module module high

`IndisputableMonolith.Masses.CoherenceExponent`

The CoherenceExponent module in the Masses domain assigns structural parameters for Recognition Science. It sets the spatial dimension D equal to the fourth Fibonacci number F₄ = 3 and fixes the coherence exponent at 5. These values support the phi-ladder mass formula and the eight-tick octave. The module proceeds via direct definitions and equalities on Fibonacci sequences.

claimThe module establishes $D = F_4 = 3$ for the number of spatial dimensions and defines the coherence exponent as 5.

background

Recognition Science derives all physics from one functional equation, with the forcing chain T0-T8 yielding D = 3 spatial dimensions at step T8 and an eight-tick octave at T7. This module depends on the Constants module, whose doc-comment states that τ₀ = 1 tick is the fundamental RS time quantum in native units. It introduces sibling definitions for Fibonacci base cases and recurrences, then maps them to D, octave, and the coherence exponent for use in mass spectra.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

This module feeds mass formula derivations by supplying the coherence exponent 5 that appears in ħ = φ^{-5} and G = φ^5 / π. It realizes the T8 landmark of the UnifiedForcingChain by setting D = 3. The assignments anchor the phi-ladder scaling yardstick * φ^(rung - 8 + gap(Z)) and the alpha band inside (137.030, 137.039).

scope and limits

Does not derive the coherence exponent from the J functional equation.
Does not prove uniqueness of the Fibonacci-to-dimension mapping.
Does not compute explicit particle masses or rung values.
Does not address extensions beyond three spatial dimensions.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (23)

theorem fib_4_eq L32
theorem fib_5_eq L35
theorem fib_6_eq L38
theorem fib_recurrence_at_6 L43
theorem fibonacci_deficit L47
def D L53
def octave L56
theorem octave_eq_8 L59
theorem D_is_fib_4 L64
theorem octave_is_fib_6 L69
def coherence_exponent L75
theorem coherence_exponent_eq_5 L78
theorem coherence_exponent_is_fib_5 L83
theorem coherence_exponent_from_fibonacci L87
def is_fibonacci L94
theorem D_1_fibonacci_constraint L98
theorem D_2_fails L102
theorem D_3_fibonacci_constraint L105
theorem D_5_fails L109
theorem D_8_fails L112
theorem coherence_exponent_unique L123
def E_coh L133
theorem E_coh_eq L136