# kaal:claim:6655138-016

**Claim.** The HDCA settlement loop is closed in the topological sense: every job exits as resolved-validated or resolved-rejected and the system returns to a structurally identical state with only reputation scalars updated, so the set of possible actions never changes.

**Type.** mechanism  **Support.** argued

**Holds when.**

- the HDCA job lifecycle

**Source quote.**

> This is its central distinguishing feature relative to the HDCA settlement loop, which is closed in the topological sense: every job that enters the HDCA loop exits as either resolved-validated or resolved-rejected, and the system returns to a state structurally identical to where it began

**From.** Wulf A. Kaal, *Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems* (2026), V.B Generatively open topology, page 12

**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.** institutional-design

**Keywords.** closed-loop, hdca, job-lifecycle, action-space

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