pith. sign in
theorem

recognition_event_12_dof

proved
show as:
module
IndisputableMonolith.Information.RecognitionEntropy
domain
Information
line
67 · github
papers citing
none yet

plain-language theorem explainer

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.

Claim. The 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 $S = k_B (ln Z + beta )$ from the partition function. The module sets the local context as phi-based information theory in which recognition capacity exceeds the Shannon limit for the same space.

proof idea

The proof is a one-line wrapper that applies norm_num to the arithmetic identity 12 = 2 * 6.

why it matters

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.

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