# Convexity

`kaal:entity:convexity`

**Status.** derived

This node is assembled mechanically from the 2 claims that carry the concept tag `convexity`. 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 2 works, 2026 to 2026.

**2026**

- [6607458-022](https://wulfkaal.github.io/claims/6607458-022) [condition/argued] -- Proposition 1: if the spaces of generation functions and domain models are nonempty, compact, and convex, and the individual optimization and model-update operators are continuous, then a recursive equilibrium exists by the Brouwer fixed-point theorem.
  > Proposition 1 (Existence). Let the space of generation functions G_i and domain models M_i admit topologies under which they are nonempty, compact, and convex. Suppose the individual optimization operator and the model-update operator are both continuous. Then a recursive equilibrium exists.
  Wulf A. Kaal, Computative Economics A Framework for Economic Analysis under Computational Abundance (2026). SSRN: https://ssrn.com/abstract=6607458
- [6655138-026](https://wulfkaal.github.io/claims/6655138-026) [condition/argued] -- Each surface must carry a per-agent rate limit enforced by stake escalation, since rate limits secure compactness of the action profile space and prevent generation explosions that would violate convexity, and reflection-surface rate limits must be tighter than per-surface rate limits to prevent reflection cascades.
  > Each surface Σ has a per-agent rate limit enforced by stake escalation, ensuring compactness of the action profile space. Rate limits prevent generation explosions that would violate convexity. Σ_R rate limits are tighter than per-surface rate limits to prevent reflection cascades.
  Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026). SSRN: https://ssrn.com/abstract=6655138

## Verify

Every claim above resolves to a record carrying a verbatim source quote, the sha256 of the source PDF, and a preformatted citation. Nothing here asks to be taken on trust.

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

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