{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6EKNPDPZACBJLCETQCYDYEI5EV","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":"cadc13ea38ca4698b681b2d16821dc6544dbd4bd7023ac8d1ccc6140d29b447c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T01:01:26Z","title_canon_sha256":"d6d107b23bfbe1c733fae0de27d5f03dbea8478042ff88b6257d37a591a77531"},"schema_version":"1.0","source":{"id":"1701.02817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02817","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02817v1","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02817","created_at":"2026-05-18T00:53:00Z"},{"alias_kind":"pith_short_12","alias_value":"6EKNPDPZACBJ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6EKNPDPZACBJLCET","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6EKNPDPZ","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:14ba809d3d05e7b4aa47e32c01da04e595afc3e5305121d712cd73fdb38f8ebd","target":"graph","created_at":"2026-05-18T00:53:00Z","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 deals with the Keller--Segel system with signal-dependent sensitivity \\begin{equation*} u_t=\\Delta u - \\nabla \\cdot (u \\chi(v)\\nabla v), \\quad v_t=\\Delta v + u - v, \\quad x\\in\\Omega,\\ t>0, \\end{equation*} where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$, $n\\geq 2$; $\\chi$ is a function satisfying $\\chi(s)\\leq K(a+s)^{-k}$ for some $k\\geq 1$ and $a\\geq 0$. In the case that $k=1$, Fujie (J. Math. Anal. Appl.; 2015; 424; 675--684) established global existence of bounded solutions under the condition $K<\\sqrt{\\frac{2}{n}}$. On the other hand, when $k>1$, Winkler (Math. Nachr.; 2010;","authors_text":"Masaaki Mizukami, Tomomi Yokota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T01:01:26Z","title":"A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02817","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":"sha256:5ae3aadc97074c923a2a8e8bb8fc76e1e7b8593131dbc7653c3020a80e713adc","target":"record","created_at":"2026-05-18T00:53:00Z","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":"cadc13ea38ca4698b681b2d16821dc6544dbd4bd7023ac8d1ccc6140d29b447c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T01:01:26Z","title_canon_sha256":"d6d107b23bfbe1c733fae0de27d5f03dbea8478042ff88b6257d37a591a77531"},"schema_version":"1.0","source":{"id":"1701.02817","kind":"arxiv","version":1}},"canonical_sha256":"f114d78df9008295889380b03c111d25492682504ddee8183b79d8bf5edaef95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f114d78df9008295889380b03c111d25492682504ddee8183b79d8bf5edaef95","first_computed_at":"2026-05-18T00:53:00.099554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:00.099554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9Hz9ztiEI6Vgaj9xxl++BWXn0GrEFZWOzN82pRcRT+cxbPNGGiJWcdar4YXj9mR2adAsFWSewzVX708cIFPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:00.100126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ae3aadc97074c923a2a8e8bb8fc76e1e7b8593131dbc7653c3020a80e713adc","sha256:14ba809d3d05e7b4aa47e32c01da04e595afc3e5305121d712cd73fdb38f8ebd"],"state_sha256":"73ca0e8877a2a25d418e0f71ced04712121702a598a2939ed0bc707ef814ff74"}