Implement LawAdherence module: constraint-residual metrics and diagnostics

[jc-macdonald]

Motivation

The lawful-learning manuscript (jcm-sci/lawful-learning) defines a formal taxonomy of
Law-Adherence Metrics (Definition 2.5) and Law-Adherence Diagnostics (Definition 2.6)
that quantify structural constraint satisfaction independently of data-fit accuracy. These are
complementary to the probabilistic scoring rules in ScoringRules.jl (#32): scoring rules
assess distributional calibration, law-adherence metrics assess structural fidelity.

TradeStudy.jl should expose both axes so that Pareto surfaces can span
(accuracy × lawfulness × calibration).

Scope

A LawAdherence submodule providing:

Core metric types

Following the manuscript's Definition 2.5, a law-adherence metric M : H²(D) → R≥0 satisfies:

1. Constraint sensitivity — depends on surrogate only through constraint residuals
2. Monotonicity — larger violations ⟹ larger metric values
3. Interpretability — admits domain-meaningful interpretation

Concrete implementations

Metric	Formula	Notes
law_adherence_score	S_law = (1/m) Σ 1[O_i(Ψ) ∈ A_i]	Proportion of observables in admissible range; soft sigmoid variant for differentiable use
drift_index	D = ‖Ψ - Ψ_ref‖ / ‖Ψ_ref‖	Relative deviation from lawful reference
violation_magnitude	V = Σ_j ‖(H_j[Ψ])₋‖	Aggregate constraint violation size
margin	M = min_j H_j[Ψ]	Distance to nearest constraint boundary
violation_rate	R = (1/N) Σ 1[∃j: H_j[Ψ(x_n)] < 0]	Proportion of points with any violation
elasticity	E = (x/Y)(∂Y/∂x)	Signed diagnostic; abs(E) is a metric

Tier-stratified scoring

law_adherence_score(trial; tier=:all)   # aggregate
law_adherence_score(trial; tier=:E)     # embedded only (should be 1.0 for PESFs)
law_adherence_score(trial; tier=:P)     # penalized
law_adherence_score(trial; tier=:D)     # diagnostic

Dynamical-system extensions

Metric	Description
conservation_drift	Relative change in conserved quantity over horizon
time_to_violation	First time any constraint is violated
violation_duration	Total time constraints are violated
stability_fraction	Proportion of trajectories remaining bounded
degradation_rate	Rate of S_law decay under rollout

Integration with TradeStudy protocols

• Law-adherence metrics should implement the AbstractScorer protocol from Scaffold Protocols module: abstract types and core structs #25
• score() dispatch (score() dispatch: CRPS, WIS, interval, energy, RMSE, MAE #4) should route law-adherence metrics alongside ScoringRules.jl metrics
• Results should appear as columns in ResultsTable (TrialResult and ResultsTable types #2) for Pareto extraction (extract_front() and pareto_rank() via Metaheuristics.jl #8)

Dependencies

• Scaffold Protocols module: abstract types and core structs #25 (Protocols — AbstractScorer, AbstractConstraint types)
• Add ScoringRules.jl as scoring backend #32 (ScoringRules.jl backend — complementary scoring axis)
• Formal definitions from lawful-learning manuscript (Definitions 2.5, 2.6; Appendix A.7)

Non-goals

• This module does not implement PESF training or constraint enforcement —
  that belongs in LawfulSurrogates.jl (Phase 5)
• This module only evaluates constraint satisfaction, it does not enforce it

Cross-references

• lawful-learning Axis-aware observable scoring: score observables defined on structured axes #24 (Discussion connecting scoring rules to law-adherence)
• ScoringRules.jl build_grid: full factorial and LHS via QuasiMonteCarlo.jl #6 (unified score() dispatcher)
• Python trade-study will get an equivalent module later