{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:G5SOSZTXD5HNGEZ6PGNID6ETF7","short_pith_number":"pith:G5SOSZTX","canonical_record":{"source":{"id":"1610.02463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-08T02:28:21Z","cross_cats_sorted":["hep-th","math.MP","physics.flu-dyn","physics.plasm-ph"],"title_canon_sha256":"d05e9ff3f8005370f984df8805e46abd32a94e50d83f64fe55ce7654c0e3bb2f","abstract_canon_sha256":"d258f4e341c48803b1110e75beffc2c377fb09f26eb83f2761358a39bc5ed335"},"schema_version":"1.0"},"canonical_sha256":"3764e966771f4ed3133e799a81f8932fe8d6644e8154988ee39baea7f336133d","source":{"kind":"arxiv","id":"1610.02463","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02463","created_at":"2026-05-18T00:53:50Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02463v1","created_at":"2026-05-18T00:53:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02463","created_at":"2026-05-18T00:53:50Z"},{"alias_kind":"pith_short_12","alias_value":"G5SOSZTXD5HN","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G5SOSZTXD5HNGEZ6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G5SOSZTX","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:G5SOSZTXD5HNGEZ6PGNID6ETF7","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-08T02:28:21Z","cross_cats_sorted":["hep-th","math.MP","physics.flu-dyn","physics.plasm-ph"],"title_canon_sha256":"d05e9ff3f8005370f984df8805e46abd32a94e50d83f64fe55ce7654c0e3bb2f","abstract_canon_sha256":"d258f4e341c48803b1110e75beffc2c377fb09f26eb83f2761358a39bc5ed335"},"schema_version":"1.0"},"canonical_sha256":"3764e966771f4ed3133e799a81f8932fe8d6644e8154988ee39baea7f336133d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:50.581918Z","signature_b64":"V7wOIV/MPeKzUfpxlWFaCB0tUdSaJ2atqRn36qfsGbx57liBIhzd8ewpgN2FMOcYSFxCzfZ8M/X52gfnfwtGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3764e966771f4ed3133e799a81f8932fe8d6644e8154988ee39baea7f336133d","last_reissued_at":"2026-05-18T00:53:50.581498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:50.581498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02463","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRdDZzJNWvvMads8VsI9WFJbt8+wJWuZkmaQNbYhpwPD4kTAuoOt5WmGLeTIvAvIAIdzH6CN2ckZojkgi0mSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:31:05.828665Z"},"content_sha256":"083ac01ba4953d87c9245b6f98c08f08a92ec5d52f3e0260687bbbec0f843d0d","schema_version":"1.0","event_id":"sha256:083ac01ba4953d87c9245b6f98c08f08a92ec5d52f3e0260687bbbec0f843d0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:G5SOSZTXD5HNGEZ6PGNID6ETF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weaving knotted vector fields with tunable helicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","physics.flu-dyn","physics.plasm-ph"],"primary_cat":"math-ph","authors_text":"David Foster, Hridesh Kedia, Mark R. Dennis, William T. M. Irvine","submitted_at":"2016-10-08T02:28:21Z","abstract_excerpt":"We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot and its generalizations. As finite-energy physical fields they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knott"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02463","kind":"arxiv","version":1},"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":"2026-05-18T00:53:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0o0sgSE2EUCbplAD/DyCUvrJyOvXdsndII+ZK4/GEhdb4nCKDIhKeD59Q1L3xXzMoeMHZH/3fNn0sZmnu/gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:31:05.829021Z"},"content_sha256":"13bf73d904cce0dbc319080c8b98d573c30bc9bff245206edcbcdc72d3685a87","schema_version":"1.0","event_id":"sha256:13bf73d904cce0dbc319080c8b98d573c30bc9bff245206edcbcdc72d3685a87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5SOSZTXD5HNGEZ6PGNID6ETF7/bundle.json","state_url":"https://pith.science/pith/G5SOSZTXD5HNGEZ6PGNID6ETF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5SOSZTXD5HNGEZ6PGNID6ETF7/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":"2026-05-29T17:31:05Z","links":{"resolver":"https://pith.science/pith/G5SOSZTXD5HNGEZ6PGNID6ETF7","bundle":"https://pith.science/pith/G5SOSZTXD5HNGEZ6PGNID6ETF7/bundle.json","state":"https://pith.science/pith/G5SOSZTXD5HNGEZ6PGNID6ETF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5SOSZTXD5HNGEZ6PGNID6ETF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G5SOSZTXD5HNGEZ6PGNID6ETF7","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":"d258f4e341c48803b1110e75beffc2c377fb09f26eb83f2761358a39bc5ed335","cross_cats_sorted":["hep-th","math.MP","physics.flu-dyn","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-08T02:28:21Z","title_canon_sha256":"d05e9ff3f8005370f984df8805e46abd32a94e50d83f64fe55ce7654c0e3bb2f"},"schema_version":"1.0","source":{"id":"1610.02463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02463","created_at":"2026-05-18T00:53:50Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02463v1","created_at":"2026-05-18T00:53:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02463","created_at":"2026-05-18T00:53:50Z"},{"alias_kind":"pith_short_12","alias_value":"G5SOSZTXD5HN","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G5SOSZTXD5HNGEZ6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G5SOSZTX","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:13bf73d904cce0dbc319080c8b98d573c30bc9bff245206edcbcdc72d3685a87","target":"graph","created_at":"2026-05-18T00:53:50Z","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":"We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot and its generalizations. As finite-energy physical fields they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knott","authors_text":"David Foster, Hridesh Kedia, Mark R. Dennis, William T. M. Irvine","cross_cats":["hep-th","math.MP","physics.flu-dyn","physics.plasm-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-08T02:28:21Z","title":"Weaving knotted vector fields with tunable helicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02463","kind":"arxiv","version":1},"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":"sha256:083ac01ba4953d87c9245b6f98c08f08a92ec5d52f3e0260687bbbec0f843d0d","target":"record","created_at":"2026-05-18T00:53:50Z","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":"d258f4e341c48803b1110e75beffc2c377fb09f26eb83f2761358a39bc5ed335","cross_cats_sorted":["hep-th","math.MP","physics.flu-dyn","physics.plasm-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-08T02:28:21Z","title_canon_sha256":"d05e9ff3f8005370f984df8805e46abd32a94e50d83f64fe55ce7654c0e3bb2f"},"schema_version":"1.0","source":{"id":"1610.02463","kind":"arxiv","version":1}},"canonical_sha256":"3764e966771f4ed3133e799a81f8932fe8d6644e8154988ee39baea7f336133d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3764e966771f4ed3133e799a81f8932fe8d6644e8154988ee39baea7f336133d","first_computed_at":"2026-05-18T00:53:50.581498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:50.581498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V7wOIV/MPeKzUfpxlWFaCB0tUdSaJ2atqRn36qfsGbx57liBIhzd8ewpgN2FMOcYSFxCzfZ8M/X52gfnfwtGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:50.581918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:083ac01ba4953d87c9245b6f98c08f08a92ec5d52f3e0260687bbbec0f843d0d","sha256:13bf73d904cce0dbc319080c8b98d573c30bc9bff245206edcbcdc72d3685a87"],"state_sha256":"cbb3a4daf48cd85c1b591e4857855fc9a989d3a3623c32b96ab02bd18402808f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bvg4Z9wDC6wccrwonEgO/K26lzB4jahXhUV8EWNCuUf2Nn5sghC10WRJD5JDNQJIEpDeTSh9IEqDF5mWYnmeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:31:05.831021Z","bundle_sha256":"f2588aa5e689cc3906fa9d49ef9d614cda591183b81a1f77f37bd05ea70b3006"}}