{
 "@context": "https://schema.org",
 "@type": "DefinedTerm",
 "@id": "https://wulfkaal.github.io/entities/contraction",
 "identifier": "kaal:entity:contraction",
 "name": "Contraction",
 "termCode": "contraction",
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  "@id": "https://wulfkaal.github.io/entities/index.json"
 },
 "author": {
  "@type": "Person",
  "name": "Wulf A. Kaal",
  "identifier": "https://orcid.org/0000-0003-0757-275X"
 },
 "dateModified": "2026-07-29",
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   "value": [
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 "subjectOf": [
  {
   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/6655138-029",
   "identifier": "kaal:claim:6655138-029",
   "text": "The composite best-response map is contractive on the population-distribution component of the state space only when the agent population exceeds a threshold set by per-surface stake parameters; below that threshold the architecture may admit multiple equilibria, and above it convergence is guaranteed.",
   "abstract": "The composite map Ψ is contractive on the population-distribution component of the state space when the agent population exceeds a threshold determined by per-surface stake parameters. Below the threshold, the architecture may admit multiple equilibria; above the threshold, convergence is guaranteed.",
   "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": [
    "agent populations above the stake-parameter-determined threshold"
   ],
   "source_pdf_sha256": "52cb210167f06f0c7a2581214b156326216543de80b8394320b629c045c9e214",
   "status": "current"
  },
  {
   "@type": "Claim",
   "@id": "https://wulfkaal.github.io/claims/6655138-032",
   "identifier": "kaal:claim:6655138-032",
   "text": "Without the reflection-mass invariant, the reflection layer can grow to dominate the first-order surfaces it is meant to reflect on, and the contraction property of the composite best-response map is lost.",
   "abstract": "Without INV5, the reflection layer can grow to dominate the first-order surfaces it is meant to reflect on, and the contraction property of Ψ is lost.",
   "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": "failure",
   "confidence": "argued",
   "is_failure_mode": true,
   "scope_conditions": [
    "architectures with an isolated cross-surface reflection surface"
   ],
   "source_pdf_sha256": "52cb210167f06f0c7a2581214b156326216543de80b8394320b629c045c9e214",
   "status": "current"
  }
 ],
 "description": "2 claims in the published works of Wulf A. Kaal carry the concept tag 'contraction'. Derived node: a roster, not an adjudicated definition."
}