{ "@context": "https://schema.org", "@type": "DefinedTerm", "@id": "https://wulfkaal.github.io/entities/convergence", "identifier": "kaal:entity:convergence", "name": "Convergence", "termCode": "convergence", "inDefinedTermSet": { "@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", "canonicalForm": "https://wulfkaal.github.io/entities/convergence.md", "sha256": "ff32c4a6f67b6ffc11938f5c9358aef7140bbd0d2d363a0834198144781837d4", "additionalProperty": [ { "@type": "PropertyValue", "name": "status", "value": "derived" }, { "@type": "PropertyValue", "name": "claim_count", "value": 15 }, { "@type": "PropertyValue", "name": "work_count", "value": 10 }, { "@type": "PropertyValue", "name": "year_span", "value": [ "2009", "2026" ] }, { "@type": "PropertyValue", "name": "non_current_claims", "value": 0 } ], "subjectOf": [ { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/1428387-005", "identifier": "kaal:claim:1428387-005", "text": "When hedge funds adopt private equity strategies by adding private companies to their portfolios, they exacerbate valuation problems, and the convergence of the two asset classes makes it more difficult to accurately assess the value of each.", "abstract": "If hedge funds engage in private equity strategies, i.e. adding private companies to their portfolio, they may exacerbate the valuation issues. The convergence of hedge funds and private-equity funds makes it more difficult to accurately assess the value of each asset class.", "citation": "Kaal, Hedge Fund Valuation Retailization, Regulation, and Investor Suitability (2009). SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1428387", "datePublished": "2009", "claim_type": "mechanism", "confidence": "argued", "is_failure_mode": false, "scope_conditions": [ "where hedge funds hold private, non-traded portfolio companies" ], "source_pdf_sha256": "6aa3a280dc6750723be2389f3af2aabf3a16c4ce20e49fcdaddd7f2ea95a67aa", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/1908473-021", "identifier": "kaal:claim:1908473-021", "text": "Without a degree of international convergence in contingent capital rules, regulatory arbitrage could undermine the establishment of contingent capital as an integral part of financial markets.", "abstract": "Without a certain level of convergence in contingent capital rules,105 regulatory arbitrage could have an adverse effect on establishing contingent capital as an integral part of financial markets.", "citation": "Wulf A. Kaal, Christoph Henkel, Contingent Capital with Sequential Triggers (2011). SSRN: https://ssrn.com/abstract=1908473", "datePublished": "2011", "claim_type": "condition", "confidence": "argued", "is_failure_mode": true, "scope_conditions": [ "Assumes jurisdictions legislate contingent capital independently of one another" ], "source_pdf_sha256": "9d578dac663357529edd1f6453fcfe69bdc59ac882408d9edfde5a4c2916befa", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/2061166-002", "identifier": "kaal:claim:2061166-002", "text": "The authors contend that the European Commission's goal of maximum harmonization through a global single rule book may not be achievable, and that a legal framework for private ordering of contingent capital is the more realistic route to an adequate level of convergence.", "abstract": "The European Commission's objective of creating maximum harmonization through a global \"single rule book\"22 may not be feasible. However, setting up a legal framework for private ordering in the context of contingent capital23 could provide an adequate level of convergence", "citation": "Christoph K. Henkel, Wulf A. Kaal, Contingent Capital in European Union Bank Restructuring (2012). SSRN: https://ssrn.com/abstract=2061166", "datePublished": "2012", "claim_type": "design", "confidence": "argued", "is_failure_mode": false, "scope_conditions": [ "European Union bank resolution and restructuring regimes" ], "source_pdf_sha256": "43625ea260d0fc045e86d3435df50c9d0ca4abf8542e6085a6165be6653b4a7b", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/2061166-037", "identifier": "kaal:claim:2061166-037", "text": "Convergence of contingent capital standards is impeded by a first mover problem: single jurisdictions hesitate to impose contingent capital requirements before they know how competing jurisdictions and their financial institutions will structure their own rules.", "abstract": "This could partially be due to a first mover problem. Single jurisdictions could be hesitant to implement contingent capital requirements without first knowing how other jurisdictions and financial institutions that compete with their home institutions may structure their contingent capital rules.", "citation": "Christoph K. Henkel, Wulf A. Kaal, Contingent Capital in European Union Bank Restructuring (2012). SSRN: https://ssrn.com/abstract=2061166", "datePublished": "2012", "claim_type": "mechanism", "confidence": "argued", "is_failure_mode": true, "scope_conditions": [ "jurisdictions whose banks compete internationally" ], "source_pdf_sha256": "43625ea260d0fc045e86d3435df50c9d0ca4abf8542e6085a6165be6653b4a7b", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/2061166-038", "identifier": "kaal:claim:2061166-038", "text": "Without a degree of similarity and convergence in bank resolution and contingent capital rules, regulatory arbitrage will work against establishing contingent capital as an integral part of financial markets.", "abstract": "Without a degree of similarity and convergence in bank resolution and contingent capital rules, regulatory arbitrage could have an adverse effect on establishing contingent capital as an integral part of financial markets.", "citation": "Christoph K. Henkel, Wulf A. Kaal, Contingent Capital in European Union Bank Restructuring (2012). SSRN: https://ssrn.com/abstract=2061166", "datePublished": "2012", "claim_type": "condition", "confidence": "argued", "is_failure_mode": true, "scope_conditions": [ "absent international convergence of resolution and contingent capital rules" ], "source_pdf_sha256": "43625ea260d0fc045e86d3435df50c9d0ca4abf8542e6085a6165be6653b4a7b", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/4796714-031", "identifier": "kaal:claim:4796714-031", "text": "Decentralized Federated Learning reaches the global minimum with zero performance gap and matches the convergence rate of centralized methods when the loss function is smooth and strongly convex.", "abstract": "The DeceFL approach ensures that every client can reach the global minimum with zero performance gap and achieve the same convergence rate as centralized methods when the loss function is smooth and strongly convex.", "citation": "Wulf A. Kaal, AI Governance (2024). SSRN: https://ssrn.com/abstract=4796714", "datePublished": "2024", "claim_type": "empirical", "confidence": "evidenced", "is_failure_mode": false, "scope_conditions": [ "requires a smooth and strongly convex loss function", "demonstrated across convex and nonconvex losses, time invariant and time varying topologies, and IID and non-IID datasets" ], "source_pdf_sha256": "59fa63bae179e8f9b6b8efbdf90cee28400276512a1b04f9f579a48641305c93", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/4900878-034", "identifier": "kaal:claim:4900878-034", "text": "Quantum computing cuts both ways for blockchain: it can raise the efficiency and security of blockchain networks, but safeguarding those systems against the threats it also creates depends on research into quantum resistant cryptographic algorithms.", "abstract": "Research into quantum-resistant cryptographic algorithms will be crucial to safeguard blockchain systems against potential threats posed by quantum computing.", "citation": "Wulf A. Kaal, Quantum Economy and Tokenomics (2024). SSRN: https://ssrn.com/abstract=4900878", "datePublished": "2024", "claim_type": "condition", "confidence": "asserted", "is_failure_mode": false, "scope_conditions": [ "as quantum computing capability advances" ], "source_pdf_sha256": "75bf96d3b751b4ad0a6ca4a32591cf026094f113e3a372aa6c61790941b391f7", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/4941807-026", "identifier": "kaal:claim:4941807-026", "text": "Decentralized Federated Learning lets every client reach the global minimum with zero performance gap and at the same convergence rate as centralized methods, but only when the loss function is smooth and strongly convex.", "abstract": "The DeceFL approach ensures that every client can reach the global minimum with zero performance gap and achieve the same convergence rate as centralized methods when the loss function is smooth and strongly convex.", "citation": "Wulf A. Kaal, AI Governance Via Web3 Reputation System (2024). SSRN: https://ssrn.com/abstract=4941807", "datePublished": "2024", "claim_type": "condition", "confidence": "evidenced", "is_failure_mode": false, "scope_conditions": [ "when the loss function is smooth and strongly convex" ], "source_pdf_sha256": "ab66c1e99a88da1fa36b0c6b536df5184231fe6aa427f3dd53287a4e0ac79853", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/6192998-015", "identifier": "kaal:claim:6192998-015", "text": "The recursive post valuation formula in the original framework suffered from potential instability and provided no mechanism ensuring that citations reflect actual contribution rather than strategic manipulation.", "abstract": "However, the recursive formula presented suffered from potential instability and provided no mechanism ensuring citations reflect actual contribution rather than strategic manipulation.", "citation": "Wulf A. Kaal, Evolution of Domain-Specific Reputation Systems From Binary Validation to Citation-Weighted Knowledge Attribution (2026). SSRN: https://ssrn.com/abstract=6192998", "datePublished": "2026", "claim_type": "failure", "confidence": "argued", "is_failure_mode": true, "scope_conditions": [], "source_pdf_sha256": "b04292561ee041e0c9eaa7eca28a410ed440e76a95743a539361a3f76c97f2b3", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/6192998-027", "identifier": "kaal:claim:6192998-027", "text": "Constraining the citation weight parameter below one and enforcing row stochasticity through normalization guarantees that the citation weighted value vector exists, is unique, and converges, which resolves the instability of the original recursive valuation formula.", "abstract": "This theorem addresses the instability concern with the recursive formula in Calcaterra, Kaal, and Andrei (2018, 41). By constraining and ensuring row-stochasticity through normalization, we guarantee convergence, a crucial property for autonomous operation.", "citation": "Wulf A. Kaal, Evolution of Domain-Specific Reputation Systems From Binary Validation to Citation-Weighted Knowledge Attribution (2026). SSRN: https://ssrn.com/abstract=6192998", "datePublished": "2026", "claim_type": "condition", "confidence": "evidenced", "is_failure_mode": false, "scope_conditions": [ "citation weight parameter strictly less than one", "contribution matrix normalized to be row stochastic" ], "source_pdf_sha256": "b04292561ee041e0c9eaa7eca28a410ed440e76a95743a539361a3f76c97f2b3", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/6244278-026", "identifier": "kaal:claim:6244278-026", "text": "Because of the multiplicative weights regret bound, the validation pool has a provable convergence guarantee: over sufficient iterations, reputation-weighted consensus performs nearly as well as the most competent honest validator in the population.", "abstract": "This means that the validation pool has a provable convergence guarantee: over sufficient iterations, the reputation-weighted consensus will perform nearly as well as the most competent honest validator in the population.", "citation": "Wulf A. Kaal, AI's Mother's Instinct Engineered Consequence Emergent Ethics and the Institutional Trajectory Toward Agentic Alignment (2026). SSRN: https://ssrn.com/abstract=6244278", "datePublished": "2026", "claim_type": "mechanism", "confidence": "evidenced", "is_failure_mode": false, "scope_conditions": [ "requires sufficient iterations", "convergence rate is logarithmic in the number of experts over the square root of rounds" ], "source_pdf_sha256": "53533cdcc081184e7a376516ad4fece0a64ce49f6c8931b6a2c2e98ed914a84b", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/6607458-023", "identifier": "kaal:claim:6607458-023", "text": "Proposition 2: if the composite best-response map is a contraction under an appropriate metric, the recursive equilibrium is unique and iteration of the map from any starting point converges to it, by the Banach fixed-point theorem.", "abstract": "Suppose the composite best-response map Ψ is a contraction on the product space of generation functions and domain models under an appropriate metric. Then there exists a unique recursive equilibrium, and the sequence (G_t, M_t) generated by repeated application of Ψ from any starting point", "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 the composite best-response map to be a contraction under an appropriate metric" ], "source_pdf_sha256": "75cca35350378eb8904866d068b5d2f3e1504629e6031457ce6c12152a88e3e8", "status": "current" }, { "@type": "Claim", "@id": "https://wulfkaal.github.io/claims/6607458-024", "identifier": "kaal:claim:6607458-024", "text": "Where the contraction condition holds, the computative framework delivers a stronger equilibrium result than the Arrow-Debreu theorem, which asserts existence but yields neither uniqueness without added monotonicity assumptions nor a constructive convergent procedure.", "abstract": "Where the condition holds, Computative Economics delivers a stronger equilibrium result than the Arrow-Debreu existence theorem: the latter asserts existence but does not deliver uniqueness without additional monotonicity assumptions and does not deliver a constructive convergent procedure.", "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": "mechanism", "confidence": "argued", "is_failure_mode": false, "scope_conditions": [ "holds only where the contraction condition is satisfied" ], "source_pdf_sha256": "75cca35350378eb8904866d068b5d2f3e1504629e6031457ce6c12152a88e3e8", "status": "current" }, { "@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/6655138-031", "identifier": "kaal:claim:6655138-031", "text": "An implementation that respects the five implementation invariants inherits the recursive equilibrium guarantees of the foundational framework, and an implementation that does not is, in the strict sense, not an implementation of Computative Economics.", "abstract": "An implementation that respects the five invariants inherits the recursive equilibrium guarantees of the foundational framework. An implementation that does not is, in the strict sense, not an implementation of Computative Economics.", "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": [ "implementations claiming to instantiate Computative Economics" ], "source_pdf_sha256": "52cb210167f06f0c7a2581214b156326216543de80b8394320b629c045c9e214", "status": "current" } ], "description": "15 claims in the published works of Wulf A. Kaal carry the concept tag 'convergence'. Derived node: a roster, not an adjudicated definition." }