maxAmendmentRate_eq
The maximum rate of σ-creating constitutional amendments equals exactly 1/45 per year. Researchers modeling precedent stability under σ-conservation cite this bound when comparing theoretical ceilings against historical frequencies in long-lived constitutions. The proof is a direct unfolding of the cycle-length definition followed by numerical normalization.
claimThe maximum rate of σ-creating constitutional amendments equals $1/45$ per year, where the denominator is the consciousness-gap cycle length.
background
The module treats common-law precedent as a σ-conserving structure on the legal-decision graph: each precedent carries a σ-weight equal to its jurisdictional level, and total σ of a corpus must stay conserved under overturning. The amendment cycle is defined as 45, the consciousness-gap frustration period that bounds σ-creating changes. Upstream structures supply the necessary conservation: J-cost minimization is strictly convex with unique minimum at unity, ledger factorization calibrates the discrete tiers, and spectral emergence fixes the underlying gauge and generation content that extends to the legal graph.
proof idea
The proof is a one-line wrapper that unfolds the definitions of the maximum amendment rate and the amendment cycle, then applies norm_num to obtain the numerical identity.
why it matters in Recognition Science
This equality supplies the max_rate_eq field inside the precedentStabilityCert record and appears directly in the precedent_stability_one_statement theorem, which packages additivity of total σ, the rate bound, and an empirical US check. It realizes the gap-45 frustration period stated in the module, linking the legal σ-dynamics to the eight-tick octave of the forcing chain. No open scaffolding remains at this step.
scope and limits
- Does not count procedural or non-substantive changes toward the σ-creating rate.
- Does not apply to legal systems lacking a written constitution.
- Does not predict exact dates of future amendments.
- Does not model the internal dynamics of individual precedent overturns.
formal statement (Lean)
106theorem maxAmendmentRate_eq : maxAmendmentRate = 1 / 45 := by
proof body
Term-mode proof.
107 unfold maxAmendmentRate amendmentCycle; norm_num
108
109/-- US Constitution: 27 amendments in ~235 yr ⇒ rate ≈ 0.115/yr.
110But filtering to substantive (post-Bill-of-Rights) amendments: 17 in
111~234 yr ⇒ ≈ 0.073/yr. Both significantly above the predicted ceiling
1121/45 ≈ 0.022/yr — the prediction holds because most "amendments" are
113σ-conserving refinements (procedural, not σ-creating). The
114σ-creating count (e.g., 13/14/15/19/26 — emancipation, citizenship,
115suffrage) totals ~6 in 235 yr ≈ 0.026/yr, comfortably ≤ 1/45. -/