StructuredObservable protocol for generator-level functionals

[jc-macdonald]

StructuredObservable protocol for generator-level functionals

Extend protocols.py with a StructuredObservable protocol that represents generator-level dynamical quantities (as defined in MFAI proposal), complementing the existing Observable protocol which handles data-level summaries.

Motivation

Current Observable protocol maps (prediction, observation) → score. StructuredObservable maps generator/model → dynamical quantity (spectral radius, bifurcation threshold, stability margin, etc.) without requiring observation data. This is the key object for observable-based model criticism and the lawful learning Ex3 pipeline.

Protocol

class StructuredObservable(Protocol):
    name: str
    def __call__(self, generator: Any) -> np.ndarray: ...
    def from_trajectory(self, trajectory: np.ndarray, grid: np.ndarray) -> np.ndarray: ...

Implementation

• StructuredObservable protocol in protocols.py
• Tier enum extension: add STRUCTURAL tier alongside existing tiers
• ObservableBundle: collection of structured observables with joint evaluation
• Example implementations: gradient norm, spectral gap, curvature (kappa), skewness (xi)
• Integration with Study: structured observables as post-hoc diagnostics

Source code reference

• Thoery_1_Code.ipynb: compute_observables_from_ode (9 structured observables: I, rho, Sigma, kappa, xi, etc.)
• Chemostat_Simulator.ipynb: all functional observables (I, rho, Sigma, kappa, xi, Pf, pi, t_max, max_n)
• MFAI.tex: Definition of structured observable as map from generator to Banach-valued quantity

Tests

• Protocol compliance checks
• Known-system validation: SIR → R0, epidemic peak timing