stop
The stop definition returns the terminal tick of a discrete measurement window by adding its start tick to its length. Researchers modeling RS-native observables or classical fluid bridges would cite it when tracking window endpoints in tick arithmetic. The implementation is a direct one-line field sum with no lemmas or reductions required.
claimFor a measurement window with start tick $t_0$ and length $l$, the terminal tick is given by $t_0 + l$.
background
The RS-Native Measurement Framework supplies a lightweight scaffold for tick-based observables with $τ_0 = 1$, separating core theory from optional external calibrations. A measurement window is a finite discrete interval specified by its starting tick and length in ticks, with zero length denoting an instantaneous record. This module emphasizes explicit protocols so that windowing choices remain visible rather than hidden in arbitrary coarse-graining.
proof idea
One-line definition that directly sums the start-tick and length fields of the window structure.
why it matters in Recognition Science
The definition supplies endpoint arithmetic used by the bridge construction in ClassicalBridge.Fluids.CPM2D, which packages discrete states with defect and energy interpretations. It occupies a basic position in the measurement seam of the Recognition Science framework, supporting T7 tick-octave primitives without introducing new hypotheses.
scope and limits
- Does not encode uncertainty semantics or probability distributions.
- Does not impose protocol constraints or falsifiability conditions.
- Does not perform any measurement or state evolution beyond endpoint addition.
formal statement (Lean)
81@[simp] def stop (w : Window) : Nat := w.t0 + w.len
proof body
Definition body.
82
83end Window
84
85/-! ## Uncertainty and measurement record -/
86
87/-- Uncertainty semantics for scalar (real-valued) measurements.
88
89v1 used only `sigma`. v2 adds:
90- interval bounds
91- a finite discrete distribution scaffold
92
93This is intentionally lightweight: it is a *reporting seam* for measurement,
94not a full probability theory. -/