{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YDG7M34DBM6VPVFNGIQH62C33C","short_pith_number":"pith:YDG7M34D","canonical_record":{"source":{"id":"1410.1346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-06T12:30:47Z","cross_cats_sorted":[],"title_canon_sha256":"924ce172a5d93dbe2e6c43a3e1099ce86951e1997b2a22e9b29b239cd1fa553f","abstract_canon_sha256":"1f29d8f67715f694e229ae45832f63ff633054312248bac5b3107312ee2add55"},"schema_version":"1.0"},"canonical_sha256":"c0cdf66f830b3d57d4ad32207f685bd8ba684e07bfffd40927b6482f31008205","source":{"kind":"arxiv","id":"1410.1346","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1346","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1346v2","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1346","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"YDG7M34DBM6V","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YDG7M34DBM6VPVFN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YDG7M34D","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YDG7M34DBM6VPVFNGIQH62C33C","target":"record","payload":{"canonical_record":{"source":{"id":"1410.1346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-06T12:30:47Z","cross_cats_sorted":[],"title_canon_sha256":"924ce172a5d93dbe2e6c43a3e1099ce86951e1997b2a22e9b29b239cd1fa553f","abstract_canon_sha256":"1f29d8f67715f694e229ae45832f63ff633054312248bac5b3107312ee2add55"},"schema_version":"1.0"},"canonical_sha256":"c0cdf66f830b3d57d4ad32207f685bd8ba684e07bfffd40927b6482f31008205","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:37.802593Z","signature_b64":"35A3nElxPhI2OpcjxXJSICQiqOAGcXZL1sLLMd0RlqBn1urhWqIjE1iM2A2tE8ynZd2p3GzXRiPn3f1NCP7bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0cdf66f830b3d57d4ad32207f685bd8ba684e07bfffd40927b6482f31008205","last_reissued_at":"2026-05-18T01:17:37.802107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:37.802107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.1346","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NQTTtj89ZwC7ZvPsHu4xH6XXgV1pYT0d88gg9jou+s5rKibW5nBKpwvtKZvEozjb3Egy+iBJ1oDUvvJixIHRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:31:22.293519Z"},"content_sha256":"b32f2abad18e52f4b3a1cb998621707b32ec76d887ed8cb930ee45e655a6fa34","schema_version":"1.0","event_id":"sha256:b32f2abad18e52f4b3a1cb998621707b32ec76d887ed8cb930ee45e655a6fa34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YDG7M34DBM6VPVFNGIQH62C33C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chemotactic systems in the presence of conflicts: a new functional inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gershon Wolansky","submitted_at":"2014-10-06T12:30:47Z","abstract_excerpt":"The evolution of a chemotactic system involving a population of cells attracted to self-produced chemicals is described by the Keller-Segel system. In spacial dimension 2, this system demonstrates a balance between the spreading effect of diffusion and the concentration due to self-attraction. As a result, there exists a critical \"mass\" (i.e. total cell's population) above which the solution of this system collapses in a finite time, while below this critical mass there is global existence in time. The existence of this critical mass is related to a functional inequality known as the Moser-Tru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1346","kind":"arxiv","version":2},"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":"2026-05-18T01:17:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5rtYdLtxna5ao1s4+dnnZ/ZsUcOKANJknprXj+kRsqhPobs5VvlH/OaOF9n1B0qgRSSAVOSLd/BGhH19zwaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:31:22.293854Z"},"content_sha256":"6313e1ebcc93b0d56603ba141c3dad57bfa31a9edd97765a7fc1d7553cca3691","schema_version":"1.0","event_id":"sha256:6313e1ebcc93b0d56603ba141c3dad57bfa31a9edd97765a7fc1d7553cca3691"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDG7M34DBM6VPVFNGIQH62C33C/bundle.json","state_url":"https://pith.science/pith/YDG7M34DBM6VPVFNGIQH62C33C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDG7M34DBM6VPVFNGIQH62C33C/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":"2026-06-25T18:31:22Z","links":{"resolver":"https://pith.science/pith/YDG7M34DBM6VPVFNGIQH62C33C","bundle":"https://pith.science/pith/YDG7M34DBM6VPVFNGIQH62C33C/bundle.json","state":"https://pith.science/pith/YDG7M34DBM6VPVFNGIQH62C33C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDG7M34DBM6VPVFNGIQH62C33C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YDG7M34DBM6VPVFNGIQH62C33C","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":"1f29d8f67715f694e229ae45832f63ff633054312248bac5b3107312ee2add55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-06T12:30:47Z","title_canon_sha256":"924ce172a5d93dbe2e6c43a3e1099ce86951e1997b2a22e9b29b239cd1fa553f"},"schema_version":"1.0","source":{"id":"1410.1346","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1346","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1346v2","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1346","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"YDG7M34DBM6V","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YDG7M34DBM6VPVFN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YDG7M34D","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:6313e1ebcc93b0d56603ba141c3dad57bfa31a9edd97765a7fc1d7553cca3691","target":"graph","created_at":"2026-05-18T01:17:37Z","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":"The evolution of a chemotactic system involving a population of cells attracted to self-produced chemicals is described by the Keller-Segel system. In spacial dimension 2, this system demonstrates a balance between the spreading effect of diffusion and the concentration due to self-attraction. As a result, there exists a critical \"mass\" (i.e. total cell's population) above which the solution of this system collapses in a finite time, while below this critical mass there is global existence in time. The existence of this critical mass is related to a functional inequality known as the Moser-Tru","authors_text":"Gershon Wolansky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-06T12:30:47Z","title":"Chemotactic systems in the presence of conflicts: a new functional inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1346","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:b32f2abad18e52f4b3a1cb998621707b32ec76d887ed8cb930ee45e655a6fa34","target":"record","created_at":"2026-05-18T01:17:37Z","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":"1f29d8f67715f694e229ae45832f63ff633054312248bac5b3107312ee2add55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-06T12:30:47Z","title_canon_sha256":"924ce172a5d93dbe2e6c43a3e1099ce86951e1997b2a22e9b29b239cd1fa553f"},"schema_version":"1.0","source":{"id":"1410.1346","kind":"arxiv","version":2}},"canonical_sha256":"c0cdf66f830b3d57d4ad32207f685bd8ba684e07bfffd40927b6482f31008205","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0cdf66f830b3d57d4ad32207f685bd8ba684e07bfffd40927b6482f31008205","first_computed_at":"2026-05-18T01:17:37.802107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:37.802107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"35A3nElxPhI2OpcjxXJSICQiqOAGcXZL1sLLMd0RlqBn1urhWqIjE1iM2A2tE8ynZd2p3GzXRiPn3f1NCP7bDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:37.802593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1346","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b32f2abad18e52f4b3a1cb998621707b32ec76d887ed8cb930ee45e655a6fa34","sha256:6313e1ebcc93b0d56603ba141c3dad57bfa31a9edd97765a7fc1d7553cca3691"],"state_sha256":"b6afe3b2acb00ffac65070e8c24c0daff2c40d04a9bb6ea89af4b3b8e39e8107"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01Nl1DyoUDXh8r68aXk9uYEeXuM0a+2DGLNnleX+rcrhuzloyJeJEffytOvP7F2cd9Y5BOjU3oZuao0kcuL1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:31:22.295797Z","bundle_sha256":"a09a88906d2747aec2abb1a72e527d68ca7132a0f52744a73feebdb13301f786"}}