fundamental_tick
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not provide the conversion factor to SI seconds.
- Does not prove the positivity of the tick, which is handled separately.
- Does not incorporate the irrationality of phi or Landauer energy costs.
Lean usage
def max_computation_rate : ℝ := 1 / fundamental_tickformal statement (Lean)
44def fundamental_tick : ℝ := τ₀
proof body
Definition body.
45
46/-- **THEOREM IC-002.1**: The fundamental tick is positive. -/