cannot exceed the inverse tick. It connects to the eight-tick octave in the forcing chain by providing the base period. The definition closes the interface for all time-bounded computation claims in the framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.