{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ISH7DXFISYWMX5JOI3ND4JUALZ","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":"774a1ea9fcfb1ba8d4ae383c35c977043de366200939988e9dadc79653a89c22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-26T12:35:40Z","title_canon_sha256":"25ffb6b00006c21ba28396ae0afa21923c001b1dd06653530d6e1937b6c89bb3"},"schema_version":"1.0","source":{"id":"1903.10835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10835","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10835v1","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10835","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"pith_short_12","alias_value":"ISH7DXFISYWM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"ISH7DXFISYWMX5JO","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"ISH7DXFI","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:c88775dcc3b44b282adfcf351d88c495146680efaa746e1310cdfb8084aab59d","target":"graph","created_at":"2026-05-17T23:50:17Z","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":"This paper studies the following system of differential equations modeling tumor angiogenesis in a bounded smooth domain $\\Omega \\subset \\mathbb{R}^N$ ($N=1,2$): $$\\label{0}\n  \\left\\{\\begin{array}{ll}\n  p_t=\\Delta p-\\nabla\\cdotp p(\\displaystyle\\frac \\alpha {1+c}\\nabla c+\\rho\\nabla w)+\\lambda p(1-p),\\,& x\\in \\Omega, t>0,\n  c_t=\\Delta c-c-\\mu pc,\\, &x\\in \\Omega, t>0,\\\\ w_t= \\gamma p(1-w),\\,& x\\in \\Omega, t>0,\n  \\end{array}\\right. $$ where $\\alpha, \\rho, \\lambda, \\mu$ and $\\gamma$ are positive parameters. For any reasonably regular initial data $(p_0, c_0, w_0)$, we prove the global boundedness (","authors_text":"Peter Y.H.Pang, Yifu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-26T12:35:40Z","title":"Asymptotic behavior of solutions to a tumor angiogenesis model with chemotaxis--haptotaxis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10835","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":"sha256:8bb08b67638391b12d3e15ff0981ad14f9102238823b2380286b8a079980bba2","target":"record","created_at":"2026-05-17T23:50:17Z","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":"774a1ea9fcfb1ba8d4ae383c35c977043de366200939988e9dadc79653a89c22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-26T12:35:40Z","title_canon_sha256":"25ffb6b00006c21ba28396ae0afa21923c001b1dd06653530d6e1937b6c89bb3"},"schema_version":"1.0","source":{"id":"1903.10835","kind":"arxiv","version":1}},"canonical_sha256":"448ff1dca8962ccbf52e46da3e26805e599e06053d2f111bdd366fb6305eb9c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"448ff1dca8962ccbf52e46da3e26805e599e06053d2f111bdd366fb6305eb9c5","first_computed_at":"2026-05-17T23:50:17.598617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:17.598617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9xrCxgx6y9md3mAf5Q+/ZiFvthaOm33toBUo2CuKqZvA+MM7Sp+jVu5j4aIuE+uyg/BoQ4K+uHcJUBOvBgZ5Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:17.599149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bb08b67638391b12d3e15ff0981ad14f9102238823b2380286b8a079980bba2","sha256:c88775dcc3b44b282adfcf351d88c495146680efaa746e1310cdfb8084aab59d"],"state_sha256":"8d1fc5c5b705443f2fa5ff7131fcae7aa67624368d9d5a8cb01ca0d87e8a4269"}