# Dependency Linearization

> Detect cycles in the sequential Z-graph, block if any exist, and otherwise order the phases in topological Z-order with a stable tie-breaker so execution order is fixed by dependency alone.

Record: `algorithms:dependency-linearization`
Kind: algorithm
Canonical: https://banes-lab.com/ontology/algorithms#algorithms-dependency-linearization
Closure: https://banes-lab.com/json/records/algorithms/dependency-linearization/closure

Listed in [Algorithm contracts](https://banes-lab.com/api/records/algorithms.md), after [Four-Dimensional Phase Graph](https://banes-lab.com/records/algorithms/four-dimensional-phase-graph.md) and before [Severity Assignment](https://banes-lab.com/records/algorithms/severity-assignment.md).

## Domain

- [Checklist creation](https://banes-lab.com/records/algorithms-domain/checklist-creation.md)

## Stage

- [project](https://banes-lab.com/records/stage/project.md)

## Axis

- [reasoning](https://banes-lab.com/records/reasoning/axis-reasoning.md)

## Tier

- [process](https://banes-lab.com/records/vocabulary/domain-tier-process.md)

## Composed by

- [Planning Stage](https://banes-lab.com/records/algorithms/planning-stage.md)

## Math type

- [Graph](https://banes-lab.com/records/reasoning/math-type-graph.md)

## Force

- [Causality ordering](https://banes-lab.com/records/force/causality-ordering.md)
- [Control coordination](https://banes-lab.com/records/force/control-coordination.md)
- [Correctness verification](https://banes-lab.com/records/force/correctness-verification.md)

## Linked from

- [Checklist creation](https://banes-lab.com/ontology/algorithms/algorithms-domain-checklist-creation.md)
- [The derivation loop](https://banes-lab.com/ontology/reasoning/reasoning-loop-derivation-loop.md)
- [The axes](https://banes-lab.com/ontology/reasoning/the-axes.md)
- [The mathematics](https://banes-lab.com/ontology/reasoning/the-mathematics.md)
- [Domain tiers](https://banes-lab.com/ontology/schema/the-vocabulary-domain-tier.md)
- [The forces](https://banes-lab.com/ontology/schema/the-forces.md)