Constants Rsnative Units E Coh Rs Eq E Coh

The coherence quantum

The coherence quantum, written E_coh, is the fundamental energy unit in the Recognition Science (RS) measurement system. The system builds its units from two base primitives: the tick, one discrete ledger posting interval, and the voxel, the distance light travels in one tick. Energy is measured in coherence quanta, and the declaration E_coh_rs_eq_E_coh establishes that this quantum equals the golden ratio φ raised to the power −5, or φ⁻⁵. The golden ratio, approximately 1.618, is the unique positive solution to r² = r + 1.

This value is not a measured constant but a definitional choice within the RS framework. The framework's forcing chain derives φ as the unique self-similar scaling, and the unit system then places energy on a φ-ladder: φⁿ for integer n provides the natural scaling for masses, energies, times, and lengths. The coherence quantum sits at n = −5 on this ladder. The action quantum, ħ, is defined as the product of the coherence quantum and the tick, so the framework's Planck constant equivalent inherits the same φ-based structure.

The declaration also sets the speed of light to unity: c = 1 in voxels per tick. All dimensionless ratios in the system are fixed by φ alone, and conversion to SI units is explicit and optional through the ExternalCalibration structure. This means the coherence quantum is self-referential within the RS unit system: it does not depend on any external anchoring to kilogram or joule standards.

In Recognition Science, the declaration establishes the internal consistency of the unit system, not a physical measurement. The framework models energy as discrete coherence quanta, and the declaration fixes the numerical value of that quantum in RS-native units. It does not claim that physical energy in SI units equals φ⁻⁵ joules, nor does it derive the value from first principles. The value is a definitional choice that the framework's library of formal theorems supports as consistent, not as an empirical fact.

/-- Coherence energy quantum: φ⁻⁵ ≈ 0.0902. -/
@[simp] noncomputable def cohQuantum : ℝ := E_coh

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

lemma phiRung_one : phiRung 1 = phi := by simp [phiRung]

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

What this page does not claim

The coherence quantum is not a measured physical constant in SI units. The declaration does not derive φ⁻⁵ from first principles; it is a definitional choice. The declaration does not claim that all energy in nature is quantized in coherence quanta.

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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