Temporal Citation Analysis

Measures the rate of citation accrual over discrete time windows to identify accelerating or decelerating influence. A sudden spike in citations to an older case often signals doctrinal rediscovery or a new application context.

• Computed as citations per year/month for each node
• Detects sleeping precedent reactivation
• Enables early warning of emerging doctrinal shifts
• Example: A 1952 decision suddenly receiving 40+ citations in 2024 after averaging 2/year

Models the probability of citation decay over time using survival analysis techniques. Each legal decision has a characteristic half-life representing when its citation rate drops to 50% of peak.

• Fit using Weibull or exponential decay models
• Identifies cases with atypical longevity
• Distinguishes evergreen authority from transient influence
• Critical for maintaining authority freshness scores in live systems

Partitions the citation graph into discrete time-slice snapshots to observe structural evolution. Comparing snapshots reveals how community structures form, merge, or dissolve as legal doctrines mature.

• Enables change-point detection in network topology
• Tracks doctrinal drift across circuit splits
• Supports retrospective authority scoring at any historical point
• Used to validate that models don't rely on future-tainted data

Traces the propagation chains initiated by a seminal decision through time. A cascade model captures how a single ruling triggers first-generation citations, which in turn spawn second-generation references, creating a branching influence tree.

• Measures cascade depth and branching factor
• Identifies super-spreader intermediate cases
• Models diffusion patterns across jurisdictions
• Example: Miranda v. Arizona generating a 5-level cascade spanning 60 years

Identifies cases that experience a statistically significant revival after a prolonged period of dormancy. Often triggered by new legislation, technological change, or a Supreme Court decision that recontextualizes older precedent.

• Uses anomaly detection on citation time series
• Flags second-life precedents for human review
• Correlates with legislative overruling events
• Critical signal for litigation strategy and risk assessment

Applies recency bias to authority propagation algorithms so that recent citations contribute more to a node's influence score than older ones. Prevents stale authority inflation where long-dormant cases retain high scores purely from historical accumulation.

• Implements exponential or harmonic decay kernels
• Balances historical significance with current relevance
• Produces time-aware PageRank variants for legal graphs
• Essential for ranking search results by contemporary authority