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We show that\n  *) solutions are global and bounded if ${\\sigma}<m-\\frac{N-2}N$\n  *) solutions are global if $\\sigma \\le 0$\n  *) close to given radially symmetric functions there are many initial data producing unbounded solutions if $\\sigma >m-\\frac{N-2}N$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.09157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-25T10:32:03Z","cross_cats_sorted":[],"title_canon_sha256":"015075c428404c472a6e95d461a0a559d8f0bbe9e7fb2c1b58a3d82e3e35e4d8","abstract_canon_sha256":"dabe800cf44dbcf5695d767d2d5b34d06fbf8964004d0255521c240382fe24e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:00.217754Z","signature_b64":"a2GVpuhG0he7N1gMDwozSS3J0tPUJMUw1e8W9DHkTbjgU+FqDhulowLWi1l4wrHAZPGUqtiYV9fdxxhQoKW7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab8e06693d6b09dc29259bb339b83e5f1a4615370b1c486514458928d6eac505","last_reissued_at":"2026-05-18T00:32:00.217279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:00.217279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit","submitted_at":"2017-10-25T10:32:03Z","abstract_excerpt":"We consider a parabolic-elliptic chemotaxis system generalizing\n  \\[ \\begin{cases}\\begin{split} & u_t=\\nabla\\cdot((u+1)^{m-1}\\nabla u)-\\nabla \\cdot(u(u+1)^{\\sigma-1}\\nabla v)\\\\ & 0 = \\Delta v - v + u\n  \\end{split}\\end{cases} \\] in bounded smooth domains $\\Omega\\subset \\mathbb{R}^N$, $N\\ge 3$, and with homogeneous Neumann boundary conditions. We show that\n  *) solutions are global and bounded if ${\\sigma}<m-\\frac{N-2}N$\n  *) solutions are global if $\\sigma \\le 0$\n  *) close to given radially symmetric functions there are many initial data producing unbounded solutions if $\\sigma >m-\\frac{N-2}N$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09157","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.09157","created_at":"2026-05-18T00:32:00.217356+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09157v1","created_at":"2026-05-18T00:32:00.217356+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09157","created_at":"2026-05-18T00:32:00.217356+00:00"},{"alias_kind":"pith_short_12","alias_value":"VOHAM2J5NME5","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VOHAM2J5NME5YKJF","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VOHAM2J5","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4","json":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4.json","graph_json":"https://pith.science/api/pith-number/VOHAM2J5NME5YKJFTOZTTOB6L4/graph.json","events_json":"https://pith.science/api/pith-number/VOHAM2J5NME5YKJFTOZTTOB6L4/events.json","paper":"https://pith.science/paper/VOHAM2J5"},"agent_actions":{"view_html":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4","download_json":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4.json","view_paper":"https://pith.science/paper/VOHAM2J5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09157&json=true","fetch_graph":"https://pith.science/api/pith-number/VOHAM2J5NME5YKJFTOZTTOB6L4/graph.json","fetch_events":"https://pith.science/api/pith-number/VOHAM2J5NME5YKJFTOZTTOB6L4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4/action/storage_attestation","attest_author":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4/action/author_attestation","sign_citation":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4/action/citation_signature","submit_replication":"https://pith.science/pith/VOHAM2J5NME5YKJFTOZTTOB6L4/action/replication_record"}},"created_at":"2026-05-18T00:32:00.217356+00:00","updated_at":"2026-05-18T00:32:00.217356+00:00"}