instant
plain-language theorem explainer
instant defines a zero-length measurement window starting at natural number tick t. It is used in RS-native protocols to represent instantaneous observations within the discrete tick ledger. The definition applies the Window constructor directly with length set to zero.
Claim. The map sending each natural number $t$ to the window with start tick $t$ and length zero.
background
The RS-Native Measurement Framework defines core observables using ticks with τ₀ = 1, keeping SI calibration external. Window is a structure with fields t0 (start tick) and len (duration in ticks, where len = 0 denotes instantaneous). This local Window differs from the CellularAutomata version, which is a function from Fin n to CellState representing a finite tape segment.
proof idea
The definition is a direct application of the Window structure constructor, pairing the input tick t with length 0. No tactics or lemmas are involved; it is a one-line definition.
why it matters
This supplies the instantaneous window constructor for the measurement scaffold in Recognition Science. It enables explicit protocols for point-like measurements in the tick-based system, consistent with the discrete time foundation. Since no downstream uses are listed, it serves as a primitive building block for catalog observables.
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