{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:2AV5NIR7CKWEEMZ3PN4PM2XINC","short_pith_number":"pith:2AV5NIR7","schema_version":"1.0","canonical_sha256":"d02bd6a23f12ac42333b7b78f66ae86899fd6d2775c421ad29b99cd0b6ecf858","source":{"kind":"arxiv","id":"0807.3529","version":1},"attestation_state":"computed","paper":{"title":"A Kinetic Model for Grain Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Niethammer, Juan J.L. Velazquez, Michael Herrmann, Reiner Henseler","submitted_at":"2008-07-22T17:56:20Z","abstract_excerpt":"We provide a well-posedness analysis of a kinetic model for grain growth introduced by Fradkov which is based on the von Neumann-Mullins law. The model consists of an infinite number of transport equations with a tri-diagonal coupling modelling topological changes in the grain configuration. Self-consistency of this kinetic model is achieved by introducing a coupling weight which leads to a nonlinear and nonlocal system of equations.\n  We prove existence of solutions by approximation with finite dimensional systems. Key ingredients in passing to the limit are suitable super-solutions, a bound "},"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":"0807.3529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-07-22T17:56:20Z","cross_cats_sorted":[],"title_canon_sha256":"cf85c223b380764fe46c064f2b6c10580d5ba2b3fc3af304766fe382eb132015","abstract_canon_sha256":"4f40757fa0e224080d965d25c305bea226b5766558e227c1e4aae391be91a000"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:35:11.876787Z","signature_b64":"/BXUwFeT8IvxbHB8jUup9RFAEC8MhConOUTp3ct31s1NqrvBsfsi0PDFbmJQfHxwnQBl2UXDX2sahUR3YCZnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d02bd6a23f12ac42333b7b78f66ae86899fd6d2775c421ad29b99cd0b6ecf858","last_reissued_at":"2026-07-04T15:35:11.876391Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:35:11.876391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Kinetic Model for Grain Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Niethammer, Juan J.L. Velazquez, Michael Herrmann, Reiner Henseler","submitted_at":"2008-07-22T17:56:20Z","abstract_excerpt":"We provide a well-posedness analysis of a kinetic model for grain growth introduced by Fradkov which is based on the von Neumann-Mullins law. The model consists of an infinite number of transport equations with a tri-diagonal coupling modelling topological changes in the grain configuration. Self-consistency of this kinetic model is achieved by introducing a coupling weight which leads to a nonlinear and nonlocal system of equations.\n  We prove existence of solutions by approximation with finite dimensional systems. Key ingredients in passing to the limit are suitable super-solutions, a bound "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3529","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0807.3529/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0807.3529","created_at":"2026-07-04T15:35:11.876456+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.3529v1","created_at":"2026-07-04T15:35:11.876456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3529","created_at":"2026-07-04T15:35:11.876456+00:00"},{"alias_kind":"pith_short_12","alias_value":"2AV5NIR7CKWE","created_at":"2026-07-04T15:35:11.876456+00:00"},{"alias_kind":"pith_short_16","alias_value":"2AV5NIR7CKWEEMZ3","created_at":"2026-07-04T15:35:11.876456+00:00"},{"alias_kind":"pith_short_8","alias_value":"2AV5NIR7","created_at":"2026-07-04T15:35:11.876456+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/2AV5NIR7CKWEEMZ3PN4PM2XINC","json":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC.json","graph_json":"https://pith.science/api/pith-number/2AV5NIR7CKWEEMZ3PN4PM2XINC/graph.json","events_json":"https://pith.science/api/pith-number/2AV5NIR7CKWEEMZ3PN4PM2XINC/events.json","paper":"https://pith.science/paper/2AV5NIR7"},"agent_actions":{"view_html":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC","download_json":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC.json","view_paper":"https://pith.science/paper/2AV5NIR7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.3529&json=true","fetch_graph":"https://pith.science/api/pith-number/2AV5NIR7CKWEEMZ3PN4PM2XINC/graph.json","fetch_events":"https://pith.science/api/pith-number/2AV5NIR7CKWEEMZ3PN4PM2XINC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC/action/storage_attestation","attest_author":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC/action/author_attestation","sign_citation":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC/action/citation_signature","submit_replication":"https://pith.science/pith/2AV5NIR7CKWEEMZ3PN4PM2XINC/action/replication_record"}},"created_at":"2026-07-04T15:35:11.876456+00:00","updated_at":"2026-07-04T15:35:11.876456+00:00"}