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Leveraging tools from random walk theory, we derive the following closed-form approximation for the per block per unit of liquidity expected LVR under constant block time:\n  \\[ \\overline{\\mathrm{ARB}}= \\frac{\\,\\sigma_b^{2}} {\\,2+\\sqrt{2\\pi}\\,\\gamma/(|\\zeta(1/2)|\\,\\sigma_b)\\,}+O\\!\\bigl(e^{-\\mathrm{const}\\tfrac{\\gamma}{\\sigma_b}}\\bigr)\\;\\approx\\; \\fra"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.05113","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2025-05-08T10:30:24Z","cross_cats_sorted":["math.PR","q-fin.PM","q-fin.PR","q-fin.TR"],"title_canon_sha256":"5f458538c717cad1c0734c84ccf716453d2787a4c82a5e77fa81e6a0d1cc989b","abstract_canon_sha256":"2799947932b3e56c2b1c849fd75811c3bb9e6f4ac0fa48bf627f8224be93ca77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:03:24.183171Z","signature_b64":"xGdZ0fO7lyLN/pwAJk1GArqxtZOpz225lxS10MrDRt1cKDftjzrPVaxzFkBL2PoN4CxJ8b7NJTGv5fTN2Z78BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b95a25629aa13fc5559e161246b16b8daaffaa45774665ea79a901a77295ef5","last_reissued_at":"2026-07-05T11:03:24.182717Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:03:24.182717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Loss-Versus-Rebalancing under Deterministic and Generalized block-times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.PM","q-fin.PR","q-fin.TR"],"primary_cat":"q-fin.MF","authors_text":"Alex Nezlobin, Martin Tassy","submitted_at":"2025-05-08T10:30:24Z","abstract_excerpt":"Although modern blockchains almost universally produce blocks at fixed intervals, existing models still lack an analytical formula for the loss-versus-rebalancing (LVR) incurred by Automated Market Makers (AMMs) liquidity providers in this setting. Leveraging tools from random walk theory, we derive the following closed-form approximation for the per block per unit of liquidity expected LVR under constant block time:\n  \\[ \\overline{\\mathrm{ARB}}= \\frac{\\,\\sigma_b^{2}} {\\,2+\\sqrt{2\\pi}\\,\\gamma/(|\\zeta(1/2)|\\,\\sigma_b)\\,}+O\\!\\bigl(e^{-\\mathrm{const}\\tfrac{\\gamma}{\\sigma_b}}\\bigr)\\;\\approx\\; \\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05113","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.05113/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.05113","created_at":"2026-07-05T11:03:24.182772+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.05113v3","created_at":"2026-07-05T11:03:24.182772+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.05113","created_at":"2026-07-05T11:03:24.182772+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOK2EVRJVIJ7","created_at":"2026-07-05T11:03:24.182772+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOK2EVRJVIJ7YVKZ","created_at":"2026-07-05T11:03:24.182772+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOK2EVRJ","created_at":"2026-07-05T11:03:24.182772+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21769","citing_title":"Optimal Dynamic Fees for Automated Market Makers: A Stochastic Control Approach to Loss-Versus-Rebalancing","ref_index":29,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15973","citing_title":"Where Does MEV Really Come From? 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