{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BZBCF4PM25XHNSDSGVWPCEBNFL","short_pith_number":"pith:BZBCF4PM","schema_version":"1.0","canonical_sha256":"0e4222f1ecd76e76c872356cf1102d2ac304498d7679ae4d7a26f77a329ff9f2","source":{"kind":"arxiv","id":"1806.03911","version":1},"attestation_state":"computed","paper":{"title":"Existence and uniqueness of weak solutions to the singular kernels coagulation equation with collisional breakage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ankik Kumar Giri, Prasanta Kumar Barik","submitted_at":"2018-06-11T11:19:51Z","abstract_excerpt":"In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and distribution functions may have a singularity on both the coordinate axes. The proof of the existence result is based on a classical weak L^1 compactness method applied to suitably chosen to approximate equations. The question of uniqueness is also shown for some restricted class of collision kernels."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.03911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-11T11:19:51Z","cross_cats_sorted":[],"title_canon_sha256":"ad4435634458ce336fc5207699df15bfe003da00b9102ae64cc7745c97ba7802","abstract_canon_sha256":"9d73b3001ffffdeda3f57de36c5de6efa7d02ee233f18b83e2aad20635f07fb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:41.549268Z","signature_b64":"jx2dAHuTeJ4yYS2X6mKAhRcGRish1IvigzqLRRKwtPtZ4MauD2PuLdT1/qCKfx52ja+kvjlRLVpdAAQEiLBbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e4222f1ecd76e76c872356cf1102d2ac304498d7679ae4d7a26f77a329ff9f2","last_reissued_at":"2026-05-18T00:13:41.548719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:41.548719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and uniqueness of weak solutions to the singular kernels coagulation equation with collisional breakage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ankik Kumar Giri, Prasanta Kumar Barik","submitted_at":"2018-06-11T11:19:51Z","abstract_excerpt":"In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and distribution functions may have a singularity on both the coordinate axes. The proof of the existence result is based on a classical weak L^1 compactness method applied to suitably chosen to approximate equations. The question of uniqueness is also shown for some restricted class of collision kernels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03911","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.03911","created_at":"2026-05-18T00:13:41.548802+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.03911v1","created_at":"2026-05-18T00:13:41.548802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03911","created_at":"2026-05-18T00:13:41.548802+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZBCF4PM25XH","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZBCF4PM25XHNSDS","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZBCF4PM","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL","json":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL.json","graph_json":"https://pith.science/api/pith-number/BZBCF4PM25XHNSDSGVWPCEBNFL/graph.json","events_json":"https://pith.science/api/pith-number/BZBCF4PM25XHNSDSGVWPCEBNFL/events.json","paper":"https://pith.science/paper/BZBCF4PM"},"agent_actions":{"view_html":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL","download_json":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL.json","view_paper":"https://pith.science/paper/BZBCF4PM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.03911&json=true","fetch_graph":"https://pith.science/api/pith-number/BZBCF4PM25XHNSDSGVWPCEBNFL/graph.json","fetch_events":"https://pith.science/api/pith-number/BZBCF4PM25XHNSDSGVWPCEBNFL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL/action/storage_attestation","attest_author":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL/action/author_attestation","sign_citation":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL/action/citation_signature","submit_replication":"https://pith.science/pith/BZBCF4PM25XHNSDSGVWPCEBNFL/action/replication_record"}},"created_at":"2026-05-18T00:13:41.548802+00:00","updated_at":"2026-05-18T00:13:41.548802+00:00"}