# kaal:claim:6655138-040

**Claim.** The six-surface architecture is complete for the computative agent tuple up to renaming: any architecture satisfying the conditions of Computative Economics reduces to a six-surface architecture by surface aggregation, and further refinement adds expressive power only by subdividing one of the six components.

**Type.** design  **Support.** argued

**Holds when.**

- architectures satisfying the conditions of Computative Economics

**Source quote.**

> The completeness claim is that any architecture satisfying the conditions of Computative Economics can be reduced to a six-surface architecture by surface aggregation, and any further refinement adds expressive power only by subdividing one of the six components.

**From.** Wulf A. Kaal, *Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems* (2026), IX.D Proposition 4 (Architectural completeness, refined), page 24

**Cite as.** Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026). SSRN: https://ssrn.com/abstract=6655138

**Verify.** sha256 of source PDF `52cb210167f06f0c7a2581214b156326216543de80b8394320b629c045c9e214` at https://raw.githubusercontent.com/wulfkaal/Academic-Papers/main/papers/pdf/Kaal%20-%202026%20-%20Possibility%20Loops%20An%20Operational%20Architecture%20for%20Computative%20Economics%20in%20Agent%20Coordination%20Systems.pdf

**Topics.** ai-and-agents

**Keywords.** proposition-4, architectural-completeness, six-surfaces, agent-tuple

**Canonical form.** This markdown file is the canonical hashed representation of the claim. Its sha256 is the content hash used for attestation.