# kaal:claim:6655138-027

**Claim.** Reputation update functions on each surface must be continuous in the validation pool's resolution outcome, because discontinuities in reputation update destroy continuity of best-response correspondences and preclude application of Brouwer's fixed-point theorem.

**Type.** condition  **Support.** argued

**Holds when.**

- architectures relying on Brouwer for equilibrium existence

**Source quote.**

> The reputation update functions on each surface are continuous in the validation pool's resolution outcome. Discontinuities in reputation update destroy continuity of best-response correspondences and preclude application of Brouwer.

**From.** Wulf A. Kaal, *Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems* (2026), VII.D Architectural conditions for fixed-point existence, AC2, page 21

**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.** Discontinuous reputation update  (family: reputation-system-gaming)

**Topics.** reputation

**Keywords.** ac2, continuity, brouwer, best-response, reputation-update

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