# The substrate

> Beneath the loop lies the generative substrate, meaning the cycle every node passes through, the recursion that turns emergence back into a new difference, and…

Page: Ontology · Reasoning
Canonical: https://banes-lab.com/ontology/reasoning#the-substrate

Beneath the loop lies the generative substrate, meaning the cycle every node passes through, the recursion that turns emergence back into a new difference, and the math types each node yields.

Recursion · [emergence](https://banes-lab.com/records/reason/substrate-node-emergence.md) → [difference](https://banes-lab.com/records/reason/substrate-node-difference.md)

Relations diagram

The substrate cycle and its recursion.

```mermaid
flowchart LR
n_existence["existence"]
n_difference["difference"]
n_relation["relation"]
n_structure["structure"]
n_transformation["transformation"]
n_constraint["constraint"]
n_emergence["emergence"]
n_existence --> n_difference
n_difference --> n_relation
n_relation --> n_structure
n_structure --> n_transformation
n_transformation --> n_constraint
n_constraint --> n_emergence
n_emergence -.-> n_difference
```

### Existence

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [set-theory](https://banes-lab.com/records/reason/math-type-set-theory.md)

Details

Math types
[set-theory](https://banes-lab.com/records/reason/math-type-set-theory.md)

### Difference

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [logic](https://banes-lab.com/records/reason/math-type-logic.md)

Details

Math types
[logic](https://banes-lab.com/records/reason/math-type-logic.md)

### Relation

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [graph](https://banes-lab.com/records/reason/math-type-graph.md)

Details

Math types
[graph](https://banes-lab.com/records/reason/math-type-graph.md), [category-theory](https://banes-lab.com/records/reason/math-domain-category-theory.md)

### Structure

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [algebra](https://banes-lab.com/records/reason/math-type-algebra.md)

Details

Math types
[algebra](https://banes-lab.com/records/reason/math-type-algebra.md)

### Transformation

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [analysis](https://banes-lab.com/records/reason/math-type-analysis.md)

Details

Math types
[analysis](https://banes-lab.com/records/reason/math-type-analysis.md)

### Constraint

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [optimisation](https://banes-lab.com/records/reason/math-type-optimisation.md)

Details

Math types
[optimisation](https://banes-lab.com/records/reason/math-type-optimisation.md)

### Invariant

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [topology](https://banes-lab.com/records/reason/math-type-topology.md)

Details

Math types
[topology](https://banes-lab.com/records/reason/math-type-topology.md), symmetry

### Information

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [information-theory](https://banes-lab.com/records/reason/math-type-information-theory.md)

Details

Math types
[information-theory](https://banes-lab.com/records/reason/math-type-information-theory.md)

### Procedure

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [computation](https://banes-lab.com/records/reason/math-type-computation.md)

Details

Math types
[computation](https://banes-lab.com/records/reason/math-type-computation.md)

### Emergence

- Layer: [substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- Math type: [dynamical-systems](https://banes-lab.com/records/reason/math-type-dynamical-systems.md)

Details

Math types
[dynamical-systems](https://banes-lab.com/records/reason/math-type-dynamical-systems.md), [complexity](https://banes-lab.com/records/reason/lens-complexity.md)

## Links to

- [Emergence](https://banes-lab.com/records/reason/substrate-node-emergence.md)
- [Difference](https://banes-lab.com/records/reason/substrate-node-difference.md)
- [Substrate](https://banes-lab.com/records/reason/layer-substrate.md)
- [Set Theory](https://banes-lab.com/records/reason/math-type-set-theory.md)
- [Logic](https://banes-lab.com/records/reason/math-type-logic.md)
- [Graph](https://banes-lab.com/records/reason/math-type-graph.md)
- [Category Theory](https://banes-lab.com/records/reason/math-domain-category-theory.md)
- [Algebra](https://banes-lab.com/records/reason/math-type-algebra.md)
- [Analysis](https://banes-lab.com/records/reason/math-type-analysis.md)
- [Optimisation](https://banes-lab.com/records/reason/math-type-optimisation.md)
- [Topology](https://banes-lab.com/records/reason/math-type-topology.md)
- [Information Theory](https://banes-lab.com/records/reason/math-type-information-theory.md)
- [Computation](https://banes-lab.com/records/reason/math-type-computation.md)
- [Dynamical Systems](https://banes-lab.com/records/reason/math-type-dynamical-systems.md)
- [Complexity](https://banes-lab.com/records/reason/lens-complexity.md)