Module allocation_budget 

Sequential allocation leak detection using CUSUM and e-process.

This module monitors per-frame allocation counts/bytes as a time series and detects sustained mean-shift regressions with formal guarantees.

Mathematical Model

CUSUM (Cumulative Sum Control Chart)

Tracks one-sided cumulative deviation from a reference mean μ₀:

S_t⁺ = max(0, S_{t-1}⁺ + (x_t − μ₀ − k))   // detect upward shift
S_t⁻ = max(0, S_{t-1}⁻ + (μ₀ − k − x_t))   // detect downward shift

where k is the allowance (slack) parameter, typically δ/2 for a target shift of δ. Alert when S_t⁺ ≥ h or S_t⁻ ≥ h.

CUSUM is quick to detect sustained shifts but is not anytime-valid: it controls ARL (average run length) rather than Type I error.

E-Process (Anytime-Valid Sequential Test)

Maintains a wealth process over centered residuals r_t = x_t − μ₀:

E_0 = 1
E_t = E_{t-1} × exp(λ × r_t − λ² × σ² / 2)

where:

• σ² is the assumed variance under H₀
• λ is the betting fraction (adaptive via GRAPA or fixed)

Alert when E_t ≥ 1/α. This provides anytime-valid Type I control: P(∃t: E_t ≥ 1/α | H₀) ≤ α.

Dual Detection Strategy

Detector	Speed	Guarantee	Use
CUSUM	Fast (O(δ) frames)	ARL-based	Quick alerting
E-process	Moderate	Anytime-valid α	Formal confirmation

An alert fires when both detectors agree (reduces false positives) or when the e-process alone exceeds threshold (formal guarantee).

Failure Modes

Condition	Behavior	Rationale
σ² = 0	Clamp to σ²_min	Division by zero guard
E_t underflow	Clamp to E_MIN	Prevents permanent zero-lock
E_t overflow	Clamp to E_MAX	Numerical stability
No observations	No state change	Idle is not evidence

Structs

AllocationBudget

Allocation budget monitor with dual CUSUM + e-process detection.

BudgetAlert

Alert information when a leak/regression is detected.

BudgetConfig

Configuration for the allocation budget monitor.

BudgetEvidence

Evidence ledger entry for diagnostics.

BudgetSummary

Diagnostic summary.

EvidenceContext