# kaal:claim:6655138-034

**Claim.** Collapsing two distinct generative components into a single loop forces aggregation of distinct quality signals into one reputation scalar, which violates the continuity condition because the aggregate function is not Lipschitz in components whose resolution outcomes have different scales.

**Type.** failure  **Support.** argued

**Holds when.**

- components whose resolution outcomes differ in scale

**Source quote.**

> Collapsing two distinct generative components into a single loop forces aggregation of distinct quality signals into a single reputation scalar, which violates the continuity condition AC2 because the aggregate function is not Lipschitz in the underlying components

**From.** Wulf A. Kaal, *Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems* (2026), IX.A Proposition 1 (Necessity of multiple loops), page 23

**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

**Failure mode.** Surface aggregation breaks continuity  (family: research-design-limitation)

**Topics.** reputation

**Keywords.** surface-collapse, lipschitz, ac2, reputation-aggregation

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