# Contraction

`kaal:entity:contraction`

**Status.** derived

This node is assembled mechanically from the 2 claims that carry the concept tag `contraction`. It is a roster of what the corpus says under this term. It is **not** an adjudicated definition: no single statement here has been ruled canonical, and no first-appearance call has been made. Read the claims and judge for yourself.

## Every claim under this term

2 claims across 1 works, 2026 to 2026.

**2026**

- [6655138-029](https://wulfkaal.github.io/claims/6655138-029) [condition/argued] -- The composite best-response map is contractive on the population-distribution component of the state space only when the agent population exceeds a threshold set by per-surface stake parameters; below that threshold the architecture may admit multiple equilibria, and above it convergence is guaranteed.
  > The composite map Ψ is contractive on the population-distribution component of the state space when the agent population exceeds a threshold determined by per-surface stake parameters. Below the threshold, the architecture may admit multiple equilibria; above the threshold, convergence is guaranteed.
  Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026). SSRN: https://ssrn.com/abstract=6655138
- [6655138-032](https://wulfkaal.github.io/claims/6655138-032) [failure/argued] *(failure mode)* -- Without the reflection-mass invariant, the reflection layer can grow to dominate the first-order surfaces it is meant to reflect on, and the contraction property of the composite best-response map is lost.
  > Without INV5, the reflection layer can grow to dominate the first-order surfaces it is meant to reflect on, and the contraction property of Ψ is lost.
  Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026). SSRN: https://ssrn.com/abstract=6655138

## Verify

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    curl -s https://wulfkaal.github.io/entities/contraction.md | sha256sum

**Canonical form.** This markdown file is the canonical hashed representation of this entity node. Its sha256 is the content hash.