{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:S44DJORJURQICSJBF3Q5CREH3Y","short_pith_number":"pith:S44DJORJ","schema_version":"1.0","canonical_sha256":"973834ba29a4608149212ee1d14487de2dd4de1692923034a2b12919a2d9b8ac","source":{"kind":"arxiv","id":"0912.1797","version":2},"attestation_state":"computed","paper":{"title":"On a Model for Mass Aggregation with Maximal Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andrej Spielmann, Barbara Niethammer, Michael Herrmann, Ondrej Bud\\'a\\v{c}","submitted_at":"2009-12-09T16:49:00Z","abstract_excerpt":"We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study the existence of self-similar solutions, and analyze the large-time behavior mostly by numerical simulations. Depending on the parameter $\\Dconst$, which controls the probability of coagulation, we observe two different scenarios: For $\\Dconst>2$ there exist two self-similar solutions to the mean field equation, of which one is unstable. In numerical simula"},"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":"0912.1797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-12-09T16:49:00Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"089430b93785a1d1a0b84b30507a15a0231759c9e264b8075f268823ce6ba048","abstract_canon_sha256":"ba2c635946590dee850be842c987e48c45ead400848dbb338678aed0b07ebb18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:22.129979Z","signature_b64":"89tsMvmXqzryqIJHcRT8CMmtGoIr5wsCXgsqqz6KUDyC0p0XA6kE2z3ZlFxS2A2BGxqcfSwFTBa/j57SebkCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"973834ba29a4608149212ee1d14487de2dd4de1692923034a2b12919a2d9b8ac","last_reissued_at":"2026-05-18T03:55:22.129235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:22.129235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Model for Mass Aggregation with Maximal Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andrej Spielmann, Barbara Niethammer, Michael Herrmann, Ondrej Bud\\'a\\v{c}","submitted_at":"2009-12-09T16:49:00Z","abstract_excerpt":"We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study the existence of self-similar solutions, and analyze the large-time behavior mostly by numerical simulations. Depending on the parameter $\\Dconst$, which controls the probability of coagulation, we observe two different scenarios: For $\\Dconst>2$ there exist two self-similar solutions to the mean field equation, of which one is unstable. In numerical simula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1797","kind":"arxiv","version":2},"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":"0912.1797","created_at":"2026-05-18T03:55:22.129374+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.1797v2","created_at":"2026-05-18T03:55:22.129374+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1797","created_at":"2026-05-18T03:55:22.129374+00:00"},{"alias_kind":"pith_short_12","alias_value":"S44DJORJURQI","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"S44DJORJURQICSJB","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"S44DJORJ","created_at":"2026-05-18T12:26:01.383474+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/S44DJORJURQICSJBF3Q5CREH3Y","json":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y.json","graph_json":"https://pith.science/api/pith-number/S44DJORJURQICSJBF3Q5CREH3Y/graph.json","events_json":"https://pith.science/api/pith-number/S44DJORJURQICSJBF3Q5CREH3Y/events.json","paper":"https://pith.science/paper/S44DJORJ"},"agent_actions":{"view_html":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y","download_json":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y.json","view_paper":"https://pith.science/paper/S44DJORJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.1797&json=true","fetch_graph":"https://pith.science/api/pith-number/S44DJORJURQICSJBF3Q5CREH3Y/graph.json","fetch_events":"https://pith.science/api/pith-number/S44DJORJURQICSJBF3Q5CREH3Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y/action/storage_attestation","attest_author":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y/action/author_attestation","sign_citation":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y/action/citation_signature","submit_replication":"https://pith.science/pith/S44DJORJURQICSJBF3Q5CREH3Y/action/replication_record"}},"created_at":"2026-05-18T03:55:22.129374+00:00","updated_at":"2026-05-18T03:55:22.129374+00:00"}