Mathematical Utilities

Three pure-function modules provide mathematical foundations for workflow decisions. They are deterministic, dependency-free, and fully tested with hand-computed fixtures.

Bayesian Confidence Aggregation (`scripts/bayesian-confidence.mjs`)

Combines independent findings from multiple subagents into a single posterior probability using the odds form of Bayes' theorem:

posterior_odds = prior_odds × ∏(p_i / (1 - p_i))

Export	Purpose
`combineConfidence(findings, prior)`	Combine independent findings into a posterior
`classifyVerdict(posterior)`	Map posterior to `auto-merge`, `human-review`, or `reject`
`weightOfEvidence(confidence)`	Log-likelihood ratio (nats) for a single finding
`aggregateFindings(findings, prior)`	Full verdict object with counts

Thresholds: >= 0.95 auto-merge, >= 0.70 human review, < 0.70 reject.

bun run math:bayes

Formal Logic Invariants (`scripts/formal-invariants.mjs`)

Structural predicates that must hold for a plan to be well-formed. Each returns true or a violation string.

Export	Invariant
`isAcyclic(graph)`	Dependency graph is a DAG (no cycles)
`hasReferentialIntegrity(graph, taskIds)`	All dependencies reference existing tasks
`hasMutuallyExclusiveScopes(scopes)`	No two tasks claim the same file
`hasValidGateOrdering(tasks)`	Verification comes after implementation
`hasUniqueIdempotencyKeys(tasks)`	No duplicate idempotency keys
`validateInvariants(plan)`	Run all checks, return violation list

bun run math:invariants

Queueing Theory Batch Sizing (`scripts/queueing-batch.mjs`)

M/M/c queue model for optimal subagent dispatch. Computes wait probabilities, queue lengths, and cost-minimizing batch sizes.

Export	Formula
`erlangC(λ, μ, c)`	Probability an arriving task must wait
`averageQueueLength(λ, μ, c)`	Mean queue length `L_q`
`averageWaitTime(λ, μ, c)`	Mean wait time `W_q = L_q / λ`
`optimalBatchSize(λ, μ, costs)`	Cost-minimizing batch size
`completionProbability(λ, μ, c, t)`	`P(T <= t)`

bun run math:batch