omega_BIT
The BIT carrier frequency is defined as five times the golden ratio in RS-native units. Researchers deriving substrate-dependent T2 ratios under the Bosonic Identity Theorem cite this constant when calibrating decoherence channels across qubit classes. It is supplied by a direct definition with no additional steps.
claimThe BIT carrier frequency satisfies $ω_{BIT} = 5φ$, where $φ$ denotes the golden ratio.
background
The Decoherence from BIT module treats the Bosonic Identity Theorem as identifying a common carrier for dark-energy, superconductivity, and consciousness-substrate interactions. This carrier is fixed at the value 5φ in RS-native units, matching the carrier definitions already present in cortical neuromodulation and phantom-coupled GW antenna models. The upstream Constants structure supplies the abstract bundle of CPM constants that includes φ, while the module itself records that Z-rung assignments for specific qubit families remain hypothesis-grade.
proof idea
This is a one-line definition that directly assigns the constant to five times Constants.phi.
why it matters in Recognition Science
The definition supplies the canonical frequency required by the DecoherenceFromBITCert structure and the one-statement theorem decoherence_from_BIT_one_statement. It anchors the BIT-coupling model inside the Recognition Science framework at the self-similar fixed point φ (T6) and the eight-tick octave (T7). The assignment enables the structural result that cross-class T2 ratios are exact φ-powers, while leaving the per-class Z-rung assignments as open empirical hypotheses.
scope and limits
- Does not derive the numerical prefactor 5 from first principles inside this module.
- Does not assign a specific Z-rung to any named qubit family.
- Does not claim validity outside RS-native units.
- Does not address decoherence mechanisms beyond the BIT-coupling channel.
formal statement (Lean)
53def omega_BIT : ℝ := 5 * Constants.phi
proof body
Definition body.
54
55/-- The BIT carrier frequency is positive. -/