{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CRLKFRTL2MZ4KAYORGR26VW4NR","short_pith_number":"pith:CRLKFRTL","canonical_record":{"source":{"id":"1105.4429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-23T08:13:43Z","cross_cats_sorted":[],"title_canon_sha256":"b52dcb61248dbea6053fc27fb6ab1a6bed5324d770b8b14bed8db266747bc0e0","abstract_canon_sha256":"a141aaf939853cac35772ad157c9beb2a9dc820da8e014f0f7bb1bd6efe59d14"},"schema_version":"1.0"},"canonical_sha256":"1456a2c66bd333c5030e89a3af56dc6c79ab5a909c20e5c7abf51762131eb0d4","source":{"kind":"arxiv","id":"1105.4429","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4429","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4429v1","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4429","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"pith_short_12","alias_value":"CRLKFRTL2MZ4","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CRLKFRTL2MZ4KAYO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CRLKFRTL","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CRLKFRTL2MZ4KAYORGR26VW4NR","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-23T08:13:43Z","cross_cats_sorted":[],"title_canon_sha256":"b52dcb61248dbea6053fc27fb6ab1a6bed5324d770b8b14bed8db266747bc0e0","abstract_canon_sha256":"a141aaf939853cac35772ad157c9beb2a9dc820da8e014f0f7bb1bd6efe59d14"},"schema_version":"1.0"},"canonical_sha256":"1456a2c66bd333c5030e89a3af56dc6c79ab5a909c20e5c7abf51762131eb0d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:29.280732Z","signature_b64":"lmHcr6ZuO4EBg//cA3qMBdieo5ubynswXRCqrzi8iBp3iO4L49HP5qR0mQ1gCrQmVRuVMJL7Z7qhTX/YtaT7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1456a2c66bd333c5030e89a3af56dc6c79ab5a909c20e5c7abf51762131eb0d4","last_reissued_at":"2026-05-18T04:21:29.280370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:29.280370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4429","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":"2026-05-18T04:21:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EsWEtXPJHW5EcVJc5YgBHjYT/w7PzwNHr7FQnTeR3avF82trIyhRFiRnBCAFRhAb7hhf+AWJH4nusUA7Y6ckAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:45:57.608225Z"},"content_sha256":"8fd2dd20bb8991f98cf6d32ce6d023618a20326783a2a14afa8d2cd9c86d2a01","schema_version":"1.0","event_id":"sha256:8fd2dd20bb8991f98cf6d32ce6d023618a20326783a2a14afa8d2cd9c86d2a01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CRLKFRTL2MZ4KAYORGR26VW4NR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of a non local model for spontaneous cell polarisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nicolas Meunier (MAP5), Raphael Voituriez (LPTMC), Rhoda Hawkins, Vincent Calvez (UMPA-ENSL)","submitted_at":"2011-05-23T08:13:43Z","abstract_excerpt":"In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We characterize the following behaviours in the one-dimensional case: solutions are global if the mass is below the critical mass and they blow-up in finite time above the critical mass. The higher-dimensional case is also discussed. The results are reminiscent of the classical Keller-Segel system in double the dimension. In addition, in the one-dimensional case we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4429","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":"2026-05-18T04:21:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BD6j/XGjX6pu7O5Fn+q8iCaleRR0rQFZYIjr81quBCrx9hXG39vnVmInWv0Rhznim6AwNR6QZErqI5VLmkSnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:45:57.608581Z"},"content_sha256":"9a053470905350df3567c2e2facd241ec54bbd7eb77179360f96952e2810820f","schema_version":"1.0","event_id":"sha256:9a053470905350df3567c2e2facd241ec54bbd7eb77179360f96952e2810820f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRLKFRTL2MZ4KAYORGR26VW4NR/bundle.json","state_url":"https://pith.science/pith/CRLKFRTL2MZ4KAYORGR26VW4NR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRLKFRTL2MZ4KAYORGR26VW4NR/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":"2026-06-24T02:45:57Z","links":{"resolver":"https://pith.science/pith/CRLKFRTL2MZ4KAYORGR26VW4NR","bundle":"https://pith.science/pith/CRLKFRTL2MZ4KAYORGR26VW4NR/bundle.json","state":"https://pith.science/pith/CRLKFRTL2MZ4KAYORGR26VW4NR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRLKFRTL2MZ4KAYORGR26VW4NR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CRLKFRTL2MZ4KAYORGR26VW4NR","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":"a141aaf939853cac35772ad157c9beb2a9dc820da8e014f0f7bb1bd6efe59d14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-23T08:13:43Z","title_canon_sha256":"b52dcb61248dbea6053fc27fb6ab1a6bed5324d770b8b14bed8db266747bc0e0"},"schema_version":"1.0","source":{"id":"1105.4429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4429","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4429v1","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4429","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"pith_short_12","alias_value":"CRLKFRTL2MZ4","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CRLKFRTL2MZ4KAYO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CRLKFRTL","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:9a053470905350df3567c2e2facd241ec54bbd7eb77179360f96952e2810820f","target":"graph","created_at":"2026-05-18T04:21:29Z","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":"In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We characterize the following behaviours in the one-dimensional case: solutions are global if the mass is below the critical mass and they blow-up in finite time above the critical mass. The higher-dimensional case is also discussed. The results are reminiscent of the classical Keller-Segel system in double the dimension. In addition, in the one-dimensional case we p","authors_text":"Nicolas Meunier (MAP5), Raphael Voituriez (LPTMC), Rhoda Hawkins, Vincent Calvez (UMPA-ENSL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-23T08:13:43Z","title":"Analysis of a non local model for spontaneous cell polarisation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4429","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":"sha256:8fd2dd20bb8991f98cf6d32ce6d023618a20326783a2a14afa8d2cd9c86d2a01","target":"record","created_at":"2026-05-18T04:21:29Z","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":"a141aaf939853cac35772ad157c9beb2a9dc820da8e014f0f7bb1bd6efe59d14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-23T08:13:43Z","title_canon_sha256":"b52dcb61248dbea6053fc27fb6ab1a6bed5324d770b8b14bed8db266747bc0e0"},"schema_version":"1.0","source":{"id":"1105.4429","kind":"arxiv","version":1}},"canonical_sha256":"1456a2c66bd333c5030e89a3af56dc6c79ab5a909c20e5c7abf51762131eb0d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1456a2c66bd333c5030e89a3af56dc6c79ab5a909c20e5c7abf51762131eb0d4","first_computed_at":"2026-05-18T04:21:29.280370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:29.280370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lmHcr6ZuO4EBg//cA3qMBdieo5ubynswXRCqrzi8iBp3iO4L49HP5qR0mQ1gCrQmVRuVMJL7Z7qhTX/YtaT7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:29.280732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fd2dd20bb8991f98cf6d32ce6d023618a20326783a2a14afa8d2cd9c86d2a01","sha256:9a053470905350df3567c2e2facd241ec54bbd7eb77179360f96952e2810820f"],"state_sha256":"ce6600d185f5faac7b0dc84e4bb6875512f8301e68b159c0792a9d20acd37642"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZv2ZSS4J2pXJ3fUneiyx+2DSnJ5n18t/mEBSEkPTNpycNGayDZcqyhTLXR96w0ilqM3Jwc/PkrFzEGLYgdrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:45:57.610486Z","bundle_sha256":"bd76d241ec1df03338b9296bcd256267dd3b8ea88cd0da33d5f0a61230dc077b"}}