{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YJ25KM35SRJYFP6L3NDIR4S5YJ","short_pith_number":"pith:YJ25KM35","canonical_record":{"source":{"id":"1407.1596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T06:52:30Z","cross_cats_sorted":[],"title_canon_sha256":"9786f8ddc6fc3f78f85dd19a30603562b7003853ed20351d1b76b3e4dfc0acf7","abstract_canon_sha256":"1282379bb97376078bee32cfd2559bc12dcbe190ab67784cc7a6e85df2ea12f9"},"schema_version":"1.0"},"canonical_sha256":"c275d5337d945382bfcbdb4688f25dc26523e4fd9cecfa3ca0db7b3a5e08a8bc","source":{"kind":"arxiv","id":"1407.1596","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1596","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1596v1","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1596","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"YJ25KM35SRJY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YJ25KM35SRJYFP6L","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YJ25KM35","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YJ25KM35SRJYFP6L3NDIR4S5YJ","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T06:52:30Z","cross_cats_sorted":[],"title_canon_sha256":"9786f8ddc6fc3f78f85dd19a30603562b7003853ed20351d1b76b3e4dfc0acf7","abstract_canon_sha256":"1282379bb97376078bee32cfd2559bc12dcbe190ab67784cc7a6e85df2ea12f9"},"schema_version":"1.0"},"canonical_sha256":"c275d5337d945382bfcbdb4688f25dc26523e4fd9cecfa3ca0db7b3a5e08a8bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:10.965446Z","signature_b64":"RJTI2+1YkzFI3dUgE8pB5Vu+91cK1DDcsJ1hfWrBnTb9ycLP8XPegpX+D56UDQ1B3fFqbXKZ342OoOuyXSrGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c275d5337d945382bfcbdb4688f25dc26523e4fd9cecfa3ca0db7b3a5e08a8bc","last_reissued_at":"2026-05-18T02:48:10.964778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:10.964778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1596","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":"2026-05-18T02:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1WQXpZEMvid1Sb7UZQ7ymuHPUUJr8KKNyptcxny7iSciw0H/ZlYrEHSMtYagDfqZVnIIgE7rAjvi2GC+uslCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:32:32.292595Z"},"content_sha256":"23723dbd11d63007643d338d2fb48b03f34a9bd3b3a530e7bdc21c5e23732d5e","schema_version":"1.0","event_id":"sha256:23723dbd11d63007643d338d2fb48b03f34a9bd3b3a530e7bdc21c5e23732d5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YJ25KM35SRJYFP6L3NDIR4S5YJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absence of gelation and self-similar behavior for a coagulation-fragmentation equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Henry Van Roessel, Philippe Laurencot (IMT)","submitted_at":"2014-07-07T06:52:30Z","abstract_excerpt":"The dynamics of a coagulation-fragmentation equation with multiplicative coagulation kernel and critical singular fragmentation is studied. In contrast to the coagulation equation, it is proved that fragmentation prevents the occurrence of the gelation phenomenon and a mass-conserving solution is constructed. The large time behavior of this solution is shown to be described by a self-similar solution. In addition, the second moment is finite for positive times whatever its initial value. The proof relies on the Laplace transform which maps the original equation to a first-order nonlinear hyper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1596","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":"2026-05-18T02:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"76c05po6m5X/W83WbG8g/75MnNgtovHTQXuWV6JH9ZG0sfJ/831MwMicgcsd1vu3Q54RiMm1CqosoZ15AlsoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:32:32.292941Z"},"content_sha256":"f0a5b629ca27afe8d41f564d6cdbbaec1d9f7a7c334b89c00280072fab2d6a18","schema_version":"1.0","event_id":"sha256:f0a5b629ca27afe8d41f564d6cdbbaec1d9f7a7c334b89c00280072fab2d6a18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJ25KM35SRJYFP6L3NDIR4S5YJ/bundle.json","state_url":"https://pith.science/pith/YJ25KM35SRJYFP6L3NDIR4S5YJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJ25KM35SRJYFP6L3NDIR4S5YJ/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":"2026-06-01T16:32:32Z","links":{"resolver":"https://pith.science/pith/YJ25KM35SRJYFP6L3NDIR4S5YJ","bundle":"https://pith.science/pith/YJ25KM35SRJYFP6L3NDIR4S5YJ/bundle.json","state":"https://pith.science/pith/YJ25KM35SRJYFP6L3NDIR4S5YJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJ25KM35SRJYFP6L3NDIR4S5YJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YJ25KM35SRJYFP6L3NDIR4S5YJ","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":"1282379bb97376078bee32cfd2559bc12dcbe190ab67784cc7a6e85df2ea12f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T06:52:30Z","title_canon_sha256":"9786f8ddc6fc3f78f85dd19a30603562b7003853ed20351d1b76b3e4dfc0acf7"},"schema_version":"1.0","source":{"id":"1407.1596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1596","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1596v1","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1596","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"YJ25KM35SRJY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YJ25KM35SRJYFP6L","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YJ25KM35","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:f0a5b629ca27afe8d41f564d6cdbbaec1d9f7a7c334b89c00280072fab2d6a18","target":"graph","created_at":"2026-05-18T02:48:10Z","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":"The dynamics of a coagulation-fragmentation equation with multiplicative coagulation kernel and critical singular fragmentation is studied. In contrast to the coagulation equation, it is proved that fragmentation prevents the occurrence of the gelation phenomenon and a mass-conserving solution is constructed. The large time behavior of this solution is shown to be described by a self-similar solution. In addition, the second moment is finite for positive times whatever its initial value. The proof relies on the Laplace transform which maps the original equation to a first-order nonlinear hyper","authors_text":"Henry Van Roessel, Philippe Laurencot (IMT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T06:52:30Z","title":"Absence of gelation and self-similar behavior for a coagulation-fragmentation equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1596","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":"sha256:23723dbd11d63007643d338d2fb48b03f34a9bd3b3a530e7bdc21c5e23732d5e","target":"record","created_at":"2026-05-18T02:48:10Z","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":"1282379bb97376078bee32cfd2559bc12dcbe190ab67784cc7a6e85df2ea12f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T06:52:30Z","title_canon_sha256":"9786f8ddc6fc3f78f85dd19a30603562b7003853ed20351d1b76b3e4dfc0acf7"},"schema_version":"1.0","source":{"id":"1407.1596","kind":"arxiv","version":1}},"canonical_sha256":"c275d5337d945382bfcbdb4688f25dc26523e4fd9cecfa3ca0db7b3a5e08a8bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c275d5337d945382bfcbdb4688f25dc26523e4fd9cecfa3ca0db7b3a5e08a8bc","first_computed_at":"2026-05-18T02:48:10.964778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:10.964778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RJTI2+1YkzFI3dUgE8pB5Vu+91cK1DDcsJ1hfWrBnTb9ycLP8XPegpX+D56UDQ1B3fFqbXKZ342OoOuyXSrGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:10.965446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23723dbd11d63007643d338d2fb48b03f34a9bd3b3a530e7bdc21c5e23732d5e","sha256:f0a5b629ca27afe8d41f564d6cdbbaec1d9f7a7c334b89c00280072fab2d6a18"],"state_sha256":"0981db110dece24d4da1a99e17179c8e899b43472fc9b0e9874bf213cd79a3f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52/1yceea32iHRgPvJLrLkpW4wnkaXfdRqn0gU5iIWum5FLMywa5hHg8sHxrxaD25eKOVgXlgKV8nhAg913UBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:32:32.294865Z","bundle_sha256":"0939c84d6ff1e3bf5351c6983f824167e7a46821bf16bc0990f5957b7b11877d"}}