{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LYY3HZWUPZE6OF2YY5V4O7RAJS","short_pith_number":"pith:LYY3HZWU","canonical_record":{"source":{"id":"1209.2517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-12T08:13:43Z","cross_cats_sorted":[],"title_canon_sha256":"eef2bc063bda767603e932325060cf998db644c6ab5dd227f0b8a23851129668","abstract_canon_sha256":"1302ca2b8ac7d838b60b32ef29d7575ca38bf123e4494b4fb3a54b0bf152fa56"},"schema_version":"1.0"},"canonical_sha256":"5e31b3e6d47e49e71758c76bc77e204c932380d11182dee918268bf981ebbe87","source":{"kind":"arxiv","id":"1209.2517","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2517","created_at":"2026-05-18T03:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2517v1","created_at":"2026-05-18T03:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2517","created_at":"2026-05-18T03:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"LYY3HZWUPZE6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LYY3HZWUPZE6OF2Y","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LYY3HZWU","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LYY3HZWUPZE6OF2YY5V4O7RAJS","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-12T08:13:43Z","cross_cats_sorted":[],"title_canon_sha256":"eef2bc063bda767603e932325060cf998db644c6ab5dd227f0b8a23851129668","abstract_canon_sha256":"1302ca2b8ac7d838b60b32ef29d7575ca38bf123e4494b4fb3a54b0bf152fa56"},"schema_version":"1.0"},"canonical_sha256":"5e31b3e6d47e49e71758c76bc77e204c932380d11182dee918268bf981ebbe87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:42.900761Z","signature_b64":"2ovgY4f19CQmBF3yq1S9EEaClKXN67yd6Ib9fKIi38acftgDmYFiz4Vz4KUgjzasz6HySpbv4KrF6c1q5iv6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e31b3e6d47e49e71758c76bc77e204c932380d11182dee918268bf981ebbe87","last_reissued_at":"2026-05-18T03:45:42.899923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:42.899923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2517","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":"2026-05-18T03:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5a+y7u9SEM6auccVNnru64dDCW9+qxtiJDsrrSiZG/P7gBkuGpwOGYs++2j1oKysZXYRBBDpjZ9Hz630K0W9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:45:25.163327Z"},"content_sha256":"ced2e0e06c17a27e194d477556c887400567b70f471f5aee3d534967e0bdcb6f","schema_version":"1.0","event_id":"sha256:ced2e0e06c17a27e194d477556c887400567b70f471f5aee3d534967e0bdcb6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LYY3HZWUPZE6OF2YY5V4O7RAJS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the stability of critical chemotactic aggregation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pierre Raphael, Remi Schweyer","submitted_at":"2012-09-12T08:13:43Z","abstract_excerpt":"We consider the two dimensional parabolic-elliptic Patlak-Keller-Segel model of chemotactic aggregation for radially symmetric initial data. We show the existence of a stable mechanism of singularity formation and obtain a complete description of the associated aggregation process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2517","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":"2026-05-18T03:45:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Usw5pTMty9GOh7WSNepM9m1TOt4rc2lBhh0nA+j08zxHEd6okHin65vNpuIl/lCTHXnoHl6uDuqAe7M7bty6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:45:25.163665Z"},"content_sha256":"6a0277cb092bd59ed0714a92fdced360643684e4ce261978c53646bf8fae4c8e","schema_version":"1.0","event_id":"sha256:6a0277cb092bd59ed0714a92fdced360643684e4ce261978c53646bf8fae4c8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYY3HZWUPZE6OF2YY5V4O7RAJS/bundle.json","state_url":"https://pith.science/pith/LYY3HZWUPZE6OF2YY5V4O7RAJS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYY3HZWUPZE6OF2YY5V4O7RAJS/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":"2026-06-26T23:45:25Z","links":{"resolver":"https://pith.science/pith/LYY3HZWUPZE6OF2YY5V4O7RAJS","bundle":"https://pith.science/pith/LYY3HZWUPZE6OF2YY5V4O7RAJS/bundle.json","state":"https://pith.science/pith/LYY3HZWUPZE6OF2YY5V4O7RAJS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYY3HZWUPZE6OF2YY5V4O7RAJS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LYY3HZWUPZE6OF2YY5V4O7RAJS","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":"1302ca2b8ac7d838b60b32ef29d7575ca38bf123e4494b4fb3a54b0bf152fa56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-12T08:13:43Z","title_canon_sha256":"eef2bc063bda767603e932325060cf998db644c6ab5dd227f0b8a23851129668"},"schema_version":"1.0","source":{"id":"1209.2517","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2517","created_at":"2026-05-18T03:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2517v1","created_at":"2026-05-18T03:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2517","created_at":"2026-05-18T03:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"LYY3HZWUPZE6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LYY3HZWUPZE6OF2Y","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LYY3HZWU","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:6a0277cb092bd59ed0714a92fdced360643684e4ce261978c53646bf8fae4c8e","target":"graph","created_at":"2026-05-18T03:45:42Z","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 consider the two dimensional parabolic-elliptic Patlak-Keller-Segel model of chemotactic aggregation for radially symmetric initial data. We show the existence of a stable mechanism of singularity formation and obtain a complete description of the associated aggregation process.","authors_text":"Pierre Raphael, Remi Schweyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-12T08:13:43Z","title":"On the stability of critical chemotactic aggregation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2517","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:ced2e0e06c17a27e194d477556c887400567b70f471f5aee3d534967e0bdcb6f","target":"record","created_at":"2026-05-18T03:45:42Z","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":"1302ca2b8ac7d838b60b32ef29d7575ca38bf123e4494b4fb3a54b0bf152fa56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-12T08:13:43Z","title_canon_sha256":"eef2bc063bda767603e932325060cf998db644c6ab5dd227f0b8a23851129668"},"schema_version":"1.0","source":{"id":"1209.2517","kind":"arxiv","version":1}},"canonical_sha256":"5e31b3e6d47e49e71758c76bc77e204c932380d11182dee918268bf981ebbe87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e31b3e6d47e49e71758c76bc77e204c932380d11182dee918268bf981ebbe87","first_computed_at":"2026-05-18T03:45:42.899923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:42.899923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ovgY4f19CQmBF3yq1S9EEaClKXN67yd6Ib9fKIi38acftgDmYFiz4Vz4KUgjzasz6HySpbv4KrF6c1q5iv6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:42.900761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2517","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ced2e0e06c17a27e194d477556c887400567b70f471f5aee3d534967e0bdcb6f","sha256:6a0277cb092bd59ed0714a92fdced360643684e4ce261978c53646bf8fae4c8e"],"state_sha256":"7acd36eb7fd530e134b84c4521f357635b83d8db92aa57b913696f9afb96f238"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dLVTtJBISvF1SaI1SC9ioGBfhwQhC1lrdfafX0x5qBhKWoPFgKgoGbj0vzDAgljCF1/hjbXF/ATUTH7LVVdBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:45:25.165494Z","bundle_sha256":"c81b6f5d236635fd539d29bfbee05e94610ac966d644eef7f25417498e4e32f3"}}