{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EQJRQQV6JIXSXCFPWKA4JJHJFC","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":"3e07413c3d73e3ea600904ce88719642975a240f04e1a966a6b8c09b145d2899","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-15T04:09:22Z","title_canon_sha256":"7789603292b28cf2c5601aeed19a2d83c20992314c5bcbc426e32c24adfcd3e9"},"schema_version":"1.0","source":{"id":"1811.06161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06161","created_at":"2026-05-18T00:00:38Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06161v1","created_at":"2026-05-18T00:00:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06161","created_at":"2026-05-18T00:00:38Z"},{"alias_kind":"pith_short_12","alias_value":"EQJRQQV6JIXS","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQJRQQV6JIXSXCFP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQJRQQV6","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:bb3e126723053ce96d05ce9031f14793d8b16a7ad7f6a25125c8fc2809df05f6","target":"graph","created_at":"2026-05-18T00:00:38Z","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 paper we study the continuous coagulation and multiple fragmentation equation for the mean-field description of a system of particles taking into account the combined effect of the coagulation and the fragmentation processes in which a system of particles growing by successive mergers to form a bigger one and a larger particle splits into a finite number of smaller pieces. We demonstrate the global existence of mass-conserving weak solutions for a wide class of coagulation rate, selection rate and breakage function. Here, both the breakage function and the coagulation rate may have alg","authors_text":"Prasanta Kumar Barik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-15T04:09:22Z","title":"Existence of mass-conserving weak solutions to the singular coagulation equation with multiple fragmentation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06161","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:db0645ad0efc723d08938ebe31291106aec23c2a76374c4e512120dea341b3fe","target":"record","created_at":"2026-05-18T00:00:38Z","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":"3e07413c3d73e3ea600904ce88719642975a240f04e1a966a6b8c09b145d2899","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-15T04:09:22Z","title_canon_sha256":"7789603292b28cf2c5601aeed19a2d83c20992314c5bcbc426e32c24adfcd3e9"},"schema_version":"1.0","source":{"id":"1811.06161","kind":"arxiv","version":1}},"canonical_sha256":"24131842be4a2f2b88afb281c4a4e9289cb04f4a1e937179406310d5882d5242","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24131842be4a2f2b88afb281c4a4e9289cb04f4a1e937179406310d5882d5242","first_computed_at":"2026-05-18T00:00:38.480914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:38.480914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"58PHLPxS0IakXCuugpY2cF7AHsbh9sVyQ2R3fYHnE+CFa4rSrc9RzdpL/ZFofLdzZ9GTS1CCOb6FZTERzahgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:38.481488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.06161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db0645ad0efc723d08938ebe31291106aec23c2a76374c4e512120dea341b3fe","sha256:bb3e126723053ce96d05ce9031f14793d8b16a7ad7f6a25125c8fc2809df05f6"],"state_sha256":"9d49253cdeb893032bbf7b4dc04a4c8873a9f14f4f24cb8592c132bf06d285e2"}