{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2Z7X2OTAQBCHI67QWVYMDSBTXJ","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":"2e66684cb16a88ca131d1c199d6f057044862bf7e1ec7b6b68efae3ece389dd8","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-04T15:57:50Z","title_canon_sha256":"f6731f34fbdfb3945d677a7bc7d653e2d6759b7f057d6ff823f595d2b48b134f"},"schema_version":"1.0","source":{"id":"1210.1571","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1571","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1571v3","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1571","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"2Z7X2OTAQBCH","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2Z7X2OTAQBCHI67Q","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2Z7X2OTA","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:f30f8cfebb8f6226020e8fa14abb7c082853066636eff598480edc1441298252","target":"graph","created_at":"2026-05-18T03:08:38Z","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 article we prove the existence of solutions to the singular coagulation equation with multifragmentation. We use weighted $L^1$-spaces to deal with the singularities and to obtain regular solutions. The Smoluchowski kernel is covered by our proof. The weak $L^1$ compactness methods are applied to suitably chosen approximating equations as a base of our proof. A more restrictive uniqueness result is also given.","authors_text":"Carlos Cueto Camejo, Gerald Warnecke","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-04T15:57:50Z","title":"The singular kernel coagulation equation with multifragmentation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1571","kind":"arxiv","version":3},"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:bb9c5b313a44566b9419cc012f994a72dcdf216864d9007f2b5a8d4b24b47da2","target":"record","created_at":"2026-05-18T03:08:38Z","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":"2e66684cb16a88ca131d1c199d6f057044862bf7e1ec7b6b68efae3ece389dd8","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-04T15:57:50Z","title_canon_sha256":"f6731f34fbdfb3945d677a7bc7d653e2d6759b7f057d6ff823f595d2b48b134f"},"schema_version":"1.0","source":{"id":"1210.1571","kind":"arxiv","version":3}},"canonical_sha256":"d67f7d3a608044747bf0b570c1c833ba57cdf070cdbdf9df964c7297b4b5e345","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d67f7d3a608044747bf0b570c1c833ba57cdf070cdbdf9df964c7297b4b5e345","first_computed_at":"2026-05-18T03:08:38.337743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:38.337743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RfXfmXlr4luh+IwiwaX4LJynAh9d1PqRNMzvNmfTlVbpVobH7UYrP+/1E4E3E+QshEh15e6GrFdLT8JahILQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:38.338440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1571","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb9c5b313a44566b9419cc012f994a72dcdf216864d9007f2b5a8d4b24b47da2","sha256:f30f8cfebb8f6226020e8fa14abb7c082853066636eff598480edc1441298252"],"state_sha256":"4406184ea7a63881ecdfee5f6ababd2f1cc2b6163133fdcef4bf998865af3e5b"}