{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WJSBBRVHAQVNR5O5BOQL4PGPKK","short_pith_number":"pith:WJSBBRVH","canonical_record":{"source":{"id":"1812.02040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-05T15:21:16Z","cross_cats_sorted":[],"title_canon_sha256":"f6bffaa822169cfc03a670fc35498e25b713afa1eb6da0acb7ac7fa312a0d930","abstract_canon_sha256":"0a9782e2023054b04e733baca8e847f1f9dabd0145d4087a8d24bf0e7c63b27b"},"schema_version":"1.0"},"canonical_sha256":"b26410c6a7042ad8f5dd0ba0be3ccf52b57f012b0c44a239e90fdb9945c09ac6","source":{"kind":"arxiv","id":"1812.02040","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02040","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02040v1","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02040","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"WJSBBRVHAQVN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WJSBBRVHAQVNR5O5","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WJSBBRVH","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WJSBBRVHAQVNR5O5BOQL4PGPKK","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-05T15:21:16Z","cross_cats_sorted":[],"title_canon_sha256":"f6bffaa822169cfc03a670fc35498e25b713afa1eb6da0acb7ac7fa312a0d930","abstract_canon_sha256":"0a9782e2023054b04e733baca8e847f1f9dabd0145d4087a8d24bf0e7c63b27b"},"schema_version":"1.0"},"canonical_sha256":"b26410c6a7042ad8f5dd0ba0be3ccf52b57f012b0c44a239e90fdb9945c09ac6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:59.890097Z","signature_b64":"yxM4CBk76a5PfXFkihpmt9ND0gItgR8Ygwv18DLa3EM1Q61RADFt4I6np/WmFgYeAUAMN0K46VzCwW2bFXHFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b26410c6a7042ad8f5dd0ba0be3ccf52b57f012b0c44a239e90fdb9945c09ac6","last_reissued_at":"2026-05-17T23:58:59.889504Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:59.889504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02040","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":"2026-05-17T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0+7OFpH+/E9jojO5i7zaf2nZh9rMK7wGiDMd8Dk7k0e2/kqwRUV5/MeLVwlv6HsIxETlpxK0ylkvDOLv/H8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:02:29.278929Z"},"content_sha256":"62cf824d0202cce09b36e98768d73e1dd903f73f2e738cf202193d2c1fd59472","schema_version":"1.0","event_id":"sha256:62cf824d0202cce09b36e98768d73e1dd903f73f2e738cf202193d2c1fd59472"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WJSBBRVHAQVNR5O5BOQL4PGPKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite-time blow-up prevention in a two-dimensional chemotaxis-consumption model with weakly singular sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Viglialoro","submitted_at":"2018-12-05T15:21:16Z","abstract_excerpt":"In this paper we study a two-dimensional chemotaxis-consumption system with singular sensitivity and endowed with Neumann boundary conditions. Sufficient conditions on the data of the problem are given so that the globability of classical solutions is shown, thus excluding any finite-time blow-up scenario."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02040","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":"2026-05-17T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v9g/B4ouvHh0hR7rjAX9H/u8jbH9Pdjit+JBlb5/ZBn4vKEKInQYGVWRPbq1W6Rd0XweN7yiq3sFkGyMzMjdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:02:29.279272Z"},"content_sha256":"dbcb9b494fa66c6e42c2290c81d71bfbf0a7b2895b0e89d60735b2c205fa2230","schema_version":"1.0","event_id":"sha256:dbcb9b494fa66c6e42c2290c81d71bfbf0a7b2895b0e89d60735b2c205fa2230"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJSBBRVHAQVNR5O5BOQL4PGPKK/bundle.json","state_url":"https://pith.science/pith/WJSBBRVHAQVNR5O5BOQL4PGPKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJSBBRVHAQVNR5O5BOQL4PGPKK/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":"2026-05-28T13:02:29Z","links":{"resolver":"https://pith.science/pith/WJSBBRVHAQVNR5O5BOQL4PGPKK","bundle":"https://pith.science/pith/WJSBBRVHAQVNR5O5BOQL4PGPKK/bundle.json","state":"https://pith.science/pith/WJSBBRVHAQVNR5O5BOQL4PGPKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJSBBRVHAQVNR5O5BOQL4PGPKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WJSBBRVHAQVNR5O5BOQL4PGPKK","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":"0a9782e2023054b04e733baca8e847f1f9dabd0145d4087a8d24bf0e7c63b27b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-05T15:21:16Z","title_canon_sha256":"f6bffaa822169cfc03a670fc35498e25b713afa1eb6da0acb7ac7fa312a0d930"},"schema_version":"1.0","source":{"id":"1812.02040","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02040","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02040v1","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02040","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"WJSBBRVHAQVN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WJSBBRVHAQVNR5O5","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WJSBBRVH","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:dbcb9b494fa66c6e42c2290c81d71bfbf0a7b2895b0e89d60735b2c205fa2230","target":"graph","created_at":"2026-05-17T23:58:59Z","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 paper we study a two-dimensional chemotaxis-consumption system with singular sensitivity and endowed with Neumann boundary conditions. Sufficient conditions on the data of the problem are given so that the globability of classical solutions is shown, thus excluding any finite-time blow-up scenario.","authors_text":"Giuseppe Viglialoro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-05T15:21:16Z","title":"Finite-time blow-up prevention in a two-dimensional chemotaxis-consumption model with weakly singular sensitivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02040","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":"sha256:62cf824d0202cce09b36e98768d73e1dd903f73f2e738cf202193d2c1fd59472","target":"record","created_at":"2026-05-17T23:58:59Z","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":"0a9782e2023054b04e733baca8e847f1f9dabd0145d4087a8d24bf0e7c63b27b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-05T15:21:16Z","title_canon_sha256":"f6bffaa822169cfc03a670fc35498e25b713afa1eb6da0acb7ac7fa312a0d930"},"schema_version":"1.0","source":{"id":"1812.02040","kind":"arxiv","version":1}},"canonical_sha256":"b26410c6a7042ad8f5dd0ba0be3ccf52b57f012b0c44a239e90fdb9945c09ac6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b26410c6a7042ad8f5dd0ba0be3ccf52b57f012b0c44a239e90fdb9945c09ac6","first_computed_at":"2026-05-17T23:58:59.889504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:59.889504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxM4CBk76a5PfXFkihpmt9ND0gItgR8Ygwv18DLa3EM1Q61RADFt4I6np/WmFgYeAUAMN0K46VzCwW2bFXHFCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:59.890097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02040","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62cf824d0202cce09b36e98768d73e1dd903f73f2e738cf202193d2c1fd59472","sha256:dbcb9b494fa66c6e42c2290c81d71bfbf0a7b2895b0e89d60735b2c205fa2230"],"state_sha256":"2228ff73b0187f5a27a6176061d7099765194035092ce8990c0d5db847c52981"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i5LL0eD192wJvF2AO/RqliRqpyd45uXKTBapgHN/RzCqQNzpTz0qQADJDk6qB2lE5EfCZ/Lp085PammK+GrfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:02:29.281205Z","bundle_sha256":"22c7aadff4771c1068983649002b56fc162eeb0b288dd368d69b3551143a5cc0"}}