cp6CapacityPhiBits
Researchers comparing phi-bit and Shannon information measures cite the definition of CP6 capacity as phi to the twelfth power. The quantity supplies the scaling factor for recognition channel capacity on the twelve-dimensional CP6 manifold at any resolution epsilon. The definition is a direct abbreviation that invokes the pre-established phi constant from the forcing chain.
claimThe recognition capacity of the CP6 meaning manifold, measured in phi-bits, equals $phi^{12}$.
background
The Recognition Entropy module treats information in base-phi units as more fundamental than base-2 Shannon bits. CP6 is the twelve-real-dimensional meaning manifold whose channel capacity therefore scales as phi^12 times log_phi(1/epsilon). Upstream structures from SpectralEmergence establish the gauge content and fermionic degrees of freedom that fix the dimensional count at twelve, while PhiForcingDerived supplies the J-cost calibration underlying the recognition process.
proof idea
The definition is a direct abbreviation that sets the identifier to phi raised to the power twelve.
why it matters in Recognition Science
This definition supplies the recognition_capacity_phi_12 entry listed in the module documentation and supports the claim that recognition capacity exceeds the corresponding Shannon capacity. It sits inside the phi-ladder construction and the eight-tick octave of the Recognition Science framework. The result is referenced when downstream arguments compare phi-bit discrimination to 2^12 bits.
scope and limits
- Does not compute or prove the numerical value of phi^12.
- Does not establish any inequality with Shannon capacity.
- Does not encode the explicit dependence on resolution epsilon.
formal statement (Lean)
47noncomputable def cp6CapacityPhiBits : ℝ := phi ^ 12
proof body
Definition body.
48
49/-- phi^12 > 2^12 = 4096... actually phi^12 ≈ 322, which is less than 4096.
50 The correct comparison: log_phi of the capacity exceeds log_2 because
51 phi < 2, so each phi-bit carries MORE discrimination. -/