{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XK6WNAC2OIBTRQLMRNZPTT7VOE","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":"a43d596a2f070fe48c47c2eebbdeb3f48b9afc6e0942d1f07df46c6a2cc2b2ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-19T17:53:04Z","title_canon_sha256":"2091b77c03db97415249807560c588f0f470601e5c6306c2da691e0e8506c89c"},"schema_version":"1.0","source":{"id":"1412.6458","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6458","created_at":"2026-05-18T02:30:48Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6458v1","created_at":"2026-05-18T02:30:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6458","created_at":"2026-05-18T02:30:48Z"},{"alias_kind":"pith_short_12","alias_value":"XK6WNAC2OIBT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XK6WNAC2OIBTRQLM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XK6WNAC2","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:0c4f6570c79dd8d92b58a069790e5464e2cad1f76570671936fc6d2807dd3f9d","target":"graph","created_at":"2026-05-18T02:30:48Z","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":"For the discrete Cucker-Smale's flocking model with a singular communication weight $\\psi(s) = s^{-\\alpha}$, with $0<\\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result enables us to obtain existence and uniqeness of global solutions.","authors_text":"Jan Peszek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-19T17:53:04Z","title":"Discrete Cucker-Smale's flocking model with a weakly singular weight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6458","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:ed9edd2c28e8bcf85ddc4d5f88f362a97171b614d8a008096c6f6a5c6b00b5fc","target":"record","created_at":"2026-05-18T02:30:48Z","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":"a43d596a2f070fe48c47c2eebbdeb3f48b9afc6e0942d1f07df46c6a2cc2b2ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-19T17:53:04Z","title_canon_sha256":"2091b77c03db97415249807560c588f0f470601e5c6306c2da691e0e8506c89c"},"schema_version":"1.0","source":{"id":"1412.6458","kind":"arxiv","version":1}},"canonical_sha256":"babd66805a720338c16c8b72f9cff5711cf04bce27e07b730aac38933beeb868","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"babd66805a720338c16c8b72f9cff5711cf04bce27e07b730aac38933beeb868","first_computed_at":"2026-05-18T02:30:48.327684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:48.327684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bABJbTOYoCAumU43k5WMSWV93Z3uN2kcqXTk25Zuu/eFbAKMnqHze9qQUTTIfnuz29q6wyUHxOnLMwbCW1baBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:48.328112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6458","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed9edd2c28e8bcf85ddc4d5f88f362a97171b614d8a008096c6f6a5c6b00b5fc","sha256:0c4f6570c79dd8d92b58a069790e5464e2cad1f76570671936fc6d2807dd3f9d"],"state_sha256":"8faa5ebfdc0e2164333eeaeda4b001d7f34f08f5647c213eadcccdf45acdbb51"}