{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7LITFROUKYDNZ7KEPVZ5UPC35H","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":"ce62d536d9aeb424d097d40d8b61deab2b6fd636794481436f1f141df280d0d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-16T13:48:51Z","title_canon_sha256":"915979fc16c86f1db4325567bb78aa2e2178f18434b854870ad9d1936e87cca8"},"schema_version":"1.0","source":{"id":"1509.04917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04917","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04917v2","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04917","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"7LITFROUKYDN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7LITFROUKYDNZ7KE","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7LITFROU","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:7a3f5280cf9197ac7989085678adfc50655d50cac94c8de20b27a3948dc8d6a4","target":"graph","created_at":"2026-05-18T01:01:52Z","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":"We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many particles, we prove existence of solutions under a reasonable density assumption on the initial data and show that the vanishing of particles and the localized interactions can lead to non-uniqueness. Moreover, we provide a rigorous upper coarsening estimate and discuss the generic statistical properties as well as some non-generic behavior of the evolution by","authors_text":"Barbara Niethammer, Juan J. L. Velazquez, Michael Helmers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-16T13:48:51Z","title":"Mathematical analysis of a coarsening model with local interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04917","kind":"arxiv","version":2},"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":"sha256:85f825a7148474bede5720ea2000153e497a8919b95e080e9f1db98a12c91e92","target":"record","created_at":"2026-05-18T01:01:52Z","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":"ce62d536d9aeb424d097d40d8b61deab2b6fd636794481436f1f141df280d0d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-16T13:48:51Z","title_canon_sha256":"915979fc16c86f1db4325567bb78aa2e2178f18434b854870ad9d1936e87cca8"},"schema_version":"1.0","source":{"id":"1509.04917","kind":"arxiv","version":2}},"canonical_sha256":"fad132c5d45606dcfd447d73da3c5be9ca79ad1c84bcc025d47017ed60da38f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fad132c5d45606dcfd447d73da3c5be9ca79ad1c84bcc025d47017ed60da38f9","first_computed_at":"2026-05-18T01:01:52.210174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:52.210174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rsmS9q6onMsRa/hmXn+lP/3Hb1lCxQC0jKTIBj+EE+1BdpQP+gUQuzl2cIyWLmA7vOFqYlbAToAKy+8U5tWfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:52.210972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85f825a7148474bede5720ea2000153e497a8919b95e080e9f1db98a12c91e92","sha256:7a3f5280cf9197ac7989085678adfc50655d50cac94c8de20b27a3948dc8d6a4"],"state_sha256":"b87cff8196bd05bea07f38a160179d62f13a30841e8fa54c4fdd748909837522"}