{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VXWOLZLX3RWUDXIWSSD3RY2BOZ","short_pith_number":"pith:VXWOLZLX","canonical_record":{"source":{"id":"1808.09294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-26T16:52:38Z","cross_cats_sorted":[],"title_canon_sha256":"36ac92247611bc98bc47039cc2c394d50925093b0339e09d95522e6a3eaca72c","abstract_canon_sha256":"2e282b0b1cc608082bef9fb8d111e1b9e273cff739345741b43c4c8b89f470e1"},"schema_version":"1.0"},"canonical_sha256":"adece5e577dc6d41dd169487b8e3417669c6fa4bc6e7451f20f31c3d972f2be0","source":{"kind":"arxiv","id":"1808.09294","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09294","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09294v1","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09294","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"pith_short_12","alias_value":"VXWOLZLX3RWU","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXWOLZLX3RWUDXIW","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXWOLZLX","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VXWOLZLX3RWUDXIWSSD3RY2BOZ","target":"record","payload":{"canonical_record":{"source":{"id":"1808.09294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-26T16:52:38Z","cross_cats_sorted":[],"title_canon_sha256":"36ac92247611bc98bc47039cc2c394d50925093b0339e09d95522e6a3eaca72c","abstract_canon_sha256":"2e282b0b1cc608082bef9fb8d111e1b9e273cff739345741b43c4c8b89f470e1"},"schema_version":"1.0"},"canonical_sha256":"adece5e577dc6d41dd169487b8e3417669c6fa4bc6e7451f20f31c3d972f2be0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:01.792255Z","signature_b64":"UpVWm3EYU6l9j645Di2zoINbOrw7t2NNBy3GxF0noszGt4P/sO78nRdxvwhhVSlhpfRnSI2TAIqlx2ApCBAkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adece5e577dc6d41dd169487b8e3417669c6fa4bc6e7451f20f31c3d972f2be0","last_reissued_at":"2026-05-18T00:07:01.791627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:01.791627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.09294","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9jih6taKVJGfmgHpWnD1opX5yPozdQAmpnLbSkDFMQMfauRoHgvxUjFihi1fFPwvG+SMldhqdebuaz3neviGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:33:33.014236Z"},"content_sha256":"4e010cc36c7b6d7fd9aa19355122dfe0b03744bd2f78ae5bd24ad189d7f1fcbf","schema_version":"1.0","event_id":"sha256:4e010cc36c7b6d7fd9aa19355122dfe0b03744bd2f78ae5bd24ad189d7f1fcbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VXWOLZLX3RWUDXIWSSD3RY2BOZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A regularity criterion for a 3D chemo-repulsion system and its application to a bilinear optimal control problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Exequiel Mallea-Zepeda, Francisco Guill\\'en-Gonz\\'alez, Mar\\'ia \\'Angeles Rodr\\'iguez-Bellido","submitted_at":"2018-08-26T16:52:38Z","abstract_excerpt":"In this paper we study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions and we establish a regularity criterion to get global in time strong solutions. As a consequence, we deduce the existence of a global optimal solution with bilinear control and, using a Lagrange multipliers theorem, we derive first-order optimality conditions for local optimal solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09294","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IY+7DWJBhrda8VHpyfjRTVfgkb626RCHstYzCPgpsllxITAkOP8XlDnbUSEHAdrLqSyYlrlPOrp4RgzDcmXrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:33:33.014974Z"},"content_sha256":"19335604a714bd6fd2e6b7f71f2b6ca9529deefe5f6b1d1802e026c5c47f2e42","schema_version":"1.0","event_id":"sha256:19335604a714bd6fd2e6b7f71f2b6ca9529deefe5f6b1d1802e026c5c47f2e42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXWOLZLX3RWUDXIWSSD3RY2BOZ/bundle.json","state_url":"https://pith.science/pith/VXWOLZLX3RWUDXIWSSD3RY2BOZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXWOLZLX3RWUDXIWSSD3RY2BOZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T01:33:33Z","links":{"resolver":"https://pith.science/pith/VXWOLZLX3RWUDXIWSSD3RY2BOZ","bundle":"https://pith.science/pith/VXWOLZLX3RWUDXIWSSD3RY2BOZ/bundle.json","state":"https://pith.science/pith/VXWOLZLX3RWUDXIWSSD3RY2BOZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXWOLZLX3RWUDXIWSSD3RY2BOZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VXWOLZLX3RWUDXIWSSD3RY2BOZ","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":"2e282b0b1cc608082bef9fb8d111e1b9e273cff739345741b43c4c8b89f470e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-26T16:52:38Z","title_canon_sha256":"36ac92247611bc98bc47039cc2c394d50925093b0339e09d95522e6a3eaca72c"},"schema_version":"1.0","source":{"id":"1808.09294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09294","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09294v1","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09294","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"pith_short_12","alias_value":"VXWOLZLX3RWU","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXWOLZLX3RWUDXIW","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXWOLZLX","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:19335604a714bd6fd2e6b7f71f2b6ca9529deefe5f6b1d1802e026c5c47f2e42","target":"graph","created_at":"2026-05-18T00:07:01Z","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":"In this paper we study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions and we establish a regularity criterion to get global in time strong solutions. As a consequence, we deduce the existence of a global optimal solution with bilinear control and, using a Lagrange multipliers theorem, we derive first-order optimality conditions for local optimal solutions.","authors_text":"Exequiel Mallea-Zepeda, Francisco Guill\\'en-Gonz\\'alez, Mar\\'ia \\'Angeles Rodr\\'iguez-Bellido","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-26T16:52:38Z","title":"A regularity criterion for a 3D chemo-repulsion system and its application to a bilinear optimal control problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09294","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":"sha256:4e010cc36c7b6d7fd9aa19355122dfe0b03744bd2f78ae5bd24ad189d7f1fcbf","target":"record","created_at":"2026-05-18T00:07:01Z","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":"2e282b0b1cc608082bef9fb8d111e1b9e273cff739345741b43c4c8b89f470e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-26T16:52:38Z","title_canon_sha256":"36ac92247611bc98bc47039cc2c394d50925093b0339e09d95522e6a3eaca72c"},"schema_version":"1.0","source":{"id":"1808.09294","kind":"arxiv","version":1}},"canonical_sha256":"adece5e577dc6d41dd169487b8e3417669c6fa4bc6e7451f20f31c3d972f2be0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adece5e577dc6d41dd169487b8e3417669c6fa4bc6e7451f20f31c3d972f2be0","first_computed_at":"2026-05-18T00:07:01.791627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:01.791627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UpVWm3EYU6l9j645Di2zoINbOrw7t2NNBy3GxF0noszGt4P/sO78nRdxvwhhVSlhpfRnSI2TAIqlx2ApCBAkAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:01.792255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e010cc36c7b6d7fd9aa19355122dfe0b03744bd2f78ae5bd24ad189d7f1fcbf","sha256:19335604a714bd6fd2e6b7f71f2b6ca9529deefe5f6b1d1802e026c5c47f2e42"],"state_sha256":"4a7463664f04b53beaa8620cb8f90a763a0fdea254fb79bf64104755995dc7b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTqtyg7C9Dk76ev0HhWO5YtQlb/LkXoOMCsp37yuu8KNf8QpA7MRRIBSF/7Z0K+A1fnjU81j2301eZD+egn8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T01:33:33.019822Z","bundle_sha256":"347abd492f942deacc824a485383fa4ae732ba2ddfd233b45dd56aa980ad66e5"}}