{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3TWDJ6KJAZFCF7WZXZPRBNY3FJ","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":"3cc188c0dfe40696e1a1c9da113e619ab0a6b61c9d0439746b27c41ff8d76152","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-04T13:02:10Z","title_canon_sha256":"dee89d6938d2482d3e6d36e00bd1f3a90fe2b203dbd2f20c0ef23ffce3737503"},"schema_version":"1.0","source":{"id":"1303.0690","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0690","created_at":"2026-05-18T02:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0690v4","created_at":"2026-05-18T02:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0690","created_at":"2026-05-18T02:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"3TWDJ6KJAZFC","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3TWDJ6KJAZFCF7WZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3TWDJ6KJ","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:00d0c7c10ccbe603e02b34d62927fc82daffb6e86a5ec937caf4fc3115633e04","target":"graph","created_at":"2026-05-18T02:29:55Z","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 an instationary macroscopic system of self-interacting particles with an additional potential, the so called Bohm's potential. We study the existence of non-negative global solutions to the (4-th order) system of equations and allude the differences to results obtained for classical models. The problem is considered on a bounded domain up to three space dimension, subject to initial and Neumann boundary condition for the particle density, and Dirichlet boundary condition for the self-interacting potential. Moreover, the initial datum is only assumed to be non-negative and to satisf","authors_text":"Oliver Tse","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-04T13:02:10Z","title":"On the effects of Bohm's potential on a macroscopic system of self-interacting particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0690","kind":"arxiv","version":4},"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:a7f78f0ed6f1e81a3feb2dddf37e13b98c34620ccedd15c45d6e06532156e5de","target":"record","created_at":"2026-05-18T02:29:55Z","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":"3cc188c0dfe40696e1a1c9da113e619ab0a6b61c9d0439746b27c41ff8d76152","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-04T13:02:10Z","title_canon_sha256":"dee89d6938d2482d3e6d36e00bd1f3a90fe2b203dbd2f20c0ef23ffce3737503"},"schema_version":"1.0","source":{"id":"1303.0690","kind":"arxiv","version":4}},"canonical_sha256":"dcec34f949064a22fed9be5f10b71b2a48e3a8bf413fe6ff499c5493f05ca22b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcec34f949064a22fed9be5f10b71b2a48e3a8bf413fe6ff499c5493f05ca22b","first_computed_at":"2026-05-18T02:29:55.312632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:55.312632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gNblkw0gIzqt/c2FtDr0avZaG7HzvvXUI2upf01x9v/jxhVXVyfqeSkmDWqcxlqV1W4Dbtv9+TP7g22Ihi4iAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:55.313095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0690","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7f78f0ed6f1e81a3feb2dddf37e13b98c34620ccedd15c45d6e06532156e5de","sha256:00d0c7c10ccbe603e02b34d62927fc82daffb6e86a5ec937caf4fc3115633e04"],"state_sha256":"cb5b66e126b92662c5546c645ab007938f60c75accd49e546603093f48499c3e"}