J_bit
The elementary ledger bit cost equals the natural logarithm of the golden ratio. Researchers deriving information costs or coherence energies in Recognition Science would cite this when normalizing ledger entries on the phi-ladder. The definition is a direct noncomputable assignment of the real logarithm to the established phi constant.
claim$J_{bit} = ln φ$, the elementary ledger bit cost in RS-native units.
background
The Constants module sets the fundamental RS time quantum as one tick. The bit cost supplies the base ledger unit for information, drawing on the golden ratio phi established in sibling definitions as the self-similar fixed point. Upstream results include the locked amplitude C_lock = sqrt(1/phi^3) from gravity asymptotic enhancement and the 8-tick phase space defined as Fin 8 in both the ChurchTuringPhysicsStructure and EightTick modules.
proof idea
This is a one-line definition that applies the real logarithm directly to phi with no lemmas or reductions.
why it matters in Recognition Science
This constant anchors bit-cost calculations in the Recognition framework and aligns with J-uniqueness at T5 together with the eight-tick octave at T7. It supports later links between information costs and coherence energy via the locked amplitude. No downstream uses appear yet, so its role in larger chain steps remains open for integration.
scope and limits
- Does not approximate the numerical value of the bit cost.
- Does not derive any relation to coherence energy or physical observables.
- Does not invoke the Recognition Composition Law or forcing chain steps.
formal statement (Lean)
249noncomputable def J_bit : ℝ := Real.log phi
proof body
Definition body.
250
251/-- Coherence energy in RS units (dimensionless).
252 By Phase 2 derivation, E_coh = C_lock = φ⁻⁵. -/