Constants Rsnative Units Tau Rec Eq K Gate Ratio

The gate ratio

The declaration tau_rec_eq_K_gate_ratio establishes a fixed relationship between two base quantities in the Recognition Science (RS) unit system: the fundamental time unit, called the tick, and a dimensionless ratio called K. In plain terms, it says that the value of the tick, when expressed in the system's own natural units, is equal to K. This is a definitional identity, not a derived physical law. The system chooses to set the tick equal to K, and K itself is defined as the gate ratio, a number that appears elsewhere in the framework's constants.

This identity is part of a larger scheme in which RS expresses all physical quantities without reference to SI units. The system defines a tick as one discrete ledger posting interval, and a voxel as the distance light travels in one tick. In these units, the speed of light is exactly 1. The energy quantum, called coh, is set to phi^-5, where phi is the golden ratio. The action quantum, hbar, is then coh times the tick. The declaration tau_rec_eq_K_gate_ratio pins down the tick's value in terms of K, which is itself defined as the gate ratio, a number that appears elsewhere in the framework's constants.

What the declaration does not claim is any empirical content. It does not state that K has a particular measured value, nor does it relate the tick to any SI second. The relationship is a definitional choice within the RS framework, not a theorem about the physical world. The framework's own documentation notes that SI conversion is explicit and optional, handled by a separate structure called ExternalCalibration. The declaration is a piece of internal bookkeeping: it fixes the scale of the time unit so that other quantities, like energy and action, can be expressed consistently.

In the context of the framework, this identity is a building block. It allows the system to express all physics in terms of phi and the ledger primitives, without needing external anchors. The practical consequence is that any quantity in RS can be traced back to a small set of defined constants, and the tick's value is one of those. The declaration does not, by itself, make any prediction about measurements; it is a definition that the framework uses to construct its unit system.

/-- One tick: the fundamental time quantum. -/
@[simp] def tick : Time := Constants.tick

/-- One tick: the fundamental time quantum. -/
@[simp] def tick : Time := Constants.tick

/-- Speed of light: c = ℓ₀/τ₀ = 1 voxel/tick. -/
@[simp] def c : Velocity := 1

What this page does not claim

The declaration does not state that K has a particular measured value. The declaration does not relate the tick to any SI second. The declaration is a definitional choice within the RS framework, not a theorem about the physical world.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Constants/RSNativeUnits.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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