{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JXYAMVHLBK4FGZU2TNYJWNCXAK","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":"db024fcaa48295b209d89a26d555f264cae24916d48af0bdc0fb416b1351fe20","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-30T18:42:58Z","title_canon_sha256":"19eea56d4a19b00c2e8eaef416b80cea140d38f92b404e9d5ff0dc28aedf1270"},"schema_version":"1.0","source":{"id":"1208.6259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6259","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6259v1","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6259","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"pith_short_12","alias_value":"JXYAMVHLBK4F","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JXYAMVHLBK4FGZU2","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JXYAMVHL","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:075a0c083f16df1d2e409007963c064a4f541d7b992cb5c3d8fa31c91a79aa6a","target":"graph","created_at":"2026-05-18T03:46:46Z","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":"We prove the existence of ground state in a multidimensional nonlinear Schrodinger model of paraxial beam propagation in isotropic local media with saturable nonlinearity. Such ground states exist in the form of bright counterpropagating solitons. From the proof, a general threshold condition on the beam coupling constant for the existence of such fundamental solitons follows.","authors_text":"Goong Chen, Milan S. Petrovi\\'c, Milivoj R. Beli\\'c, Tai-Chia Lin","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-30T18:42:58Z","title":"Ground state of nonlinear Schrodinger systems with saturable nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6259","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:de538d7c682f882b5e4ed446f35a092f16e41458496fa77a6bc642f33402de02","target":"record","created_at":"2026-05-18T03:46:46Z","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":"db024fcaa48295b209d89a26d555f264cae24916d48af0bdc0fb416b1351fe20","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-30T18:42:58Z","title_canon_sha256":"19eea56d4a19b00c2e8eaef416b80cea140d38f92b404e9d5ff0dc28aedf1270"},"schema_version":"1.0","source":{"id":"1208.6259","kind":"arxiv","version":1}},"canonical_sha256":"4df00654eb0ab853669a9b709b34570283f902a4222dfdd68efd07a68385d0ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4df00654eb0ab853669a9b709b34570283f902a4222dfdd68efd07a68385d0ed","first_computed_at":"2026-05-18T03:46:46.074702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:46.074702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n63Qz3PFxUIkqoMb7n+QUtC5beLz0tSMhibCe/YuWanSBMU1yR2/kJ36NZ3BZIeYNy/9Lqy9b/DETJnGzFsUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:46.075499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de538d7c682f882b5e4ed446f35a092f16e41458496fa77a6bc642f33402de02","sha256:075a0c083f16df1d2e409007963c064a4f541d7b992cb5c3d8fa31c91a79aa6a"],"state_sha256":"7dc3341f0f8d98355f97c73342bb84e586252151804c3631b133eb65d951a2ca"}