{"paper":{"title":"Aharanov-Bohm Type Arbitrage and Homological Obstructions in Financial Markets","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Non-trivial holonomy in market filtrations converts into a predictable self-financing trading strategy under admissibility conditions.","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Keisuke Hara, Takanori Adachi","submitted_at":"2026-04-12T06:51:08Z","abstract_excerpt":"We introduce a simplicial and categorical formulation of Aharonov-Bohm (AB) type arbitrage in filtered market systems. Given a filtration modeled as a contravariant functor $F : \\mathcal T^{op} \\to \\mathbf{Prob},$ we consider the associated conditional expectation transport functor $\\mathcal E \\circ F : \\mathcal T^{op} \\to \\mathbf{Ban},$ and the canonical distortion $dF(i) := (\\mathcal E \\circ F)(i)(1),$ which measures the failure of constant functions to be preserved under non-measure-preserving transitions. Motivated by the multiplicative transport structure of $dF$, we introduce a simplicia"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under suitable admissibility conditions, non-trivial holonomy can be converted into a predictable self-financing trading strategy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the multiplicative distortion dF(i) induced by the conditional expectation functor has direct economic meaning as arbitrage and that the holonomy along loops in the time category T corresponds to a realizable trading opportunity rather than a purely formal quantity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Non-trivial holonomy of the multiplicative distortion induced by the conditional expectation functor on a market filtration corresponds to Aharonov-Bohm arbitrage realizable as a self-financing trading strategy under admissibility conditions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Non-trivial holonomy in market filtrations converts into a predictable self-financing trading strategy under admissibility conditions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3544bd18ec983242068254597a40d7415c7cb447c2377206d83c11790feab903"},"source":{"id":"2604.10492","kind":"arxiv","version":3},"verdict":{"id":"d3a91805-5327-4028-a70f-fec033512aa4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:07:09.983587Z","strongest_claim":"Under suitable admissibility conditions, non-trivial holonomy can be converted into a predictable self-financing trading strategy.","one_line_summary":"Non-trivial holonomy of the multiplicative distortion induced by the conditional expectation functor on a market filtration corresponds to Aharonov-Bohm arbitrage realizable as a self-financing trading strategy under admissibility conditions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the multiplicative distortion dF(i) induced by the conditional expectation functor has direct economic meaning as arbitrage and that the holonomy along loops in the time category T corresponds to a realizable trading opportunity rather than a purely formal quantity.","pith_extraction_headline":"Non-trivial holonomy in market filtrations converts into a predictable self-financing trading strategy under admissibility conditions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.10492/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}