Time
plain-language theorem explainer
Time is the real line serving as the codomain for all temporal quantities in the Recognition Science native unit system, with the tick as the base atomic interval. Modelers of action functionals and relaxation dynamics cite this abbreviation when writing time-dependent expressions in tick units. The declaration is a direct type abbreviation that imports the standard real structure with no additional axioms or reductions.
Claim. In the RS-native units the time coordinate belongs to the real numbers: $t : T$ where $T = {t | t : ℝ}$.
background
The RS-native measurement system takes ledger primitives as base standards. The tick τ₀ is one discrete posting interval and the voxel ℓ₀ is the causal spatial step light traverses in one tick. Derived quanta are the coherence energy E_coh = φ^{-5} and the action quantum ħ = E_coh · τ₀, with c = 1 fixed and all dimensionless ratios set by φ alone. Measures are organized on the φ-ladder where φ^n supplies natural scalings for times, lengths, masses and energies.
proof idea
The declaration is a one-line abbreviation that sets the type Time equal to the real numbers ℝ, inheriting ordering, field operations and metric from the Mathlib real numbers.
why it matters
This abbreviation supplies the time carrier for the native unit system and is referenced by RealAction (J-action on real trajectories), isFragileGlass (fragility range with relaxation time τ = τ₀ × φ^n), RSPreserving (complexity bounds), tau0_pos (fundamental time quantum), and G_codata_ne_zero. It supports the forcing-chain steps that fix the eight-tick octave and D = 3 while keeping all constants inside the α^{-1} band (137.030, 137.039).
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