Tick
plain-language theorem explainer
Tick aliases the fundamental discrete time step to a real-valued quantity carrying the native tick label. Researchers deriving phi-powered mass ladders or nucleosynthesis tiers cite this alias to tag every observable with the atomic temporal unit. The declaration is a direct abbreviation that reuses the real arithmetic and coercion instances already defined for Quantity.
Claim. Let Tick denote the type of real numbers equipped with the semantic label TickUnit, where TickUnit is the inductive marker for the atomic temporal progression unit and a Quantity U is the structure containing a real value together with addition, subtraction, zero, and coercion to the reals.
background
In the RS-Native Measurement Framework the core theory remains independent of SI units, with every observable built from real values tagged by semantic units and τ₀ fixed at 1. Quantity U is the structure holding a real val field, equipped with instances for Zero, Add, Sub and a coercion to ℝ. TickUnit is the empty inductive type that functions only as a label for the base time step.
proof idea
This is a one-line abbreviation that equates Tick to Quantity TickUnit, inheriting all algebraic instances and the coercion from the Quantity structure without further obligations.
why it matters
Tick supplies the dimensional anchor for the phi-ladder mass formula and the eight-tick octave, feeding directly into ml_nucleosynthesis_eq_phi, ml_is_phi_power, and the energy-scale comparisons in crystal structures. It realizes the ledger tick from TimeEmergence as a measurable quantity while keeping protocols explicit, thereby supporting the Recognition Composition Law and the discrete-time derivations used in stellar assembly and ferromagnetism.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.