{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P5TRHZII5ESJQHEZTFFGRKNAYC","short_pith_number":"pith:P5TRHZII","canonical_record":{"source":{"id":"1809.00046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-31T20:15:43Z","cross_cats_sorted":["math.CA","math.FA","math.NA"],"title_canon_sha256":"1053e3b9298f60eaf73c22bd849449ef0a7770103ce333cb4d74280c1b452e82","abstract_canon_sha256":"3c4a709bd8d6c681e33c26340b4c1089926232c49633f6087d0ce09b157e8c64"},"schema_version":"1.0"},"canonical_sha256":"7f6713e508e924981c99994a68a9a0c0811e247d3bf025a02bc81f816ab078f6","source":{"kind":"arxiv","id":"1809.00046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00046","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00046v1","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00046","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"pith_short_12","alias_value":"P5TRHZII5ESJ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P5TRHZII5ESJQHEZ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P5TRHZII","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P5TRHZII5ESJQHEZTFFGRKNAYC","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-31T20:15:43Z","cross_cats_sorted":["math.CA","math.FA","math.NA"],"title_canon_sha256":"1053e3b9298f60eaf73c22bd849449ef0a7770103ce333cb4d74280c1b452e82","abstract_canon_sha256":"3c4a709bd8d6c681e33c26340b4c1089926232c49633f6087d0ce09b157e8c64"},"schema_version":"1.0"},"canonical_sha256":"7f6713e508e924981c99994a68a9a0c0811e247d3bf025a02bc81f816ab078f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:36.325444Z","signature_b64":"N4+HG1L0+07yT+UgmtPi/tD3zYGEWIy+gmsJ2abeHAeITQK26B9IMb2DkxsynGwa47juzxgVvpwIToTTkX5aDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f6713e508e924981c99994a68a9a0c0811e247d3bf025a02bc81f816ab078f6","last_reissued_at":"2026-05-18T00:06:36.324963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:36.324963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00046","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":"2026-05-18T00:06:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KnALY8dWouP1uPZR1If9tLGfLcMh2t681fWwidOmCPeKilIRvBPzpUZXtNR5NoWkodZT727Ri4VCv0We69UAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:34:59.834348Z"},"content_sha256":"1a9e6db474b17d4d10f91f91055dd4be86e52df07568e34634fff90744d913c0","schema_version":"1.0","event_id":"sha256:1a9e6db474b17d4d10f91f91055dd4be86e52df07568e34634fff90744d913c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P5TRHZII5ESJQHEZTFFGRKNAYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Discrete Unbounded Coagulation-Fragmentation Equation with Growth, Decay and Sedimentation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.NA"],"primary_cat":"math.DS","authors_text":"Jacek Banasiak, Luke O. Joel, Sergey Shindin","submitted_at":"2018-08-31T20:15:43Z","abstract_excerpt":"In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong. This paper extends several previous results both by considering a more general model and and also signnificantly weakening the assumptions. Theoretical conclusions are supported by numerical simulations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00046","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":"2026-05-18T00:06:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QuT59KLsfq1gkDvWFJ0sFdIPAAngvw7pw+Jf8OdNlbC3mJq1yMF5u94oLWaW+jGESXNOvHzyqZUOpl/HfrgTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:34:59.835044Z"},"content_sha256":"1cff8fbb87d4b9ff60f7bcc2a169eb37ddff061bd0f72db2681b1f3e3e1992b2","schema_version":"1.0","event_id":"sha256:1cff8fbb87d4b9ff60f7bcc2a169eb37ddff061bd0f72db2681b1f3e3e1992b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5TRHZII5ESJQHEZTFFGRKNAYC/bundle.json","state_url":"https://pith.science/pith/P5TRHZII5ESJQHEZTFFGRKNAYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5TRHZII5ESJQHEZTFFGRKNAYC/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":"2026-05-22T17:34:59Z","links":{"resolver":"https://pith.science/pith/P5TRHZII5ESJQHEZTFFGRKNAYC","bundle":"https://pith.science/pith/P5TRHZII5ESJQHEZTFFGRKNAYC/bundle.json","state":"https://pith.science/pith/P5TRHZII5ESJQHEZTFFGRKNAYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5TRHZII5ESJQHEZTFFGRKNAYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P5TRHZII5ESJQHEZTFFGRKNAYC","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":"3c4a709bd8d6c681e33c26340b4c1089926232c49633f6087d0ce09b157e8c64","cross_cats_sorted":["math.CA","math.FA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-31T20:15:43Z","title_canon_sha256":"1053e3b9298f60eaf73c22bd849449ef0a7770103ce333cb4d74280c1b452e82"},"schema_version":"1.0","source":{"id":"1809.00046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00046","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00046v1","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00046","created_at":"2026-05-18T00:06:36Z"},{"alias_kind":"pith_short_12","alias_value":"P5TRHZII5ESJ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P5TRHZII5ESJQHEZ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P5TRHZII","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:1cff8fbb87d4b9ff60f7bcc2a169eb37ddff061bd0f72db2681b1f3e3e1992b2","target":"graph","created_at":"2026-05-18T00:06:36Z","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 discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong. This paper extends several previous results both by considering a more general model and and also signnificantly weakening the assumptions. Theoretical conclusions are supported by numerical simulations.","authors_text":"Jacek Banasiak, Luke O. Joel, Sergey Shindin","cross_cats":["math.CA","math.FA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-31T20:15:43Z","title":"The Discrete Unbounded Coagulation-Fragmentation Equation with Growth, Decay and Sedimentation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00046","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":"sha256:1a9e6db474b17d4d10f91f91055dd4be86e52df07568e34634fff90744d913c0","target":"record","created_at":"2026-05-18T00:06:36Z","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":"3c4a709bd8d6c681e33c26340b4c1089926232c49633f6087d0ce09b157e8c64","cross_cats_sorted":["math.CA","math.FA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-31T20:15:43Z","title_canon_sha256":"1053e3b9298f60eaf73c22bd849449ef0a7770103ce333cb4d74280c1b452e82"},"schema_version":"1.0","source":{"id":"1809.00046","kind":"arxiv","version":1}},"canonical_sha256":"7f6713e508e924981c99994a68a9a0c0811e247d3bf025a02bc81f816ab078f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f6713e508e924981c99994a68a9a0c0811e247d3bf025a02bc81f816ab078f6","first_computed_at":"2026-05-18T00:06:36.324963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:36.324963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N4+HG1L0+07yT+UgmtPi/tD3zYGEWIy+gmsJ2abeHAeITQK26B9IMb2DkxsynGwa47juzxgVvpwIToTTkX5aDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:36.325444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a9e6db474b17d4d10f91f91055dd4be86e52df07568e34634fff90744d913c0","sha256:1cff8fbb87d4b9ff60f7bcc2a169eb37ddff061bd0f72db2681b1f3e3e1992b2"],"state_sha256":"033f72cf49381add894fbc759879852a073578a4bb13d5d58a68f13964058432"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zd6oTjnNpn73ZMoAYt0R3EFTL5pOkJoH/EEyNhAszxkspcH8V5p47clwH54kZh7jawrtOOu1vW7jDH18D/b4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T17:34:59.838556Z","bundle_sha256":"08009ce277e469e51429ccbac37ceb54edff18acffb1a8188e868c4cc71fb994"}}