{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FFI2URLUSP6XUKETKZ67FGBYMA","short_pith_number":"pith:FFI2URLU","canonical_record":{"source":{"id":"1511.03746","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-12T01:17:33Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"689ad3c27f542012dec6978c7ac94b8599c7cb15c52f63a85a76862f625883a8","abstract_canon_sha256":"0ef0992d261301c83f7215e23101e7ed2649613018f9e09454ae5190e2e99ade"},"schema_version":"1.0"},"canonical_sha256":"2951aa457493fd7a2893567df29838601e422a2fc609ca569e34f7b70ce15d80","source":{"kind":"arxiv","id":"1511.03746","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03746","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03746v2","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03746","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"pith_short_12","alias_value":"FFI2URLUSP6X","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FFI2URLUSP6XUKET","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FFI2URLU","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FFI2URLUSP6XUKETKZ67FGBYMA","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03746","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-12T01:17:33Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"689ad3c27f542012dec6978c7ac94b8599c7cb15c52f63a85a76862f625883a8","abstract_canon_sha256":"0ef0992d261301c83f7215e23101e7ed2649613018f9e09454ae5190e2e99ade"},"schema_version":"1.0"},"canonical_sha256":"2951aa457493fd7a2893567df29838601e422a2fc609ca569e34f7b70ce15d80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:04.768707Z","signature_b64":"6vPe/g6LAbJRHxPtLwoHHyrgLYHj6XkVtR8JscjwJrZSJo5wENKou38QjhhsMUkxcOjRKVFO8ctoR5z98wxrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2951aa457493fd7a2893567df29838601e422a2fc609ca569e34f7b70ce15d80","last_reissued_at":"2026-05-18T00:49:04.768261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:04.768261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03746","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xqjGQdBkbnJNxgmJzAZ0Xqk1HwQN0qEXQqyWeuzBwZpBMTIrsbb1A1QTmxzUV2T043AdDseJxSOkTvzHpxdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:09:44.261089Z"},"content_sha256":"7e710172e634681b385115addef1fc4cea6adbc09e2f22cc802205e9205406ec","schema_version":"1.0","event_id":"sha256:7e710172e634681b385115addef1fc4cea6adbc09e2f22cc802205e9205406ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FFI2URLUSP6XUKETKZ67FGBYMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Helicity is the only invariant of incompressible flows whose derivative is continuous in $C^1$-topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.DS","authors_text":"Elena A. Kudryavtseva","submitted_at":"2015-11-12T01:17:33Z","abstract_excerpt":"Let $Q$ be a smooth compact orientable 3--manifold with smooth boundary $\\partial Q$. Let $\\mathcal{B}$ be the set of exact 2--forms $B\\in\\Omega^2(Q)$ such that $j_{\\partial Q}^*B=0$, where $j_{\\partial Q}:{\\partial Q}\\to Q$ is the inclusion map. The group $\\mathcal{D}=\\mathrm{Diff}_0(Q)$ of self-diffeomorphisms of $Q$ isotopic to the identity acts on the set $\\mathcal{B}$ by $\\mathcal{D}\\times\\mathcal{B}\\to\\mathcal{B}$, $(h,B)\\mapsto h^*B$. Let $\\mathcal{B}^\\circ$ be the set of 2--forms $B\\in\\mathcal{B}$ without zeros. We prove that every $\\mathcal{D}$--invariant functional $I:\\mathcal{B}^\\ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03746","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nb2g2H7lAfDPis8Q6kHDgGrsn+JkTXsCrlT233C8Pk0XCxUjmQJae9LKrrHwkiDQRiDKuQ7AEgCF3jG9CBASAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:09:44.261448Z"},"content_sha256":"13d81455b6a7ff163646afbebb66bfb1a7724bae78ca9f8eed93f4f5a4f9e952","schema_version":"1.0","event_id":"sha256:13d81455b6a7ff163646afbebb66bfb1a7724bae78ca9f8eed93f4f5a4f9e952"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFI2URLUSP6XUKETKZ67FGBYMA/bundle.json","state_url":"https://pith.science/pith/FFI2URLUSP6XUKETKZ67FGBYMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFI2URLUSP6XUKETKZ67FGBYMA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T18:09:44Z","links":{"resolver":"https://pith.science/pith/FFI2URLUSP6XUKETKZ67FGBYMA","bundle":"https://pith.science/pith/FFI2URLUSP6XUKETKZ67FGBYMA/bundle.json","state":"https://pith.science/pith/FFI2URLUSP6XUKETKZ67FGBYMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFI2URLUSP6XUKETKZ67FGBYMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FFI2URLUSP6XUKETKZ67FGBYMA","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":"0ef0992d261301c83f7215e23101e7ed2649613018f9e09454ae5190e2e99ade","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-12T01:17:33Z","title_canon_sha256":"689ad3c27f542012dec6978c7ac94b8599c7cb15c52f63a85a76862f625883a8"},"schema_version":"1.0","source":{"id":"1511.03746","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03746","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03746v2","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03746","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"pith_short_12","alias_value":"FFI2URLUSP6X","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FFI2URLUSP6XUKET","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FFI2URLU","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:13d81455b6a7ff163646afbebb66bfb1a7724bae78ca9f8eed93f4f5a4f9e952","target":"graph","created_at":"2026-05-18T00:49:04Z","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":"Let $Q$ be a smooth compact orientable 3--manifold with smooth boundary $\\partial Q$. Let $\\mathcal{B}$ be the set of exact 2--forms $B\\in\\Omega^2(Q)$ such that $j_{\\partial Q}^*B=0$, where $j_{\\partial Q}:{\\partial Q}\\to Q$ is the inclusion map. The group $\\mathcal{D}=\\mathrm{Diff}_0(Q)$ of self-diffeomorphisms of $Q$ isotopic to the identity acts on the set $\\mathcal{B}$ by $\\mathcal{D}\\times\\mathcal{B}\\to\\mathcal{B}$, $(h,B)\\mapsto h^*B$. Let $\\mathcal{B}^\\circ$ be the set of 2--forms $B\\in\\mathcal{B}$ without zeros. We prove that every $\\mathcal{D}$--invariant functional $I:\\mathcal{B}^\\ci","authors_text":"Elena A. Kudryavtseva","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-12T01:17:33Z","title":"Helicity is the only invariant of incompressible flows whose derivative is continuous in $C^1$-topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03746","kind":"arxiv","version":2},"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":"sha256:7e710172e634681b385115addef1fc4cea6adbc09e2f22cc802205e9205406ec","target":"record","created_at":"2026-05-18T00:49:04Z","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":"0ef0992d261301c83f7215e23101e7ed2649613018f9e09454ae5190e2e99ade","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-12T01:17:33Z","title_canon_sha256":"689ad3c27f542012dec6978c7ac94b8599c7cb15c52f63a85a76862f625883a8"},"schema_version":"1.0","source":{"id":"1511.03746","kind":"arxiv","version":2}},"canonical_sha256":"2951aa457493fd7a2893567df29838601e422a2fc609ca569e34f7b70ce15d80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2951aa457493fd7a2893567df29838601e422a2fc609ca569e34f7b70ce15d80","first_computed_at":"2026-05-18T00:49:04.768261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:04.768261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6vPe/g6LAbJRHxPtLwoHHyrgLYHj6XkVtR8JscjwJrZSJo5wENKou38QjhhsMUkxcOjRKVFO8ctoR5z98wxrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:04.768707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03746","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e710172e634681b385115addef1fc4cea6adbc09e2f22cc802205e9205406ec","sha256:13d81455b6a7ff163646afbebb66bfb1a7724bae78ca9f8eed93f4f5a4f9e952"],"state_sha256":"ca9705857f69af747020b7dc24c3a628c4072028e16fcbf26183737daed81a13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7uBcGW7qbhywqHFK7xW0WYd6LKtUY5kk1J6hdW3yATG2pW3l/ypc74BCrEOQIpI8sbCIa3Twa2+RqIY6OjulBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T18:09:44.263477Z","bundle_sha256":"98b46c27d01af34e537348457678221aead8d4115f2367379a603798587cd772"}}