{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CNXRB23P3FCOU44CC3PLIO7ZNW","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":"660354d49ce11ab6a3402169790b3902d4414721d055e900412f26bde30bd9a0","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-08-21T04:59:09Z","title_canon_sha256":"710152f4eb82fe47d97edbc9019d2a5790a529711ee0cf162c038b6583524158"},"schema_version":"1.0","source":{"id":"1208.4191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4191","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4191v1","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4191","created_at":"2026-05-18T01:55:08Z"},{"alias_kind":"pith_short_12","alias_value":"CNXRB23P3FCO","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CNXRB23P3FCOU44C","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CNXRB23P","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:37a145dba606c088701dcd8574f579f2ebd5bea7492291dbfbd77b320e5bc786","target":"graph","created_at":"2026-05-18T01:55:08Z","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 consider two-dimensional (2D) localized modes in the second-harmonic-generating \\chi ^{(2)} system with the harmonic-oscillator (HO) trapping potential. In addition to its realization in optics, the system describes the mean-field dynamics of mixed atomic-molecular Bose-Einstein condensates (BECs). The existence and stability of various modes is determined by their total power, N, topological charge, m/2 [m is the intrinsic vorticity of the second-harmonic (SH) field], and \\chi ^{(2)} mismatch, q. The analysis is carried out in a numerical form and, in parallel, by means of the variational ","authors_text":"Boris A. Malomed, Hidetsugu Sakaguchi","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-08-21T04:59:09Z","title":"Stabilizing single- and two-color vortex beams in quadratic media by a trapping potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4191","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:b32885f6e1b96238cca0f07d94d8d6667159759ce9b3486a824f48e909516e65","target":"record","created_at":"2026-05-18T01:55:08Z","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":"660354d49ce11ab6a3402169790b3902d4414721d055e900412f26bde30bd9a0","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-08-21T04:59:09Z","title_canon_sha256":"710152f4eb82fe47d97edbc9019d2a5790a529711ee0cf162c038b6583524158"},"schema_version":"1.0","source":{"id":"1208.4191","kind":"arxiv","version":1}},"canonical_sha256":"136f10eb6fd944ea738216deb43bf96d95e25d37eb4cd42e00e6d365bdbca526","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"136f10eb6fd944ea738216deb43bf96d95e25d37eb4cd42e00e6d365bdbca526","first_computed_at":"2026-05-18T01:55:08.915272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:08.915272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f4EPAzdUGvB8XhU6OLaKkPEd5FHMn8BYvEpyiwjpm4NTPqbKCxJ+xMAXDbz+XALzWy471ONekOxeCYJRQFMKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:08.915789Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b32885f6e1b96238cca0f07d94d8d6667159759ce9b3486a824f48e909516e65","sha256:37a145dba606c088701dcd8574f579f2ebd5bea7492291dbfbd77b320e5bc786"],"state_sha256":"1756c57e435d53b3f81f17344c2db31705a7c44486fffd0785665f37184a2843"}