{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:35IHRQXROBANLWZXS76JWAB6IC","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":"7b07700701049ea4dae424830ec5007416b66515d5c572f8df482113762b3456","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-25T19:42:33Z","title_canon_sha256":"bcad138998aabeb68cdaae7f988583789eb059e378d14eadf908395d4ac54c8b"},"schema_version":"1.0","source":{"id":"1108.5167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5167","created_at":"2026-05-18T04:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5167v2","created_at":"2026-05-18T04:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5167","created_at":"2026-05-18T04:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"35IHRQXROBAN","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"35IHRQXROBANLWZX","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"35IHRQXR","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:ff4849f625e2b1850b4a101b08c45a78ac49a9d23ca1935bad7bd80139294f71","target":"graph","created_at":"2026-05-18T04:14:27Z","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":"Aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with nonlinear diffusion are popular models for nonlocal aggregation phenomenon and are a source of a number of interesting mathematical problems in nonlinear PDE. The purpose of this work is twofold. First, we continue our previous work, which focused on nonlocal aggregation, modeled with a convolution. The goal was to unify the local and global theory of these convolution-type models, including the identification of a sharp critical mass; however, some cases involving unbounded domains were left open. In particular, th","authors_text":"Jacob Bedrossian, Nancy Rodriguez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-25T19:42:33Z","title":"Inhomogeneous Patlak-Keller-Segel models and Aggregation Equations with Nonlinear Diffusion in $\\Real^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5167","kind":"arxiv","version":2},"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":"sha256:5a4a2f01450906b4c151725b45c146ac539cc8f7c724153240aca08ccc497180","target":"record","created_at":"2026-05-18T04:14:27Z","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":"7b07700701049ea4dae424830ec5007416b66515d5c572f8df482113762b3456","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-25T19:42:33Z","title_canon_sha256":"bcad138998aabeb68cdaae7f988583789eb059e378d14eadf908395d4ac54c8b"},"schema_version":"1.0","source":{"id":"1108.5167","kind":"arxiv","version":2}},"canonical_sha256":"df5078c2f17040d5db3797fc9b003e409f38b3f15749fceeb8782d1424bb9b90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df5078c2f17040d5db3797fc9b003e409f38b3f15749fceeb8782d1424bb9b90","first_computed_at":"2026-05-18T04:14:27.230170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:27.230170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XaTwSsL5/RXqUSKe6tKiD7c3xGFjIunhaIkv8GN05i6TEEbwG5P3kAUY1p9jZg9C2p6HIDq/pVF52s0qdJL+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:27.230683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a4a2f01450906b4c151725b45c146ac539cc8f7c724153240aca08ccc497180","sha256:ff4849f625e2b1850b4a101b08c45a78ac49a9d23ca1935bad7bd80139294f71"],"state_sha256":"8409570f796087d5f22e4a9609944aa5d959d1e0bfd6b1d93b2117d052d80b52"}