{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:M6VUOFPKGKSUMU2VTWPC7VWINB","short_pith_number":"pith:M6VUOFPK","canonical_record":{"source":{"id":"1608.00909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T17:31:20Z","cross_cats_sorted":["math.MP","nlin.CD","physics.comp-ph"],"title_canon_sha256":"4d7706e7b43e9b4c09945156efaceccc52636c30fc25923e9e6ae297a4118947","abstract_canon_sha256":"d3ffa5fffad35a40cd1214d0c1b35124de099ab549ddcecf47f44115c5ddf46a"},"schema_version":"1.0"},"canonical_sha256":"67ab4715ea32a54653559d9e2fd6c86871f3bd7ce571b3e5af3750f80025ae79","source":{"kind":"arxiv","id":"1608.00909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00909","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00909v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00909","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"M6VUOFPKGKSU","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6VUOFPKGKSUMU2V","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6VUOFPK","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:M6VUOFPKGKSUMU2VTWPC7VWINB","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T17:31:20Z","cross_cats_sorted":["math.MP","nlin.CD","physics.comp-ph"],"title_canon_sha256":"4d7706e7b43e9b4c09945156efaceccc52636c30fc25923e9e6ae297a4118947","abstract_canon_sha256":"d3ffa5fffad35a40cd1214d0c1b35124de099ab549ddcecf47f44115c5ddf46a"},"schema_version":"1.0"},"canonical_sha256":"67ab4715ea32a54653559d9e2fd6c86871f3bd7ce571b3e5af3750f80025ae79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:00.588837Z","signature_b64":"zssXpyRed8MJbxGSv1T51PwMSVrTDLu/Qr8td44eu3WBxgiDMVvgxQLey579Ls9kx4vaSx+BEDGPqMeIvDGZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ab4715ea32a54653559d9e2fd6c86871f3bd7ce571b3e5af3750f80025ae79","last_reissued_at":"2026-05-18T01:10:00.588222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:00.588222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00909","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l48gq07BRt3qc3BKoL70KTEaWna1bjfgJk3gPnfIj7YkA1Z1ipId3n4vnblwjTz3mNk9emk7RdW2VnIszk4hBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:21:33.416825Z"},"content_sha256":"aa5a754c0a803c7a2885500a152673102f3eac230e1503fc10f5de548e0af571","schema_version":"1.0","event_id":"sha256:aa5a754c0a803c7a2885500a152673102f3eac230e1503fc10f5de548e0af571"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:M6VUOFPKGKSUMU2VTWPC7VWINB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vortex knots in tangled quantum eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.CD","physics.comp-ph"],"primary_cat":"math-ph","authors_text":"Alexander J Taylor, Mark R Dennis","submitted_at":"2016-08-02T17:31:20Z","abstract_excerpt":"Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic 3-dimensional harmo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00909","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UyjhCy/n9WOjDSdJ+vCDZFmwSteuxtY+Z2Ya070+cq9ozL5fekX/cn6imuO5mL85Zj9Icmj3cuFdrBh1evj1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:21:33.417166Z"},"content_sha256":"ed6d8bef1535cb546a40586467db2ab79c716524f37f82c71532e8f7022b6c2d","schema_version":"1.0","event_id":"sha256:ed6d8bef1535cb546a40586467db2ab79c716524f37f82c71532e8f7022b6c2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6VUOFPKGKSUMU2VTWPC7VWINB/bundle.json","state_url":"https://pith.science/pith/M6VUOFPKGKSUMU2VTWPC7VWINB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6VUOFPKGKSUMU2VTWPC7VWINB/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":"2026-06-27T09:21:33Z","links":{"resolver":"https://pith.science/pith/M6VUOFPKGKSUMU2VTWPC7VWINB","bundle":"https://pith.science/pith/M6VUOFPKGKSUMU2VTWPC7VWINB/bundle.json","state":"https://pith.science/pith/M6VUOFPKGKSUMU2VTWPC7VWINB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6VUOFPKGKSUMU2VTWPC7VWINB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M6VUOFPKGKSUMU2VTWPC7VWINB","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":"d3ffa5fffad35a40cd1214d0c1b35124de099ab549ddcecf47f44115c5ddf46a","cross_cats_sorted":["math.MP","nlin.CD","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T17:31:20Z","title_canon_sha256":"4d7706e7b43e9b4c09945156efaceccc52636c30fc25923e9e6ae297a4118947"},"schema_version":"1.0","source":{"id":"1608.00909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00909","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00909v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00909","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"M6VUOFPKGKSU","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6VUOFPKGKSUMU2V","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6VUOFPK","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:ed6d8bef1535cb546a40586467db2ab79c716524f37f82c71532e8f7022b6c2d","target":"graph","created_at":"2026-05-18T01:10:00Z","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":"Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic 3-dimensional harmo","authors_text":"Alexander J Taylor, Mark R Dennis","cross_cats":["math.MP","nlin.CD","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T17:31:20Z","title":"Vortex knots in tangled quantum eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00909","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:aa5a754c0a803c7a2885500a152673102f3eac230e1503fc10f5de548e0af571","target":"record","created_at":"2026-05-18T01:10:00Z","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":"d3ffa5fffad35a40cd1214d0c1b35124de099ab549ddcecf47f44115c5ddf46a","cross_cats_sorted":["math.MP","nlin.CD","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-02T17:31:20Z","title_canon_sha256":"4d7706e7b43e9b4c09945156efaceccc52636c30fc25923e9e6ae297a4118947"},"schema_version":"1.0","source":{"id":"1608.00909","kind":"arxiv","version":1}},"canonical_sha256":"67ab4715ea32a54653559d9e2fd6c86871f3bd7ce571b3e5af3750f80025ae79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ab4715ea32a54653559d9e2fd6c86871f3bd7ce571b3e5af3750f80025ae79","first_computed_at":"2026-05-18T01:10:00.588222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:00.588222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zssXpyRed8MJbxGSv1T51PwMSVrTDLu/Qr8td44eu3WBxgiDMVvgxQLey579Ls9kx4vaSx+BEDGPqMeIvDGZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:00.588837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa5a754c0a803c7a2885500a152673102f3eac230e1503fc10f5de548e0af571","sha256:ed6d8bef1535cb546a40586467db2ab79c716524f37f82c71532e8f7022b6c2d"],"state_sha256":"42e0df3cec4efc7a76980070a751eca6bda70f95bb9ab140b1ca083102d0a10e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2KnQ0OFxaE3W8ChjmrNLcuAzkkKgfIhiunxqCZUVPtM798y8J6n/hxV3WsAXykL8yYYGrdJxA84IfLXyNjDMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T09:21:33.419061Z","bundle_sha256":"40aa8fdf0be6cd1a472cd983d9ba18955082b859584458c3525cf6ed07fde7ad"}}