{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:COKLUAM6PYTLA23MVAPHPLN7O3","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":"d3ccf9c9ab17c7761bbfefcf0485189dc3206ecf06457c1389920a63264df6b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-15T02:43:42Z","title_canon_sha256":"8e839e3c8b10b0f698a9ccc8dfcabb077c9bc0f4a30cc9189f0b31e423e9af8f"},"schema_version":"1.0","source":{"id":"1903.06331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06331","created_at":"2026-05-17T23:51:11Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06331v1","created_at":"2026-05-17T23:51:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06331","created_at":"2026-05-17T23:51:11Z"},{"alias_kind":"pith_short_12","alias_value":"COKLUAM6PYTL","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"COKLUAM6PYTLA23M","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"COKLUAM6","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:1691977a83145b5f20926bb242236c860bdf6098b84a4966c196dd1d41c540a4","target":"graph","created_at":"2026-05-17T23:51:11Z","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 the no-flux initial-boundary value problem for the cross-diffusive evolution system \\begin{eqnarray*}\n  \\left\\{ \\begin{array}{ll}\n  u_t = u_{xx} - \\chi \\big(\\frac{u}{v} \\partial_x u \\big)_x - uv +B_1(x,t),\n  \\qquad & x\\in \\Omega, \\ t>0, \\\\[1mm]\n  v_t = v_{xx} +uv - v + B_2(x,t),\n  \\qquad & x\\in \\Omega, \\ t>0,\n  \\end{array} \\right. \\end{eqnarray*}\n  which was introduced by Short et al. in [Short2008] with $\\chi=2$ to describe the dynamics of urban crime\n  In bounded intervals $\\Omega\\subset\\mathbb{R}$ and with prescribed suitably regular nonnegative\n  functions $B_1$ and $B_2$, we f","authors_text":"Michael Winkler, Nancy Rodriguez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-15T02:43:42Z","title":"On the global existence and qualitative behavior of one-dimensional solutions to a model for urban crime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06331","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":"sha256:697eb40a66fd98a29d77e7785294e5a602fe8eefd66b080af4edb15fd1500fd0","target":"record","created_at":"2026-05-17T23:51:11Z","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":"d3ccf9c9ab17c7761bbfefcf0485189dc3206ecf06457c1389920a63264df6b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-15T02:43:42Z","title_canon_sha256":"8e839e3c8b10b0f698a9ccc8dfcabb077c9bc0f4a30cc9189f0b31e423e9af8f"},"schema_version":"1.0","source":{"id":"1903.06331","kind":"arxiv","version":1}},"canonical_sha256":"1394ba019e7e26b06b6ca81e77adbf76d0a32e957725815806971be63bdd722f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1394ba019e7e26b06b6ca81e77adbf76d0a32e957725815806971be63bdd722f","first_computed_at":"2026-05-17T23:51:11.096829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:11.096829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9fQ+Bg3hqOchknfPGKWMBixO8w/ew/kPcGjCwsPEwW5e94DL4f0e7VPebkJ6jT626TzuIaf4fIKZ7Se5TFTQBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:11.097206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:697eb40a66fd98a29d77e7785294e5a602fe8eefd66b080af4edb15fd1500fd0","sha256:1691977a83145b5f20926bb242236c860bdf6098b84a4966c196dd1d41c540a4"],"state_sha256":"d569835a7b272ab13d6617fc9e4ad2b6bbb32f6f510c84fdec9bf1a938b32ba3"}