precedent_stability_one_statement
plain-language theorem explainer
The declaration asserts additivity of total σ-charge under corpus concatenation, fixes the maximum substantive amendment rate at 1/45 per year from the consciousness-gap cycle, and bounds the US σ-creating amendment rate by 1/35 per year. Jurisprudence modelers treating stare decisis as σ-conservation would cite it to constrain constitutional change. The proof is a direct term that packages the additivity lemma, the rate equality, and the historical bound into one conjunction.
Claim. Let $C$ be a corpus of precedents and let $σ(C)$ denote its total σ-charge. Then $σ(C_1 ++ C_2) = σ(C_1) + σ(C_2)$ for any corpora $C_1, C_2$, the maximum amendment rate equals $1/45$ per year, and the US substantive σ-creating amendment rate satisfies $6/235 ≤ 1/35$.
background
The module treats common-law precedent as a σ-conserving structure on the legal-decision graph, with each precedent carrying an integer σ-weight equal to its jurisdictional level. Corpus is the type of finite lists of active precedents; totalSigma(C) is the sum of the σ-weights of its members. maxAmendmentRate is defined as the reciprocal of the amendmentCycle length and equals 1/45; US_history_yr is 235 and US_substantive_sigma_creating counts the six σ-creating amendments (13th, 14th, 15th, 19th, 26th and one more) yielding the rate bound 1/35.
proof idea
The proof is a term-mode wrapper that returns the triple (totalSigma_append, maxAmendmentRate_eq, US_substantive_rate). totalSigma_append is the list-sum identity after mapping σ-weights; maxAmendmentRate_eq unfolds the definition and normalizes to 1/45; US_substantive_rate is the direct numerical comparison of the counted amendments against the 235-year span.
why it matters
The theorem consolidates the three central claims of Track I5 (Precedent Stability from σ-Conservation) in Plan v5. It supplies the additivity and rate bounds that underwrite the prediction of one σ-conserving change per consciousness-gap cycle. The result anchors the Recognition Science application to jurisprudence by linking σ-conservation to stare decisis and supplying an empirical check against US history; it leaves open the classification of all amendments as σ-conserving or σ-creating.
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