{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YA4JLBLULTHZ2HEBWQBZC4CRDC","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":"4de5a9f28c201455a8d05e20e9c67a1b5ab8f9593adae1974bbb55c3c2697e0d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-19T16:31:34Z","title_canon_sha256":"5d072cb375bf49da3420db79f875576d8ea063473e0f94f883c54afb8b8b6280"},"schema_version":"1.0","source":{"id":"1811.07783","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07783","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07783v3","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07783","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_12","alias_value":"YA4JLBLULTHZ","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_16","alias_value":"YA4JLBLULTHZ2HEB","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_8","alias_value":"YA4JLBLU","created_at":"2026-07-05T03:21:03Z"}],"graph_snapshots":[{"event_id":"sha256:79bede0bb4f068d3bd1d60beced6aa21d5766f0b4c2802cd6e136f4ca1149b6b","target":"graph","created_at":"2026-07-05T03:21:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1811.07783/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable coupled to a reaction diffusion equation for the nutrient and a Brinkman type equation for the velocity. The system is equipped with homogeneous Neumann boundary conditions for the tumor variable and the chemical potential, Robin boundary conditions for the nutrient and a \"no-friction\" boundary condition for the velocity. The control acts as a medication by cytotoxic drugs and enters the phase field equati","authors_text":"Matthias Ebenbeck, Patrik Knopf","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-19T16:31:34Z","title":"Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07783","kind":"arxiv","version":3},"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:dbf17eddc2666074a43c5c82c27b05633c6af9f94066cd45ef873767094729f5","target":"record","created_at":"2026-07-05T03:21:03Z","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":"4de5a9f28c201455a8d05e20e9c67a1b5ab8f9593adae1974bbb55c3c2697e0d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-19T16:31:34Z","title_canon_sha256":"5d072cb375bf49da3420db79f875576d8ea063473e0f94f883c54afb8b8b6280"},"schema_version":"1.0","source":{"id":"1811.07783","kind":"arxiv","version":3}},"canonical_sha256":"c0389585745ccf9d1c81b40391705118ba043305f7b2eb1e6d7b7bb2174c3dec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0389585745ccf9d1c81b40391705118ba043305f7b2eb1e6d7b7bb2174c3dec","first_computed_at":"2026-07-05T03:21:03.727016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:21:03.727016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7SWdBznYi4roKAIGeWH7aJKOb2+YtE8yAA08aeGq0GMEaI4MCHYezvq7w/hLDuXZPhQJmNnTbizB2uYfS49CDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:21:03.727651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07783","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbf17eddc2666074a43c5c82c27b05633c6af9f94066cd45ef873767094729f5","sha256:79bede0bb4f068d3bd1d60beced6aa21d5766f0b4c2802cd6e136f4ca1149b6b"],"state_sha256":"ad9cd519431f3ac488e17ac38474d803bbd282324a53d511de57b17716fb3a9d"}