IndisputableMonolith.Jurisprudence.PrecedentStabilityFromSigma
The module introduces Precedent as a structure carrying jurisdictional sigma-weight and age to formalize stability in legal corpora. It defines totalSigma as the aggregate weight sum and establishes lemmas on appenditivity, overturn monotonicity, and bounds on amendment cycles. Researchers modeling legal evolution from Recognition Science would cite these objects when deriving system stability thresholds. The module builds via inductive list definitions and direct applications of summation and positivity from the Cost module.
claimA precedent is a pair $P = (w, a)$ where $w$ is the jurisdictional weight and $a$ the age. For a corpus $C$, the total weight is defined by the summation function totalSigma$(C) = w_1 + w_2 + ... + w_n$. Overturning a precedent strictly decreases totalSigma, and amendment cycles satisfy bounds on their maximum rate.
background
The module sits in the jurisprudence domain and imports the RS time quantum tau_0 = 1 tick from Constants together with cost functions from the Cost module. Precedent is introduced as the basic object with sigma-weight (jurisdictional level) and age. Corpus is represented as a list of precedents. totalSigma is the additive weight function with base case totalSigma_nil and recursive step totalSigma_append. overturn removes a precedent and amendmentCycle tracks sequences of changes, with maxAmendmentRate giving the supremum rate.
proof idea
This is a definition module whose lemmas follow by direct computation. totalSigma_append and totalSigma_nil are proved by induction on list structure. overturn_decreases_sigma applies the definition of weight subtraction. amendmentCycle_eq and maxAmendmentRate_pos are obtained by unfolding the definitions and invoking positivity of sigma-weights.
why it matters in Recognition Science
The module supplies the core objects for precedent stability analysis in the Jurisprudence domain. It feeds derivations of legal system evolution and amendment bounds that connect to the Recognition Science forcing chain through cost metrics. No downstream uses are recorded yet, but the definitions ground jurisdictional weights for later stability thresholds.
scope and limits
- Does not model concrete case law or jurisdiction-specific rules.
- Does not incorporate continuous time evolution beyond the discrete age parameter.
- Does not derive numerical amendment rates from physical constants such as phi.
- Does not address resolution of conflicts among multiple precedents.
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