IndisputableMonolith.Jurisprudence.PrecedentStabilityFromSigma
The module defines structures for modeling legal precedents in the Recognition Science jurisprudence domain using σ-weights and age. It introduces Precedent, Corpus, totalSigma summation, overturn operations that reduce aggregate weight, and amendment cycle bounds. Legal theorists extending RS cost concepts to formal jurisprudence would cite these objects. The module consists of definitions and supporting lemmas on summation and rate properties.
claimA precedent $P$ carries weight $\sigma$ (jurisdictional level) and age $a$. For a corpus $C$ of precedents, $\text{totalSigma}(C)$ sums the $\sigma$ values. Overturn decreases total $\sigma$, while amendment cycles satisfy equality and maximum rate bounds.
background
The module sits in the jurisprudence domain and imports the RS time quantum $\tau_0 = 1$ tick from Constants together with cost structures from the Cost module. It defines Precedent as the basic object with $\sigma$-weight and age, Corpus as an aggregate collection, and totalSigma as the summation function over corpus weights.
Supporting definitions cover overturn (an operation that strictly decreases total sigma), amendmentCycle (periodic changes with equality lemmas), and maxAmendmentRate (a positive bound with explicit value). These build directly on the imported cost and constant primitives to formalize stability from sigma.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the foundational objects for applying sigma-based cost measures to legal precedent stability. It provides the building blocks (Precedent, totalSigma, overturn, amendmentCycle, maxAmendmentRate) that higher jurisprudence results would invoke for stability arguments, though no downstream uses are recorded yet. It extends the Cost module's defect measures into the legal setting without yet linking to the T0-T8 forcing chain or physical constants.
scope and limits
- Does not derive numerical stability thresholds or physical predictions.
- Does not model time evolution beyond the age parameter.
- Does not connect to phi-ladder, alpha band, or spatial dimensions.
- Does not prove global uniqueness or convergence of amendment processes.
depends on (2)
declarations in this module (18)
-
structure
Precedent -
abbrev
Corpus -
def
totalSigma -
theorem
totalSigma_append -
theorem
totalSigma_nil -
def
overturn -
theorem
overturn_decreases_sigma -
def
amendmentCycle -
theorem
amendmentCycle_eq -
def
maxAmendmentRate -
theorem
maxAmendmentRate_pos -
theorem
maxAmendmentRate_eq -
def
US_substantive_sigma_creating -
def
US_history_yr -
theorem
US_substantive_rate -
structure
PrecedentStabilityCert -
def
precedentStabilityCert -
theorem
precedent_stability_one_statement