recognition_event_12_dof
A single recognition event carries exactly twelve real degrees of freedom, identified with the dimension of CP^6. Researchers working on phi-based information measures cite this when mapping the eight-tick cycle output to complex projective geometry. The proof consists of a direct numerical reduction that confirms the arithmetic identity.
claimThe information capacity of one recognition event (one 8-tick cycle) equals exactly twelve real degrees of freedom, the dimension of $CP^6$.
background
Recognition entropy is measured in phi-bits rather than Shannon bits, with the recognition channel capacity of CP^6 scaling as phi^12. Entropy of a configuration equals its total defect, and thermodynamic entropy is given by $S = k_B (ln Z + beta
proof idea
The proof is a one-line wrapper that applies norm_num to the arithmetic identity 12 = 2 * 6.
why it matters in Recognition Science
This declaration supplies the explicit numerical link between the eight-tick octave and the CP^6 dimension inside the recognition entropy module. It supports the broader claim that phi-bit capacity exceeds Shannon capacity. No downstream uses are recorded yet.
scope and limits
- Does not derive the CP^6 dimension from the forcing chain or J-uniqueness.
- Does not prove entropy maximization; that is handled by a sibling result.
- Does not connect to mass ladders, alpha bounds, or spatial dimension D=3.
formal statement (Lean)
67theorem recognition_event_12_dof : (12 : ℕ) = 2 * 6 := by norm_num
proof body
Term-mode proof.
68
69/-- Uniform distribution maximizes recognition entropy (same as Shannon). -/