{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:BXTJIE4UZLSXJC6KRKPGSGVZDB","short_pith_number":"pith:BXTJIE4U","schema_version":"1.0","canonical_sha256":"0de6941394cae5748bca8a9e691ab9187ad8f8ebcc936eba28b024e9b8fc2af2","source":{"kind":"arxiv","id":"nlin/0609026","version":1},"attestation_state":"computed","paper":{"title":"The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Govind Menon, Robert L. Pego","submitted_at":"2006-09-11T17:43:12Z","abstract_excerpt":"We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this l"},"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":"nlin/0609026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.AO","submitted_at":"2006-09-11T17:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"1cb00ca94440cf19e4364cd04fec60eb86597fd163ee97e874f7daa7f4a47baa","abstract_canon_sha256":"ee03b00500b01582bcfce9b4a5f012531ea3df6ef24f2fa4c8c62476c0f1c4bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:35.447889Z","signature_b64":"mhqLzRrWiTq5lLaEySH1i/vFGPfuQYzwpZPAmWypdKSNEKf5dLU5Vhy3p7z7XxLRVtcio3FKc1WwAy6+Chc5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0de6941394cae5748bca8a9e691ab9187ad8f8ebcc936eba28b024e9b8fc2af2","last_reissued_at":"2026-05-18T03:25:35.447226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:35.447226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Govind Menon, Robert L. Pego","submitted_at":"2006-09-11T17:43:12Z","abstract_excerpt":"We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0609026","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":"nlin/0609026","created_at":"2026-05-18T03:25:35.447308+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0609026v1","created_at":"2026-05-18T03:25:35.447308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0609026","created_at":"2026-05-18T03:25:35.447308+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXTJIE4UZLSX","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXTJIE4UZLSXJC6K","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXTJIE4U","created_at":"2026-05-18T12:25:53.939244+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/BXTJIE4UZLSXJC6KRKPGSGVZDB","json":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB.json","graph_json":"https://pith.science/api/pith-number/BXTJIE4UZLSXJC6KRKPGSGVZDB/graph.json","events_json":"https://pith.science/api/pith-number/BXTJIE4UZLSXJC6KRKPGSGVZDB/events.json","paper":"https://pith.science/paper/BXTJIE4U"},"agent_actions":{"view_html":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB","download_json":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB.json","view_paper":"https://pith.science/paper/BXTJIE4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0609026&json=true","fetch_graph":"https://pith.science/api/pith-number/BXTJIE4UZLSXJC6KRKPGSGVZDB/graph.json","fetch_events":"https://pith.science/api/pith-number/BXTJIE4UZLSXJC6KRKPGSGVZDB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB/action/storage_attestation","attest_author":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB/action/author_attestation","sign_citation":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB/action/citation_signature","submit_replication":"https://pith.science/pith/BXTJIE4UZLSXJC6KRKPGSGVZDB/action/replication_record"}},"created_at":"2026-05-18T03:25:35.447308+00:00","updated_at":"2026-05-18T03:25:35.447308+00:00"}