{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DPGQ4IXFCDJ4O2T244XCZWW53K","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":"8a6dce040f87943cfc1b337730f44d5d8e1d2f291b1cd76e280e9ab45bd4d9ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-07-25T04:15:25Z","title_canon_sha256":"01ebe9637afef98d25c2f11fe179fb7a6417e0e25f3c642f06e8370fbe44b9c7"},"schema_version":"1.0","source":{"id":"2307.13245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.13245","created_at":"2026-07-05T07:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"2307.13245v2","created_at":"2026-07-05T07:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.13245","created_at":"2026-07-05T07:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"DPGQ4IXFCDJ4","created_at":"2026-07-05T07:30:03Z"},{"alias_kind":"pith_short_16","alias_value":"DPGQ4IXFCDJ4O2T2","created_at":"2026-07-05T07:30:03Z"},{"alias_kind":"pith_short_8","alias_value":"DPGQ4IXF","created_at":"2026-07-05T07:30:03Z"}],"graph_snapshots":[{"event_id":"sha256:53ad4aa5c7f27407915fd131dd7462aafab3f201de7add471a8bf7b5da348056","target":"graph","created_at":"2026-07-05T07:30:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2307.13245/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article looks at the relationship between the discrete and the continuous Redner-Ben-Avraham-Kahng (RBK) coagulation models. On the basis of a priori estimation, a weak stability principle and the weak compactness in $L_1$ for the continuous RBK model is shown. By employing a sequence of discrete models to approximate the continuous one, we show that how discrete model eventually converges to the the modified continuous one using the stability principle.","authors_text":"Pratibha Verma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-07-25T04:15:25Z","title":"Convergence of the discrete Redner-Ben-Avraham-Kahng coagulation equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.13245","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":"sha256:9312890c44a281214db0d0404fe96d4c459494079adeb7d48fe41e287b1c83a4","target":"record","created_at":"2026-07-05T07:30:03Z","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":"8a6dce040f87943cfc1b337730f44d5d8e1d2f291b1cd76e280e9ab45bd4d9ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-07-25T04:15:25Z","title_canon_sha256":"01ebe9637afef98d25c2f11fe179fb7a6417e0e25f3c642f06e8370fbe44b9c7"},"schema_version":"1.0","source":{"id":"2307.13245","kind":"arxiv","version":2}},"canonical_sha256":"1bcd0e22e510d3c76a7ae72e2cdadddaa57ea231ea7e51da6a89030ff8d723f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bcd0e22e510d3c76a7ae72e2cdadddaa57ea231ea7e51da6a89030ff8d723f5","first_computed_at":"2026-07-05T07:30:03.887477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:30:03.887477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DUTgj5E+OFcvrqdoWb26OidLJ9NdlgeFGrinKj0KWJc83POth5lXrHHhdQcaDTT8JTwYSXtXP+CCAXWVKhMxDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:30:03.887932Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.13245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9312890c44a281214db0d0404fe96d4c459494079adeb7d48fe41e287b1c83a4","sha256:53ad4aa5c7f27407915fd131dd7462aafab3f201de7add471a8bf7b5da348056"],"state_sha256":"ba6db9d80357a12c9080b4d4cda1ee9d0b9cbd2dc6337503827fbb834ddd5871"}