{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I7U2I4XEHKYR46DZIDXWB6YURR","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":"dbdfd310eeaa7dc91408a5947603fcff20719072d18505d996c502a04710a31d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-17T09:39:04Z","title_canon_sha256":"3379fdddd28d48dd3bf93530e1e6a99d588de86e1ff3de42de40abc18ecc2e05"},"schema_version":"1.0","source":{"id":"1509.05182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05182","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05182v2","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05182","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"I7U2I4XEHKYR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I7U2I4XEHKYR46DZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I7U2I4XE","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:ee24dd587a30aeb8b06558b32e31d735da0b7e41875f9b961765cccb7519485a","target":"graph","created_at":"2026-05-18T01:31:29Z","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 develop an analytic theory for the ground state patterns and their phase transitions for spin-1 Bose-Einstein condensates on a bounded domain in the presence of a uniform magnetic field. Within the Thomas-Fermi approximation, these ground state patterns are composed of four basic states: magnetic state, nematic state, two-component state and three-component state, separated by interfaces. A complete phase diagram of the ground state patterns are found analytically with different quadratic Zeeman energy q and total magnetization M for both ferromagnetic and antiferromagnetic systems. Using t","authors_text":"Chiu-Fen Chou, I-Liang Chern, Tien-Tsan Shieh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-17T09:39:04Z","title":"Ground state patterns and phase transition of spin-1 Bose-Einstein condensates via \\Gamma-convergence theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05182","kind":"arxiv","version":2},"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:ca0b35f9091c754ab5e7996bd7666578097acccbdad4849c7b2eba81d0ff7e0d","target":"record","created_at":"2026-05-18T01:31:29Z","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":"dbdfd310eeaa7dc91408a5947603fcff20719072d18505d996c502a04710a31d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-17T09:39:04Z","title_canon_sha256":"3379fdddd28d48dd3bf93530e1e6a99d588de86e1ff3de42de40abc18ecc2e05"},"schema_version":"1.0","source":{"id":"1509.05182","kind":"arxiv","version":2}},"canonical_sha256":"47e9a472e43ab11e787940ef60fb148c6fece20f030cd094240fe28589bbaffb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47e9a472e43ab11e787940ef60fb148c6fece20f030cd094240fe28589bbaffb","first_computed_at":"2026-05-18T01:31:29.565490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:29.565490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NtuCYD+83xEDmNkSAw85j6Hiz2kWLKicbGapjDeSgshcQb8zuIBOUGgcBV2/sE4Ny3l9o8PXrVkuhXIdOEhTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:29.566257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0b35f9091c754ab5e7996bd7666578097acccbdad4849c7b2eba81d0ff7e0d","sha256:ee24dd587a30aeb8b06558b32e31d735da0b7e41875f9b961765cccb7519485a"],"state_sha256":"19fcba1f540cab84bdf83abf18716f3cc296c8ff51f6e83575c12a7dc2f0c382"}