Explain the Lean theorem `coherence_exponent_eq_5` in module `IndisputableMonolith.Masses.CoherenceExponent`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

Plain English (1): The theorem coherence_exponent_eq_5 asserts that the defined quantity coherence_exponent (octave minus D) equals exactly 5.

Relevance in Recognition Science (2): RS derives the coherence energy as E_coh = φ^{-5} (see E_coh_eq). This theorem shows the exponent 5 is forced by the Fibonacci constraint on dimension: D = 3 = F_4 and 2^D = 8 = F_6 imply 8 - 3 = 5 = F_5. The exponent is therefore structural, not a free parameter.

Reading the formal statement (3): The declaration is

theorem coherence_exponent_eq_5 : coherence_exponent = 5 := by
  unfold coherence_exponent octave D
  norm_num

It unfolds the definitions coherence_exponent := octave - D, octave := 2 ^ D, D := 3 and reduces 8 - 3 to 5 by numeric computation.

Visible dependencies (4): Relies on octave_eq_8, D_is_fib_4, octave_is_fib_6, fib_4_eq, fib_5_eq, fib_6_eq and coherence_exponent_is_fib_5, all in the same module. The main bundling result is coherence_exponent_unique.

What it does not prove (5): It establishes only the numeric equality inside this module. It does not derive the mass spectrum, the fine-structure constant, or any empirical predictions; those steps lie outside the supplied source.