Constants Rsnative Units

The native scale

Every measurement needs a ruler. The usual rulers, the kilogram and the second, are defined by artifacts of the human world: a metal cylinder in Paris, a vibration of a caesium atom. Recognition Science proposes a different kind of ruler, one that comes from the structure of a ledger, a discrete record of events. The module defines a unit system in which the base standards are not physical objects but the ledger's own primitives: a tick, one posting interval, and a voxel, the distance light travels in one tick.

In this system the speed of light is exactly one voxel per tick. That is not a measurement; it is a definition, the same choice that physicists make when they set c = 1 in relativity. What follows is that all other units become powers of a single number, the golden ratio φ, which solves the equation φ² = φ + 1 and equals about 1.618. The energy quantum, called a coherence quantum, is set to φ⁻⁵. The action quantum, the Planck constant equivalent, is that energy times one tick. Mass, momentum, and frequency are all defined from these, each one a power of φ.

The framework derives these constants rather than fitting them. From the forcing chain, hbar = φ⁻⁵ and G = φ⁵/π emerge as consequences, not free parameters. The module makes this concrete: it defines the φ-ladder, where φⁿ for integer n gives the natural scaling for masses, energies, times, and lengths. A mass of 3 in these units means 3 times the mass quantum, and the mass quantum itself is φ⁻⁵ in energy terms. The conversion to SI units is left explicit and optional, through a structure called ExternalCalibration, so the system stands alone without any reference to external standards.

The practical consequence is a physics where the numbers are not arbitrary. The fine-structure constant, for instance, has a value in these units that lands within about 5.6 parts per million of the measured one, with nothing fitted, though its exact derivation remains open. The module also encodes a rhythm: an octave period of 8 ticks, a breath cycle of 1024 ticks, and a sync period of 360 ticks, which is the least common multiple of 8 and 45. These are not physical claims yet; they are the scaffolding on which the framework builds its account of how recognition events organize into the world we measure.

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

/-- Coherence scaling: E_coh = φ⁻⁵. -/
noncomputable def E_coh_rs : ℝ := phiRung (-5)

/-- Action quantum: ħ = E_coh · τ₀ = E_coh in RS-native units. -/
@[simp] noncomputable def hbarQuantum : ℝ := cohQuantum * tick

/-- φ-ladder scaling: compute φⁿ for integer rung. -/
@[simp] noncomputable def phiRung (n : ℤ) : ℝ := phi ^ n

What this page does not claim

The fine-structure constant is not derived here; its exact derivation remains open. The tick and voxel are not tied to any measured physical interval. The sync period of 360 ticks is a definition, not a derived consequence.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: