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 "identifier": "kaal:entity:convexity",
 "name": "Convexity",
 "termCode": "convexity",
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 "author": {
  "@type": "Person",
  "name": "Wulf A. Kaal",
  "identifier": "https://orcid.org/0000-0003-0757-275X"
 },
 "dateModified": "2026-07-29",
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   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/6607458-022",
   "identifier": "kaal:claim:6607458-022",
   "text": "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.",
   "abstract": "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.",
   "citation": "Wulf A. Kaal, Computative Economics A Framework for Economic Analysis under Computational Abundance (2026). SSRN: https://ssrn.com/abstract=6607458",
   "datePublished": "2026",
   "claim_type": "condition",
   "confidence": "argued",
   "is_failure_mode": false,
   "scope_conditions": [
    "requires nonempty, compact, convex topologies on generation functions and domain models",
    "requires continuity of the optimization and model-update operators"
   ],
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   "status": "current"
  },
  {
   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/6655138-026",
   "identifier": "kaal:claim:6655138-026",
   "text": "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.",
   "abstract": "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.",
   "citation": "Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026). SSRN: https://ssrn.com/abstract=6655138",
   "datePublished": "2026",
   "claim_type": "condition",
   "confidence": "argued",
   "is_failure_mode": false,
   "scope_conditions": [
    "conditions for fixed-point existence and convergence"
   ],
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 "description": "2 claims in the published works of Wulf A. Kaal carry the concept tag 'convexity'. Derived node: a roster, not an adjudicated definition."
}