pith. machine review for the scientific record. sign in
def definition def or abbrev high

omega_BIT

show as:
view Lean formalization →

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

formal statement (Lean)

  53def omega_BIT : ℝ := 5 * Constants.phi

proof body

Definition body.

  54
  55/-- The BIT carrier frequency is positive. -/

used by (4)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (7)

Lean names referenced from this declaration's body.