{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KKYV4EJQIUQ2CUM3WWL5RML57E","short_pith_number":"pith:KKYV4EJQ","canonical_record":{"source":{"id":"1505.01605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-07T07:23:20Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"3b599299521e850428e7f4bb5532626f091df8be130dd28f3d5f1d888707fb05","abstract_canon_sha256":"04abe1574138cf9f50b714990046888021b4a1341ecee2d95f897bf0c145a727"},"schema_version":"1.0"},"canonical_sha256":"52b15e11304521a1519bb597d8b17df90511bdf94f6e470f360456250dac846b","source":{"kind":"arxiv","id":"1505.01605","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01605","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01605v2","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01605","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"KKYV4EJQIUQ2","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KKYV4EJQIUQ2CUM3","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KKYV4EJQ","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KKYV4EJQIUQ2CUM3WWL5RML57E","target":"record","payload":{"canonical_record":{"source":{"id":"1505.01605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-07T07:23:20Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"3b599299521e850428e7f4bb5532626f091df8be130dd28f3d5f1d888707fb05","abstract_canon_sha256":"04abe1574138cf9f50b714990046888021b4a1341ecee2d95f897bf0c145a727"},"schema_version":"1.0"},"canonical_sha256":"52b15e11304521a1519bb597d8b17df90511bdf94f6e470f360456250dac846b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:44.990865Z","signature_b64":"43Q1EY0oZ8sHYXePfO9SfJZZcsAl9VwHnaowM8Ix9dSi9D7jibHMv0WeL8r8TbxrmpQ1ldhgpMiOJWnAo2zMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52b15e11304521a1519bb597d8b17df90511bdf94f6e470f360456250dac846b","last_reissued_at":"2026-05-18T02:03:44.990388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:44.990388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.01605","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":"2026-05-18T02:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKk5Zvn7OMBhQm1UNwnrav3WyTYvfWtxoXmsWPdfQ/cxAKrbdBJH8Q+hkEPB8QvZzljRFlWmFau9PZKprKJbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:13:25.739440Z"},"content_sha256":"743cb2ee170f059ca448d68288621af86cd7315486e4342ef316e9ad30f53345","schema_version":"1.0","event_id":"sha256:743cb2ee170f059ca448d68288621af86cd7315486e4342ef316e9ad30f53345"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KKYV4EJQIUQ2CUM3WWL5RML57E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knotted structures in high-energy Beltrami fields on the torus and the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Alberto Enciso, Daniel Peralta-Salas, Francisco Torres de Lizaur","submitted_at":"2015-05-07T07:23:20Z","abstract_excerpt":"Let S be a finite union of (pairwise disjoint but possibly knotted and linked) closed curves and tubes in the round sphere S^3 or in the flat torus T^3. In the case of the torus, S is further assumed to be contained in a contractible subset of T^3. In this paper we show that for any sufficiently large odd integer \\lambda there exists a Beltrami field on S^3 or T^3 satisfying curl u = \\lambda u and with a collection of vortex lines and vortex tubes given by S, up to an ambient diffeomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01605","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":"2026-05-18T02:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8QSizeXmxg8mrf9FYASAVBA+KgI9yg8hQnCUOqPPsGblLGEeBYejQK2PbAbAI3IU6y0qbVbWS8DwXnED7md9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:13:25.739793Z"},"content_sha256":"fb787218d647b7e752d84ff0fca41fe82e835ca92e962d88914c0fed14be9b8c","schema_version":"1.0","event_id":"sha256:fb787218d647b7e752d84ff0fca41fe82e835ca92e962d88914c0fed14be9b8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKYV4EJQIUQ2CUM3WWL5RML57E/bundle.json","state_url":"https://pith.science/pith/KKYV4EJQIUQ2CUM3WWL5RML57E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKYV4EJQIUQ2CUM3WWL5RML57E/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":"2026-06-12T10:13:25Z","links":{"resolver":"https://pith.science/pith/KKYV4EJQIUQ2CUM3WWL5RML57E","bundle":"https://pith.science/pith/KKYV4EJQIUQ2CUM3WWL5RML57E/bundle.json","state":"https://pith.science/pith/KKYV4EJQIUQ2CUM3WWL5RML57E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKYV4EJQIUQ2CUM3WWL5RML57E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KKYV4EJQIUQ2CUM3WWL5RML57E","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":"04abe1574138cf9f50b714990046888021b4a1341ecee2d95f897bf0c145a727","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-07T07:23:20Z","title_canon_sha256":"3b599299521e850428e7f4bb5532626f091df8be130dd28f3d5f1d888707fb05"},"schema_version":"1.0","source":{"id":"1505.01605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01605","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01605v2","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01605","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"KKYV4EJQIUQ2","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KKYV4EJQIUQ2CUM3","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KKYV4EJQ","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:fb787218d647b7e752d84ff0fca41fe82e835ca92e962d88914c0fed14be9b8c","target":"graph","created_at":"2026-05-18T02:03:44Z","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 S be a finite union of (pairwise disjoint but possibly knotted and linked) closed curves and tubes in the round sphere S^3 or in the flat torus T^3. In the case of the torus, S is further assumed to be contained in a contractible subset of T^3. In this paper we show that for any sufficiently large odd integer \\lambda there exists a Beltrami field on S^3 or T^3 satisfying curl u = \\lambda u and with a collection of vortex lines and vortex tubes given by S, up to an ambient diffeomorphism.","authors_text":"Alberto Enciso, Daniel Peralta-Salas, Francisco Torres de Lizaur","cross_cats":["math.DG","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-07T07:23:20Z","title":"Knotted structures in high-energy Beltrami fields on the torus and the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01605","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":"sha256:743cb2ee170f059ca448d68288621af86cd7315486e4342ef316e9ad30f53345","target":"record","created_at":"2026-05-18T02:03:44Z","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":"04abe1574138cf9f50b714990046888021b4a1341ecee2d95f897bf0c145a727","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-07T07:23:20Z","title_canon_sha256":"3b599299521e850428e7f4bb5532626f091df8be130dd28f3d5f1d888707fb05"},"schema_version":"1.0","source":{"id":"1505.01605","kind":"arxiv","version":2}},"canonical_sha256":"52b15e11304521a1519bb597d8b17df90511bdf94f6e470f360456250dac846b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52b15e11304521a1519bb597d8b17df90511bdf94f6e470f360456250dac846b","first_computed_at":"2026-05-18T02:03:44.990388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:44.990388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"43Q1EY0oZ8sHYXePfO9SfJZZcsAl9VwHnaowM8Ix9dSi9D7jibHMv0WeL8r8TbxrmpQ1ldhgpMiOJWnAo2zMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:44.990865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:743cb2ee170f059ca448d68288621af86cd7315486e4342ef316e9ad30f53345","sha256:fb787218d647b7e752d84ff0fca41fe82e835ca92e962d88914c0fed14be9b8c"],"state_sha256":"0f0cdd286e13a52fd5245993a9836ad7e30ccfa25ef41fc1277b8e7ed5bbcbf1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBFd3mWoKK/WJw80YVS+hndGewxBBVEOOed76Sb5uLJX5Kko7gSDzzHzJKYW31Ntikd0ls1GR3+wLtHVnsJEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:13:25.741734Z","bundle_sha256":"79f60c86433e6a7b0b6862b7d530fe5b9595a58c522fae119e5d37f18a0da802"}}