Module validation_pipeline 

Expected-cost validation ordering with Bayesian online learning.

This module provides a validation pipeline that orders validators by expected cost, using Beta-posterior failure probabilities and early exit.

Mathematical Model

Each validator i has:

• cost c_i: measured execution time (running exponential average)
• failure probability p_i = α_i / (α_i + β_i): Beta posterior mean

The optimal ordering minimises expected total cost under early-exit (stop on first failure). By the classic optimal search theorem (Blackwell 1953), the minimum-expected-cost ordering sorts validators by decreasing p_i / c_i (highest “bang per buck” first).

E[cost(π)] = Σ_k  c_{π_k} × Π_{j<k} (1 − p_{π_j})

Online Learning

After each validation run the pipeline updates its Beta posteriors:

• Failure observed: α_i += 1
• Success observed: β_i += 1

Cost estimates use an exponential moving average with configurable smoothing factor γ ∈ (0,1].

Evidence Ledger

Every ordering decision is recorded in an evidence ledger so that the ranking is fully explainable. Each entry contains:

• validator id, p_i, c_i, score = p_i / c_i, rank

Failure Modes

Condition	Behavior	Rationale
c_i = 0	Clamp to c_min (1μs)	Division by zero guard
α + β = 0	Use prior (1, 1)	Uniform prior assumption
All validators pass	Full cost incurred	No early exit possible
No validators	Return success, zero cost	Vacuously valid

Determinism

Given identical history (same sequence of update calls), the ordering is fully deterministic. Ties are broken by validator index (stable sort).

Structs

LedgerEntry

A single entry in the evidence ledger recording an ordering decision.

PipelineConfig

Configuration for the validation pipeline.

PipelineResult

Result of running the full pipeline.

PipelineSummary

Diagnostic summary of pipeline state.

ValidationOutcome

Result of running one validation.

ValidationPipeline

Expected-cost validation pipeline with Bayesian ordering.

ValidatorStats

Per-validator statistics tracked by the pipeline.