{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SKTPW4A5QWEMHJNTZUBK66YBFF","short_pith_number":"pith:SKTPW4A5","canonical_record":{"source":{"id":"1808.03544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-10T13:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"72f0cff67acfa0c9b3b4cb93c8877b59c6e7530a290d1b9374c9d022250623e2","abstract_canon_sha256":"eb3ed54522d7de0b63adcba6ee402ee85e30239469507c24d694a637c99f8884"},"schema_version":"1.0"},"canonical_sha256":"92a6fb701d8588c3a5b3cd02af7b01294c83c9247d7dcd5fade2ee4109c055c4","source":{"kind":"arxiv","id":"1808.03544","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03544","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03544v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03544","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"SKTPW4A5QWEM","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SKTPW4A5QWEMHJNT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SKTPW4A5","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SKTPW4A5QWEMHJNTZUBK66YBFF","target":"record","payload":{"canonical_record":{"source":{"id":"1808.03544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-10T13:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"72f0cff67acfa0c9b3b4cb93c8877b59c6e7530a290d1b9374c9d022250623e2","abstract_canon_sha256":"eb3ed54522d7de0b63adcba6ee402ee85e30239469507c24d694a637c99f8884"},"schema_version":"1.0"},"canonical_sha256":"92a6fb701d8588c3a5b3cd02af7b01294c83c9247d7dcd5fade2ee4109c055c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:24.708204Z","signature_b64":"gVO8w6AlZswCt1PRozqIO8YTjEnecZdbcWaw839FYnXqNSnPhXGHcmc8ragK/8t7GziigS2jHgdSTFmIUlo8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92a6fb701d8588c3a5b3cd02af7b01294c83c9247d7dcd5fade2ee4109c055c4","last_reissued_at":"2026-05-18T00:08:24.707626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:24.707626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.03544","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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TzWWYOgRFlFOvVfS19iYNXdpVHEgX3vgEiPMSzq643DNELD1vPrypjfnzLG54kRvYRYhIVbWf/rRIXYYEtPiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:28:22.021603Z"},"content_sha256":"618d7ab7c05e4cd8d7101ba3bff85fad0eaa6b80fa83b54d48a9a20c032f5bd5","schema_version":"1.0","event_id":"sha256:618d7ab7c05e4cd8d7101ba3bff85fad0eaa6b80fa83b54d48a9a20c032f5bd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SKTPW4A5QWEMHJNTZUBK66YBFF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new result for boundedness in the quasilinear parabolic-parabolic Keller-Segel model (with logistic source)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2018-08-10T13:51:01Z","abstract_excerpt":"The current paper considers the boundedness of solutions to the following quasilinear Keller-Segel model (with logistic source) $$\\left\\{\\begin{array}{ll} u_t = \\nabla\\cdot(D(u)\\nabla u)-\\chi\\nabla\\cdot(u\\nabla v)+\\mu (u-u^2),\\quad x\\in \\Omega, t>0,\\\\ v_t-\\Delta v = u-v,\\quad x\\in \\Omega, t>0,\\\\ (D(u)\\nabla u-\\chi u\\cdot \\nabla v)\\cdot \\nu = \\frac{\\partial v}{\\partial\\nu}=0,\\quad x\\in \\partial\\Omega, t>0,\\\\  u(x,0) = u_0(x),\\quad v(x,0) = v_0(x),\\ \\ x\\in \\Omega, \\end{array}\\right.$$ where $\\Omega\\subset\\mathbb{R}^N(N\\geq1)$ is a bounded domain with smooth boundary $\\partial\\Omega,$ $\\chi>0$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03544","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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGMCMOn5U0kXbDXFAnZxe3maP/lr58wqyILGopBgcn6DhEwXzrOnd1Zy3faShXnp2leGCJkosaT3mZHsNpZ+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:28:22.021945Z"},"content_sha256":"8f49ec7196cbefce50a40d9496e38c6ed8d3e8e3eb5e0773978b633dc2f91da5","schema_version":"1.0","event_id":"sha256:8f49ec7196cbefce50a40d9496e38c6ed8d3e8e3eb5e0773978b633dc2f91da5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKTPW4A5QWEMHJNTZUBK66YBFF/bundle.json","state_url":"https://pith.science/pith/SKTPW4A5QWEMHJNTZUBK66YBFF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKTPW4A5QWEMHJNTZUBK66YBFF/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":"2026-06-26T08:28:22Z","links":{"resolver":"https://pith.science/pith/SKTPW4A5QWEMHJNTZUBK66YBFF","bundle":"https://pith.science/pith/SKTPW4A5QWEMHJNTZUBK66YBFF/bundle.json","state":"https://pith.science/pith/SKTPW4A5QWEMHJNTZUBK66YBFF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKTPW4A5QWEMHJNTZUBK66YBFF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SKTPW4A5QWEMHJNTZUBK66YBFF","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":"eb3ed54522d7de0b63adcba6ee402ee85e30239469507c24d694a637c99f8884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-10T13:51:01Z","title_canon_sha256":"72f0cff67acfa0c9b3b4cb93c8877b59c6e7530a290d1b9374c9d022250623e2"},"schema_version":"1.0","source":{"id":"1808.03544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03544","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03544v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03544","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"SKTPW4A5QWEM","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SKTPW4A5QWEMHJNT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SKTPW4A5","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:8f49ec7196cbefce50a40d9496e38c6ed8d3e8e3eb5e0773978b633dc2f91da5","target":"graph","created_at":"2026-05-18T00:08:24Z","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":"The current paper considers the boundedness of solutions to the following quasilinear Keller-Segel model (with logistic source) $$\\left\\{\\begin{array}{ll} u_t = \\nabla\\cdot(D(u)\\nabla u)-\\chi\\nabla\\cdot(u\\nabla v)+\\mu (u-u^2),\\quad x\\in \\Omega, t>0,\\\\ v_t-\\Delta v = u-v,\\quad x\\in \\Omega, t>0,\\\\ (D(u)\\nabla u-\\chi u\\cdot \\nabla v)\\cdot \\nu = \\frac{\\partial v}{\\partial\\nu}=0,\\quad x\\in \\partial\\Omega, t>0,\\\\  u(x,0) = u_0(x),\\quad v(x,0) = v_0(x),\\ \\ x\\in \\Omega, \\end{array}\\right.$$ where $\\Omega\\subset\\mathbb{R}^N(N\\geq1)$ is a bounded domain with smooth boundary $\\partial\\Omega,$ $\\chi>0$ an","authors_text":"Jiashan Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-10T13:51:01Z","title":"A new result for boundedness in the quasilinear parabolic-parabolic Keller-Segel model (with logistic source)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03544","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":"sha256:618d7ab7c05e4cd8d7101ba3bff85fad0eaa6b80fa83b54d48a9a20c032f5bd5","target":"record","created_at":"2026-05-18T00:08:24Z","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":"eb3ed54522d7de0b63adcba6ee402ee85e30239469507c24d694a637c99f8884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-10T13:51:01Z","title_canon_sha256":"72f0cff67acfa0c9b3b4cb93c8877b59c6e7530a290d1b9374c9d022250623e2"},"schema_version":"1.0","source":{"id":"1808.03544","kind":"arxiv","version":1}},"canonical_sha256":"92a6fb701d8588c3a5b3cd02af7b01294c83c9247d7dcd5fade2ee4109c055c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92a6fb701d8588c3a5b3cd02af7b01294c83c9247d7dcd5fade2ee4109c055c4","first_computed_at":"2026-05-18T00:08:24.707626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:24.707626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVO8w6AlZswCt1PRozqIO8YTjEnecZdbcWaw839FYnXqNSnPhXGHcmc8ragK/8t7GziigS2jHgdSTFmIUlo8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:24.708204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:618d7ab7c05e4cd8d7101ba3bff85fad0eaa6b80fa83b54d48a9a20c032f5bd5","sha256:8f49ec7196cbefce50a40d9496e38c6ed8d3e8e3eb5e0773978b633dc2f91da5"],"state_sha256":"d7fac49b39396af12e6ad5c5e3d5cc1ba5cdcf12f447eba808988ed729315261"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5u/Payzb69l5epvI5o//3QyywdEf0HkEsHc9omlicqec/BLr0BmI8jTagfdjtdGowpNUDktp3XzDuURQBOx+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:28:22.023817Z","bundle_sha256":"c5ccb5549abb85534c7033186e6cce9544d19d188a0d8409defa6298b9ba364e"}}