# PAG Node Decomposition

> Group directives into nodes, each one decision on one reasoning axis, headed by its layer, axis, math type and the shape its decision yields, tagged with the substrate stage its artifact comes to be at, and contracted so that its input names the prior node's output or a declared slot, its transform is stated in semantic operations, and its output is the one record the next node reads.

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

Listed in [Algorithm contracts](https://banes-lab.com/api/records/algorithms.md), after [PAG Keyword Ontology](https://banes-lab.com/records/algorithms/pag-keyword-ontology.md) and before [PAG Handoff Gate](https://banes-lab.com/records/algorithms/pag-validation-gate.md).

## Domain

- [Pattern Abstract Grammar](https://banes-lab.com/records/algorithms-domain/pag.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

- [PAG Authoring Kernel](https://banes-lab.com/records/algorithms/pag-authoring-kernel.md)

## Named in the derivation of

- [PAG Authoring Kernel](https://banes-lab.com/records/algorithms/pag-authoring-kernel.md)

## Math type

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

## Force

- [Contract compatibility](https://banes-lab.com/records/force/contract-compatibility.md)
- [Domain boundary](https://banes-lab.com/records/force/domain-boundary.md)
- [Modularity](https://banes-lab.com/records/force/modularity.md)

## Linked from

- [Pattern Abstract Grammar](https://banes-lab.com/ontology/algorithms/algorithms-domain-pag.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)