{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OB553QOC6PGWWRGJMLRX2X7QPQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4f4811d545b8850db31f08ef113abbb2686fc0a844f339996f4fd639cfd1ae69","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-03-08T23:30:41Z","title_canon_sha256":"9b63aba48b4fa529bd46dd638f155750024f48e9b1a286b84fda108c34f68023"},"schema_version":"1.0","source":{"id":"0903.1465","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1465","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1465v3","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1465","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"OB553QOC6PGW","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OB553QOC6PGWWRGJ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OB553QOC","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:e706b155a5e286b40145e04bfb815b74a183641a76b13bdb76b292d650a87e9e","target":"graph","created_at":"2026-05-18T02:24:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The helicity of a vector field is a measure of the average linking of pairs of integral curves of the field. Computed by a six-dimensional integral, it is widely useful in the physics of fluids. For a divergence-free field tangent to the boundary of a domain in 3-space, helicity is known to be invariant under volume-preserving diffeomorphisms of the domain that are homotopic to the identity. We give a new construction of helicity for closed $(k+1)$-forms on a domain in $(2k+1)$-space that vanish when pulled back to the boundary of the domain. Our construction expresses helicity in terms of a c","authors_text":"Jason Cantarella, Jason Parsley","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-03-08T23:30:41Z","title":"A new cohomological formula for helicity in $\\R^{2k+1}$ reveals the effect of a diffeomorphism on helicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1465","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7e7791fdc0a9dac2f083f3c523fcd64faf0943814d9bcd26e71f445597ad38cc","target":"record","created_at":"2026-05-18T02:24:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4f4811d545b8850db31f08ef113abbb2686fc0a844f339996f4fd639cfd1ae69","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-03-08T23:30:41Z","title_canon_sha256":"9b63aba48b4fa529bd46dd638f155750024f48e9b1a286b84fda108c34f68023"},"schema_version":"1.0","source":{"id":"0903.1465","kind":"arxiv","version":3}},"canonical_sha256":"707bddc1c2f3cd6b44c962e37d5ff07c3abaa2456058eb87cbc94bda1d61cb23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"707bddc1c2f3cd6b44c962e37d5ff07c3abaa2456058eb87cbc94bda1d61cb23","first_computed_at":"2026-05-18T02:24:56.310055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:56.310055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+UEtBGNN5uZF/Y4TRiVN0GjB/Tg1TjUAwv2pYNAm1w9JNYl+tSseE9RdWcBjcprIgOtE4nzNUaUfrQZXaoanAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:56.310752Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1465","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e7791fdc0a9dac2f083f3c523fcd64faf0943814d9bcd26e71f445597ad38cc","sha256:e706b155a5e286b40145e04bfb815b74a183641a76b13bdb76b292d650a87e9e"],"state_sha256":"ffffeb799a86ea994622a9fda4186317c7803071acb04a597d5bf83485fa233d"}