{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FKRHXBS4EORRWF7NE7TZOM5COI","short_pith_number":"pith:FKRHXBS4","canonical_record":{"source":{"id":"1510.04344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-10-14T23:01:56Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"88e78067015484c7da724441d36142b3c25320607b55488e9bf1101c15f4531e","abstract_canon_sha256":"6a33bc8d2fad6a812b81c1005fac763282ea3133795d89528de4512f13eca31b"},"schema_version":"1.0"},"canonical_sha256":"2aa27b865c23a31b17ed27e79733a2723aa1cfc5810d4dfa896c065b8cd236f9","source":{"kind":"arxiv","id":"1510.04344","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04344","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04344v1","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04344","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"pith_short_12","alias_value":"FKRHXBS4EORR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FKRHXBS4EORRWF7N","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FKRHXBS4","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FKRHXBS4EORRWF7NE7TZOM5COI","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-10-14T23:01:56Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"88e78067015484c7da724441d36142b3c25320607b55488e9bf1101c15f4531e","abstract_canon_sha256":"6a33bc8d2fad6a812b81c1005fac763282ea3133795d89528de4512f13eca31b"},"schema_version":"1.0"},"canonical_sha256":"2aa27b865c23a31b17ed27e79733a2723aa1cfc5810d4dfa896c065b8cd236f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:47.897684Z","signature_b64":"T1RiNZEb47b/QLW2jEYIxdyVdiFsexJFGW2zaU+GNcVCZ5EgUYxE7zXH2bwQDAInwPHtJ4NHwCbqAsP9PhOABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2aa27b865c23a31b17ed27e79733a2723aa1cfc5810d4dfa896c065b8cd236f9","last_reissued_at":"2026-05-18T01:22:47.896986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:47.896986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04344","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":"2026-05-18T01:22:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCDJvkR08DbRNIT9XhRTQgynkGsVQu+tCe2tRAhTgTErN93ERbNS+20hhQ81SFjlAQxu8YiDwZjMbNVueKqRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:15:45.497343Z"},"content_sha256":"cc476fe9a326611f63a73038872c3b3f703fd9cc90898d9ff5ca405b976c74e1","schema_version":"1.0","event_id":"sha256:cc476fe9a326611f63a73038872c3b3f703fd9cc90898d9ff5ca405b976c74e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FKRHXBS4EORRWF7NE7TZOM5COI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Vortex Lines, Vortex Rings and Hopfions in 3D Bose-Einstein Condensates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"cond-mat.quant-gas","authors_text":"C. Ticknor, D.J. Frantzeskakis, L.A. Collins, P.G. Kevrekidis, R. Carretero-Gonzalez, R.N. Bisset, Wenlong Wang","submitted_at":"2015-10-14T23:01:56Z","abstract_excerpt":"Performing a systematic Bogoliubov-de Gennes spectral analysis, we illustrate that stationary vortex lines, vortex rings and more exotic states, such as hopfions, are robust in three-dimensional atomic Bose-Einstein condensates, for large parameter intervals. Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions. We supplement our spectral analysis by studying the dynamics of such stationary states; we find them to be robust against significant perturbations of the initial state. In the unstable regi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04344","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":"2026-05-18T01:22:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XL/VEoONJgDqnDE36tC3/0UIdNZyLDdOIWcIQut8LVqNC6R2yDACn71J/5DjnilhorZTzn+LywCgWVV5425fDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:15:45.497700Z"},"content_sha256":"c3bb3b2420f537909103623aa0025f0d71cc976dc212cca77aca0c2ce818d3bf","schema_version":"1.0","event_id":"sha256:c3bb3b2420f537909103623aa0025f0d71cc976dc212cca77aca0c2ce818d3bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FKRHXBS4EORRWF7NE7TZOM5COI/bundle.json","state_url":"https://pith.science/pith/FKRHXBS4EORRWF7NE7TZOM5COI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FKRHXBS4EORRWF7NE7TZOM5COI/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":"2026-05-28T12:15:45Z","links":{"resolver":"https://pith.science/pith/FKRHXBS4EORRWF7NE7TZOM5COI","bundle":"https://pith.science/pith/FKRHXBS4EORRWF7NE7TZOM5COI/bundle.json","state":"https://pith.science/pith/FKRHXBS4EORRWF7NE7TZOM5COI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FKRHXBS4EORRWF7NE7TZOM5COI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FKRHXBS4EORRWF7NE7TZOM5COI","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":"6a33bc8d2fad6a812b81c1005fac763282ea3133795d89528de4512f13eca31b","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-10-14T23:01:56Z","title_canon_sha256":"88e78067015484c7da724441d36142b3c25320607b55488e9bf1101c15f4531e"},"schema_version":"1.0","source":{"id":"1510.04344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04344","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04344v1","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04344","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"pith_short_12","alias_value":"FKRHXBS4EORR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FKRHXBS4EORRWF7N","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FKRHXBS4","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:c3bb3b2420f537909103623aa0025f0d71cc976dc212cca77aca0c2ce818d3bf","target":"graph","created_at":"2026-05-18T01:22:47Z","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":"Performing a systematic Bogoliubov-de Gennes spectral analysis, we illustrate that stationary vortex lines, vortex rings and more exotic states, such as hopfions, are robust in three-dimensional atomic Bose-Einstein condensates, for large parameter intervals. Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions. We supplement our spectral analysis by studying the dynamics of such stationary states; we find them to be robust against significant perturbations of the initial state. In the unstable regi","authors_text":"C. Ticknor, D.J. Frantzeskakis, L.A. Collins, P.G. Kevrekidis, R. Carretero-Gonzalez, R.N. Bisset, Wenlong Wang","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-10-14T23:01:56Z","title":"Robust Vortex Lines, Vortex Rings and Hopfions in 3D Bose-Einstein Condensates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04344","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:cc476fe9a326611f63a73038872c3b3f703fd9cc90898d9ff5ca405b976c74e1","target":"record","created_at":"2026-05-18T01:22:47Z","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":"6a33bc8d2fad6a812b81c1005fac763282ea3133795d89528de4512f13eca31b","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-10-14T23:01:56Z","title_canon_sha256":"88e78067015484c7da724441d36142b3c25320607b55488e9bf1101c15f4531e"},"schema_version":"1.0","source":{"id":"1510.04344","kind":"arxiv","version":1}},"canonical_sha256":"2aa27b865c23a31b17ed27e79733a2723aa1cfc5810d4dfa896c065b8cd236f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2aa27b865c23a31b17ed27e79733a2723aa1cfc5810d4dfa896c065b8cd236f9","first_computed_at":"2026-05-18T01:22:47.896986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:47.896986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T1RiNZEb47b/QLW2jEYIxdyVdiFsexJFGW2zaU+GNcVCZ5EgUYxE7zXH2bwQDAInwPHtJ4NHwCbqAsP9PhOABQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:47.897684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc476fe9a326611f63a73038872c3b3f703fd9cc90898d9ff5ca405b976c74e1","sha256:c3bb3b2420f537909103623aa0025f0d71cc976dc212cca77aca0c2ce818d3bf"],"state_sha256":"26222a981cfb3be388369de07847e1078d4b8e2106d2c8c0581c3c8df23fab38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uFM3GAgZX0FqfYBql2QDqZqsI/Y5cfzl7nGCdDUfOx7V4rVqy4RvdS1u/6p6CbDou0Z3Lc0i798AqGzB9A3SAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:15:45.499664Z","bundle_sha256":"5b48818aa95145d9859a35b41ac8ba7e60ba25957c269797492dddfecc4f9261"}}