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We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines, $$ H= \\frac{\\kappa^2}{8 \\pi}\\int_{|{\\bf s}-{\\bf s}'|>\\xi_*} \\frac{d{\\bf s} \\cdot d {\\bf s}'}{|{\\bf s}-{\\bf s}'|} \\,,$$ with cut-off length $\\xi_* \\approx 0.3416293 /\\sqrt{\\rho_0},$ where $\\rho_0$ is the background condensate density fa"},"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":"1507.07806","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-07-28T15:19:17Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"dd696ea32b0481a3b2e42df95a2104387c6f7d5c8d7f09369adab8d4eb2d9bb0","abstract_canon_sha256":"a27dc8788518cd740cfe509329ad80fe4f1bc5f58e9b516c078bdc23bb4c5607"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:33.320929Z","signature_b64":"7ad6pqhL8S0mg8ULX5d2JKBXLGvLpwvmb+5MDVo19r/XTJ4Y4bYM9E7RV3EwIGviZ8Ixf7NRZuzXexsEH3HUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04f69d928f302f0335f574931aee8fc2108495497862c0431e5b8904e238ad1e","last_reissued_at":"2026-05-18T01:16:33.320309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:33.320309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derivation of the Biot-Savart equation from the Nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"physics.flu-dyn","authors_text":"Miguel D. Bustamante, Sergey V. Nazarenko","submitted_at":"2015-07-28T15:19:17Z","abstract_excerpt":"We present a systematic derivation of the Biot-Savart equation from the Nonlinear Schr\\\"odinger equation, in the limit when the curvature radius of vortex lines and the inter-vortex distance are much greater than the vortex healing length, or core radius. We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines, $$ H= \\frac{\\kappa^2}{8 \\pi}\\int_{|{\\bf s}-{\\bf s}'|>\\xi_*} \\frac{d{\\bf s} \\cdot d {\\bf s}'}{|{\\bf s}-{\\bf s}'|} \\,,$$ with cut-off length $\\xi_* \\approx 0.3416293 /\\sqrt{\\rho_0},$ where $\\rho_0$ is the background condensate density fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07806","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1507.07806","created_at":"2026-05-18T01:16:33.320434+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.07806v2","created_at":"2026-05-18T01:16:33.320434+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07806","created_at":"2026-05-18T01:16:33.320434+00:00"},{"alias_kind":"pith_short_12","alias_value":"AT3J3EUPGAXQ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AT3J3EUPGAXQGNPV","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AT3J3EUP","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI","json":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI.json","graph_json":"https://pith.science/api/pith-number/AT3J3EUPGAXQGNPVOSJRV3UPYI/graph.json","events_json":"https://pith.science/api/pith-number/AT3J3EUPGAXQGNPVOSJRV3UPYI/events.json","paper":"https://pith.science/paper/AT3J3EUP"},"agent_actions":{"view_html":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI","download_json":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI.json","view_paper":"https://pith.science/paper/AT3J3EUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.07806&json=true","fetch_graph":"https://pith.science/api/pith-number/AT3J3EUPGAXQGNPVOSJRV3UPYI/graph.json","fetch_events":"https://pith.science/api/pith-number/AT3J3EUPGAXQGNPVOSJRV3UPYI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI/action/storage_attestation","attest_author":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI/action/author_attestation","sign_citation":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI/action/citation_signature","submit_replication":"https://pith.science/pith/AT3J3EUPGAXQGNPVOSJRV3UPYI/action/replication_record"}},"created_at":"2026-05-18T01:16:33.320434+00:00","updated_at":"2026-05-18T01:16:33.320434+00:00"}