{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PGEL3UVRH5A3NJZ63BNVOHOD7E","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":"c93b1fd9a44b4a5678d93237c073dc8d7025051390d63e3be39514a5327d3fc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T14:59:57Z","title_canon_sha256":"3a16cd7ec002aeef0856e4801e7a44062bd931bbb6a5ef3d423a1327780fcf05"},"schema_version":"1.0","source":{"id":"1603.06445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06445","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06445v1","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06445","created_at":"2026-05-18T01:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"PGEL3UVRH5A3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PGEL3UVRH5A3NJZ6","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PGEL3UVR","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:9ec905a84f3955818276428b673195a5497ab3ba2965f1bb6af8e3a6bb715b46","target":"graph","created_at":"2026-05-18T01:18:48Z","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 study the existence of steady states to the Keller-Segel system with linear chemotactical sensitivity function on a smooth bounded domain in $\\mathbb R^N,$ $N\\ge3,$ having rotational symmetry. We find three different types of chemoattractant concentration which concentrate along suitable $(N-2)-$dimensional minimal submanifolds of the boundary. The corresponding density of the cellular slime molds exhibit in the limit one or more Dirac measures supported on those boundary submanifolds.","authors_text":"Angela Pistoia, Oscar Agudelo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T14:59:57Z","title":"Boundary concentration phenomena for the higher-dimensional Keller-Segel system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06445","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":"sha256:390080eaf6204ecbd0c8c59c46c28cfc889efff0e94483846c157183a744652b","target":"record","created_at":"2026-05-18T01:18:48Z","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":"c93b1fd9a44b4a5678d93237c073dc8d7025051390d63e3be39514a5327d3fc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-21T14:59:57Z","title_canon_sha256":"3a16cd7ec002aeef0856e4801e7a44062bd931bbb6a5ef3d423a1327780fcf05"},"schema_version":"1.0","source":{"id":"1603.06445","kind":"arxiv","version":1}},"canonical_sha256":"7988bdd2b13f41b6a73ed85b571dc3f9011b1bdc302c9715a46372c8292a08ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7988bdd2b13f41b6a73ed85b571dc3f9011b1bdc302c9715a46372c8292a08ba","first_computed_at":"2026-05-18T01:18:48.508938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:48.508938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+oJbQzk3bagNebS94+ZakInkfVLsF2R5arAhZP0wKnjQD5nibZpOIkVq7cBVKXCP3YGx6zM6sWhF+afdX52ZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:48.509626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:390080eaf6204ecbd0c8c59c46c28cfc889efff0e94483846c157183a744652b","sha256:9ec905a84f3955818276428b673195a5497ab3ba2965f1bb6af8e3a6bb715b46"],"state_sha256":"39b64e341acf7e4ca0d7c56c115191e34b0141559e39a6de0e98f3e4dca5c52e"}