{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JQFSBWJECEFXEB72MSNHAAD3YV","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":"20acdc86ec86e1a3ae8e43138bb948f9e68955e73d86f4e940064a36b7fd6320","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-30T10:48:03Z","title_canon_sha256":"f83f4b992234a96045c2f4c534367d97e55dc4015af71dba633d6067147bcdc6"},"schema_version":"1.0","source":{"id":"1507.08446","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08446","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08446v1","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08446","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"JQFSBWJECEFX","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JQFSBWJECEFXEB72","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JQFSBWJE","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:d8f057f712240a66c018a9959a776edf1705f62112845c44e8f91dd39cf27d8b","target":"graph","created_at":"2026-05-18T01:36:06Z","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 a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations.","authors_text":"Lucia De Luca, Marcello Ponsiglione, Marco Cicalese, Matteo Novaga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-30T10:48:03Z","title":"Ground states of a two phase model with cross and self attractive interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08446","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":"sha256:7a2e56c217e623437ff7bed9c592e4bc419525b429fa1126f0d7695a85e017d8","target":"record","created_at":"2026-05-18T01:36:06Z","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":"20acdc86ec86e1a3ae8e43138bb948f9e68955e73d86f4e940064a36b7fd6320","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-30T10:48:03Z","title_canon_sha256":"f83f4b992234a96045c2f4c534367d97e55dc4015af71dba633d6067147bcdc6"},"schema_version":"1.0","source":{"id":"1507.08446","kind":"arxiv","version":1}},"canonical_sha256":"4c0b20d924110b7207fa649a70007bc55baf5ff2aa538bb211e5c3e2ce68f9ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c0b20d924110b7207fa649a70007bc55baf5ff2aa538bb211e5c3e2ce68f9ce","first_computed_at":"2026-05-18T01:36:06.437205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:06.437205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L0F+q9LhJndlT5Q0wa/iRfrW/gJQKulHz5eAnmttwVgTthUVrkdQLdD/UEkUGltEyxd3U1PPLMl3/aIJZdUlAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:06.437671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08446","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a2e56c217e623437ff7bed9c592e4bc419525b429fa1126f0d7695a85e017d8","sha256:d8f057f712240a66c018a9959a776edf1705f62112845c44e8f91dd39cf27d8b"],"state_sha256":"deb96923797a5938ab02820c8ebc66dd3ba6222090cb7e34973453ef0c39e5f5"}