{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TYZ6YDNYWMLZKDZ5MLM75SBFAV","short_pith_number":"pith:TYZ6YDNY","canonical_record":{"source":{"id":"1407.5085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T19:25:12Z","cross_cats_sorted":[],"title_canon_sha256":"61c5527e0a24189a82fe694589e47e4882beb6bdbf8211f334e2d7fba1011eb3","abstract_canon_sha256":"2a4d365e056d48cfab8daa4c0c16c2490163c0441ba9596c017b3ab76a238a82"},"schema_version":"1.0"},"canonical_sha256":"9e33ec0db8b317950f3d62d9fec8250576330a0ad613028774ab506552f045df","source":{"kind":"arxiv","id":"1407.5085","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5085","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5085v1","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5085","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"TYZ6YDNYWMLZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TYZ6YDNYWMLZKDZ5","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TYZ6YDNY","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TYZ6YDNYWMLZKDZ5MLM75SBFAV","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T19:25:12Z","cross_cats_sorted":[],"title_canon_sha256":"61c5527e0a24189a82fe694589e47e4882beb6bdbf8211f334e2d7fba1011eb3","abstract_canon_sha256":"2a4d365e056d48cfab8daa4c0c16c2490163c0441ba9596c017b3ab76a238a82"},"schema_version":"1.0"},"canonical_sha256":"9e33ec0db8b317950f3d62d9fec8250576330a0ad613028774ab506552f045df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:22.026396Z","signature_b64":"GeneJpGF41Lnc76hsRVzaxYOGYN3yn8/lcuCKPYpZRKNlFeBzM4uxAMWft9E1dKhCBUy3qpuRdQvUFKzzi7nDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e33ec0db8b317950f3d62d9fec8250576330a0ad613028774ab506552f045df","last_reissued_at":"2026-05-18T02:47:22.025781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:22.025781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5085","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":"2026-05-18T02:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bgXTyCRxH3lzsjLIAQUK9hCDUkbHM/sibb44O/ubN/xB1bv1xqoMF6HP8QZ2k7SZ+3t6Fve2wZQBxstyndreDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:59:09.941305Z"},"content_sha256":"2ef64c59b05f74e242de76c779347ff8ae11de304242c9802d34782d89c17065","schema_version":"1.0","event_id":"sha256:2ef64c59b05f74e242de76c779347ff8ae11de304242c9802d34782d89c17065"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TYZ6YDNYWMLZKDZ5MLM75SBFAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit","submitted_at":"2014-07-18T19:25:12Z","abstract_excerpt":"We prove existence of global weak solutions to the chemotaxis system\n  $ u_t=\\Delta u - \\nabla\\cdot (u\\nabla v) +\\kappa u -\\mu u^2 $\n  $ v_t=\\Delta v-v+u $\n  under homogeneous Neumann boundary conditions in a smooth bounded convex domain $\\Omega\\subset R^n$, for arbitrarily small values of $\\mu>0$.\n  Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that $\\kappa$ is not too large. In this case, we also consider their large-time behaviour: We prove decay if $\\kappa\\leq 0$ and the existence of an absorbing set if $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5085","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":"2026-05-18T02:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oNekGs/iwSa2902ZbgR2pGh4qXRXc4XWGoC9XgBWsZ+ovOA5ztiohWxzHd9y5//pT8n08xRSrsV3nzYkRurpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:59:09.941671Z"},"content_sha256":"c6fbe720fec8bd423507f0525ee851d187eeaeb65e8ab7d457b27efcec605993","schema_version":"1.0","event_id":"sha256:c6fbe720fec8bd423507f0525ee851d187eeaeb65e8ab7d457b27efcec605993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYZ6YDNYWMLZKDZ5MLM75SBFAV/bundle.json","state_url":"https://pith.science/pith/TYZ6YDNYWMLZKDZ5MLM75SBFAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYZ6YDNYWMLZKDZ5MLM75SBFAV/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":"2026-06-21T19:59:09Z","links":{"resolver":"https://pith.science/pith/TYZ6YDNYWMLZKDZ5MLM75SBFAV","bundle":"https://pith.science/pith/TYZ6YDNYWMLZKDZ5MLM75SBFAV/bundle.json","state":"https://pith.science/pith/TYZ6YDNYWMLZKDZ5MLM75SBFAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYZ6YDNYWMLZKDZ5MLM75SBFAV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TYZ6YDNYWMLZKDZ5MLM75SBFAV","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":"2a4d365e056d48cfab8daa4c0c16c2490163c0441ba9596c017b3ab76a238a82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T19:25:12Z","title_canon_sha256":"61c5527e0a24189a82fe694589e47e4882beb6bdbf8211f334e2d7fba1011eb3"},"schema_version":"1.0","source":{"id":"1407.5085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5085","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5085v1","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5085","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"TYZ6YDNYWMLZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TYZ6YDNYWMLZKDZ5","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TYZ6YDNY","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:c6fbe720fec8bd423507f0525ee851d187eeaeb65e8ab7d457b27efcec605993","target":"graph","created_at":"2026-05-18T02:47:22Z","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 prove existence of global weak solutions to the chemotaxis system\n  $ u_t=\\Delta u - \\nabla\\cdot (u\\nabla v) +\\kappa u -\\mu u^2 $\n  $ v_t=\\Delta v-v+u $\n  under homogeneous Neumann boundary conditions in a smooth bounded convex domain $\\Omega\\subset R^n$, for arbitrarily small values of $\\mu>0$.\n  Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that $\\kappa$ is not too large. In this case, we also consider their large-time behaviour: We prove decay if $\\kappa\\leq 0$ and the existence of an absorbing set if $\\","authors_text":"Johannes Lankeit","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T19:25:12Z","title":"Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5085","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":"sha256:2ef64c59b05f74e242de76c779347ff8ae11de304242c9802d34782d89c17065","target":"record","created_at":"2026-05-18T02:47:22Z","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":"2a4d365e056d48cfab8daa4c0c16c2490163c0441ba9596c017b3ab76a238a82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T19:25:12Z","title_canon_sha256":"61c5527e0a24189a82fe694589e47e4882beb6bdbf8211f334e2d7fba1011eb3"},"schema_version":"1.0","source":{"id":"1407.5085","kind":"arxiv","version":1}},"canonical_sha256":"9e33ec0db8b317950f3d62d9fec8250576330a0ad613028774ab506552f045df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e33ec0db8b317950f3d62d9fec8250576330a0ad613028774ab506552f045df","first_computed_at":"2026-05-18T02:47:22.025781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:22.025781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GeneJpGF41Lnc76hsRVzaxYOGYN3yn8/lcuCKPYpZRKNlFeBzM4uxAMWft9E1dKhCBUy3qpuRdQvUFKzzi7nDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:22.026396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ef64c59b05f74e242de76c779347ff8ae11de304242c9802d34782d89c17065","sha256:c6fbe720fec8bd423507f0525ee851d187eeaeb65e8ab7d457b27efcec605993"],"state_sha256":"e0ddec4d2fb14a1a7157360cf9e79bffc9873c6be589b24f71ffcae4d71d4525"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DcRDrJEBWUussOJUnbmLjpfgBGhj5GHXFDNe2keJc3X2nUlXJMPZfMz0oCxxRBax4ANRfkmohrewjqaYMrX1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:59:09.943644Z","bundle_sha256":"f3a2755b4b9628d36d5a5675b411d02d2b80922362980562aaceb17ef5bb3808"}}