{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:WDLMYUUCQ7OK6RFZEB5XQHPVGK","short_pith_number":"pith:WDLMYUUC","schema_version":"1.0","canonical_sha256":"b0d6cc528287dcaf44b9207b781df53295fe0f6d7923e60cfca54952cf4ae07c","source":{"kind":"arxiv","id":"0906.3494","version":2},"attestation_state":"computed","paper":{"title":"The third order helicity of magnetic fields via link maps II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.GT","math.MP"],"primary_cat":"math.DS","authors_text":"R. Komendarczyk","submitted_at":"2009-06-18T18:10:17Z","abstract_excerpt":"In this sequel we extend the derivation of the third order helicity to magnetic fields supported on unlinked domains in 3-space. The formula is expressed in terms of generators of the deRham cohomology of the configuration space of three points in $\\R^3$, which is a more practical domain from the perspective of applications. It also admits an ergodic interpretation as an average asymptotic Milnor $\\bar{\\mu}_{123}$-invariant and allows us to obtain the $L^2$-energy bound for the magnetic field. As an intermediate step we derive an integral formula for Milnor $\\bar{\\mu}_{123}$-invariant for para"},"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":"0906.3494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-06-18T18:10:17Z","cross_cats_sorted":["math-ph","math.DG","math.GT","math.MP"],"title_canon_sha256":"88938206b08e243127527839128982ef32413ee3a965a1389cec2688505df4f6","abstract_canon_sha256":"e23dcd8636e85280e35a22c81714fe5c9ab67285c7d290f4a0cef6ddc313475f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:52.968111Z","signature_b64":"VTDhfgrzETHHJ4SKL4B1a4hqZZ0j7y2CCiXjPbCEhetibFBcs6vgMRYXDj6HGJ0Uve+QTFkb0KroXhpUxK0DCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0d6cc528287dcaf44b9207b781df53295fe0f6d7923e60cfca54952cf4ae07c","last_reissued_at":"2026-05-18T02:34:52.967646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:52.967646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The third order helicity of magnetic fields via link maps II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.GT","math.MP"],"primary_cat":"math.DS","authors_text":"R. Komendarczyk","submitted_at":"2009-06-18T18:10:17Z","abstract_excerpt":"In this sequel we extend the derivation of the third order helicity to magnetic fields supported on unlinked domains in 3-space. The formula is expressed in terms of generators of the deRham cohomology of the configuration space of three points in $\\R^3$, which is a more practical domain from the perspective of applications. It also admits an ergodic interpretation as an average asymptotic Milnor $\\bar{\\mu}_{123}$-invariant and allows us to obtain the $L^2$-energy bound for the magnetic field. As an intermediate step we derive an integral formula for Milnor $\\bar{\\mu}_{123}$-invariant for para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3494","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":"0906.3494","created_at":"2026-05-18T02:34:52.967719+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.3494v2","created_at":"2026-05-18T02:34:52.967719+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3494","created_at":"2026-05-18T02:34:52.967719+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDLMYUUCQ7OK","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDLMYUUCQ7OK6RFZ","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDLMYUUC","created_at":"2026-05-18T12:26:02.257875+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/WDLMYUUCQ7OK6RFZEB5XQHPVGK","json":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK.json","graph_json":"https://pith.science/api/pith-number/WDLMYUUCQ7OK6RFZEB5XQHPVGK/graph.json","events_json":"https://pith.science/api/pith-number/WDLMYUUCQ7OK6RFZEB5XQHPVGK/events.json","paper":"https://pith.science/paper/WDLMYUUC"},"agent_actions":{"view_html":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK","download_json":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK.json","view_paper":"https://pith.science/paper/WDLMYUUC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.3494&json=true","fetch_graph":"https://pith.science/api/pith-number/WDLMYUUCQ7OK6RFZEB5XQHPVGK/graph.json","fetch_events":"https://pith.science/api/pith-number/WDLMYUUCQ7OK6RFZEB5XQHPVGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK/action/storage_attestation","attest_author":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK/action/author_attestation","sign_citation":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK/action/citation_signature","submit_replication":"https://pith.science/pith/WDLMYUUCQ7OK6RFZEB5XQHPVGK/action/replication_record"}},"created_at":"2026-05-18T02:34:52.967719+00:00","updated_at":"2026-05-18T02:34:52.967719+00:00"}