{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RCT3P3XKDWFAP7V4MDQ3MYQLBR","short_pith_number":"pith:RCT3P3XK","canonical_record":{"source":{"id":"1406.7056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-06-27T03:07:23Z","cross_cats_sorted":[],"title_canon_sha256":"5399d667b539888963bdc58f999c09f8307b2b8d1269d0236ad792d36d3dbdbc","abstract_canon_sha256":"3d360edc1ed0e2e124c3e31c119046b38a112ce409935f611b99fda5a054879a"},"schema_version":"1.0"},"canonical_sha256":"88a7b7eeea1d8a07febc60e1b6620b0c6a493a7131e15aa431ab6f8134e8afff","source":{"kind":"arxiv","id":"1406.7056","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7056","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7056v1","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7056","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"RCT3P3XKDWFA","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RCT3P3XKDWFAP7V4","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RCT3P3XK","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RCT3P3XKDWFAP7V4MDQ3MYQLBR","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-06-27T03:07:23Z","cross_cats_sorted":[],"title_canon_sha256":"5399d667b539888963bdc58f999c09f8307b2b8d1269d0236ad792d36d3dbdbc","abstract_canon_sha256":"3d360edc1ed0e2e124c3e31c119046b38a112ce409935f611b99fda5a054879a"},"schema_version":"1.0"},"canonical_sha256":"88a7b7eeea1d8a07febc60e1b6620b0c6a493a7131e15aa431ab6f8134e8afff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:46.018807Z","signature_b64":"pIF9hIwPJIJ78gNCd47eBI3R5HVPlhnb92UzQq5gxAGsgupThOXHPu9XlUwpKxKF6M0tsYUHd/cBNwD/4rBoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88a7b7eeea1d8a07febc60e1b6620b0c6a493a7131e15aa431ab6f8134e8afff","last_reissued_at":"2026-05-18T01:42:46.018239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:46.018239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7056","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":"2026-05-18T01:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GhCKltIE7+OpJX+gAQBkgpuBS/nTpR1uogtQPg2lc6nqsYVim95mfL2GHFdXOpp6M4H0SV4hIIEnK4RhFCBMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T00:00:45.959522Z"},"content_sha256":"2a2d4e4f0041594e24fde18515de47ae7b1385f89892f7b2fb7e137869be661b","schema_version":"1.0","event_id":"sha256:2a2d4e4f0041594e24fde18515de47ae7b1385f89892f7b2fb7e137869be661b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RCT3P3XKDWFAP7V4MDQ3MYQLBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable knots in the trapped Bose-Einstein condensates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Shi-jie Yang, Shiping Feng, Yong-Kai Liu","submitted_at":"2014-06-27T03:07:23Z","abstract_excerpt":"The knot of spin texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the non-interacting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a non-trivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7056","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":"2026-05-18T01:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLmb0B5Gotvgxsb8JLU2O3b/S+Dkqc2gXGdkwGAeoq38NEoOPminffKXF6Ismfj+sVLOmKiDoqJLjsZifXKgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T00:00:45.960209Z"},"content_sha256":"ee92d0cd91d1067d9900dd93478729947fae18d9d83bba685aa3344bcb2c543e","schema_version":"1.0","event_id":"sha256:ee92d0cd91d1067d9900dd93478729947fae18d9d83bba685aa3344bcb2c543e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCT3P3XKDWFAP7V4MDQ3MYQLBR/bundle.json","state_url":"https://pith.science/pith/RCT3P3XKDWFAP7V4MDQ3MYQLBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCT3P3XKDWFAP7V4MDQ3MYQLBR/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":"2026-05-19T00:00:45Z","links":{"resolver":"https://pith.science/pith/RCT3P3XKDWFAP7V4MDQ3MYQLBR","bundle":"https://pith.science/pith/RCT3P3XKDWFAP7V4MDQ3MYQLBR/bundle.json","state":"https://pith.science/pith/RCT3P3XKDWFAP7V4MDQ3MYQLBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCT3P3XKDWFAP7V4MDQ3MYQLBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RCT3P3XKDWFAP7V4MDQ3MYQLBR","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":"3d360edc1ed0e2e124c3e31c119046b38a112ce409935f611b99fda5a054879a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-06-27T03:07:23Z","title_canon_sha256":"5399d667b539888963bdc58f999c09f8307b2b8d1269d0236ad792d36d3dbdbc"},"schema_version":"1.0","source":{"id":"1406.7056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7056","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7056v1","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7056","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"RCT3P3XKDWFA","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RCT3P3XKDWFAP7V4","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RCT3P3XK","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:ee92d0cd91d1067d9900dd93478729947fae18d9d83bba685aa3344bcb2c543e","target":"graph","created_at":"2026-05-18T01:42:46Z","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 knot of spin texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the non-interacting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a non-trivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time.","authors_text":"Shi-jie Yang, Shiping Feng, Yong-Kai Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-06-27T03:07:23Z","title":"Stable knots in the trapped Bose-Einstein condensates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7056","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":"sha256:2a2d4e4f0041594e24fde18515de47ae7b1385f89892f7b2fb7e137869be661b","target":"record","created_at":"2026-05-18T01:42:46Z","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":"3d360edc1ed0e2e124c3e31c119046b38a112ce409935f611b99fda5a054879a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-06-27T03:07:23Z","title_canon_sha256":"5399d667b539888963bdc58f999c09f8307b2b8d1269d0236ad792d36d3dbdbc"},"schema_version":"1.0","source":{"id":"1406.7056","kind":"arxiv","version":1}},"canonical_sha256":"88a7b7eeea1d8a07febc60e1b6620b0c6a493a7131e15aa431ab6f8134e8afff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88a7b7eeea1d8a07febc60e1b6620b0c6a493a7131e15aa431ab6f8134e8afff","first_computed_at":"2026-05-18T01:42:46.018239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:46.018239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pIF9hIwPJIJ78gNCd47eBI3R5HVPlhnb92UzQq5gxAGsgupThOXHPu9XlUwpKxKF6M0tsYUHd/cBNwD/4rBoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:46.018807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a2d4e4f0041594e24fde18515de47ae7b1385f89892f7b2fb7e137869be661b","sha256:ee92d0cd91d1067d9900dd93478729947fae18d9d83bba685aa3344bcb2c543e"],"state_sha256":"5ea58b9c44ed22e11a9593f132718bb2ae9be2988f5ef9d2ece7a3ee16e8a8b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PF4BhjtYT2OsWidlew5rSwqDR13mrkdkHe8MHLMbWHXrSt2ajKcmlmIVJud61luiMQnBe7dpXDzxKH5G6z4zBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T00:00:45.962240Z","bundle_sha256":"14ca0b05bd310cb1f7809f3f7937e97846f2ef58115cbd5d137b95eba710260e"}}