{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ISSZBMA7773OJSFEAHGBVT6TB6","short_pith_number":"pith:ISSZBMA7","schema_version":"1.0","canonical_sha256":"44a590b01ffff6e4c8a401cc1acfd30faf39062b9ccd5b2c3169e5b7f7a76b64","source":{"kind":"arxiv","id":"1505.03892","version":2},"attestation_state":"computed","paper":{"title":"On Diffusion Limited Deposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Asselah, B. Scoppola, E. Cirillo, E. Scoppola","submitted_at":"2015-05-14T21:24:43Z","abstract_excerpt":"We propose a simple model of columnar growth through {\\it diffusion limited aggregation} (DLA). Consider a graph $G_N\\times\\N$, where the basis has $N$ vertices $G_N:=\\{1,\\dots,N\\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if $|h-h'|\\le 1$. Consider there a simple random walk {\\it coming from infinity} which {\\it deposits} on a growing cluster as follows: the cluster is a collection of columns, and the height of the column first hit by the walk immediately grows by one unit. Thus, columns do not grow laterally.\n  We prove that there is a critical time scale $N/\\log(N)$ for the maxi"},"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":"1505.03892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-14T21:24:43Z","cross_cats_sorted":[],"title_canon_sha256":"965505b6b6ab899734d042b638d9d331e65cadcb5aa3569dcc0606587555baff","abstract_canon_sha256":"ab6678b9ecee70845c4f0cd06c642a05d6fb4ec97e3ede54ec51d5c48eec9efc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:18.365385Z","signature_b64":"xHiF6v+zcbu3zAjI/U/pxp/L32B4t2TqXVBgSOIyyIzRw2+dJVSfUqlsL+gYj1sZX5Egx/juQzGvPT5vBsbDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44a590b01ffff6e4c8a401cc1acfd30faf39062b9ccd5b2c3169e5b7f7a76b64","last_reissued_at":"2026-05-18T01:26:18.364704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:18.364704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Diffusion Limited Deposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Asselah, B. Scoppola, E. Cirillo, E. Scoppola","submitted_at":"2015-05-14T21:24:43Z","abstract_excerpt":"We propose a simple model of columnar growth through {\\it diffusion limited aggregation} (DLA). Consider a graph $G_N\\times\\N$, where the basis has $N$ vertices $G_N:=\\{1,\\dots,N\\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if $|h-h'|\\le 1$. Consider there a simple random walk {\\it coming from infinity} which {\\it deposits} on a growing cluster as follows: the cluster is a collection of columns, and the height of the column first hit by the walk immediately grows by one unit. Thus, columns do not grow laterally.\n  We prove that there is a critical time scale $N/\\log(N)$ for the maxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03892","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":"1505.03892","created_at":"2026-05-18T01:26:18.364825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03892v2","created_at":"2026-05-18T01:26:18.364825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03892","created_at":"2026-05-18T01:26:18.364825+00:00"},{"alias_kind":"pith_short_12","alias_value":"ISSZBMA7773O","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"ISSZBMA7773OJSFE","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"ISSZBMA7","created_at":"2026-05-18T12:29:25.134429+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/ISSZBMA7773OJSFEAHGBVT6TB6","json":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6.json","graph_json":"https://pith.science/api/pith-number/ISSZBMA7773OJSFEAHGBVT6TB6/graph.json","events_json":"https://pith.science/api/pith-number/ISSZBMA7773OJSFEAHGBVT6TB6/events.json","paper":"https://pith.science/paper/ISSZBMA7"},"agent_actions":{"view_html":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6","download_json":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6.json","view_paper":"https://pith.science/paper/ISSZBMA7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03892&json=true","fetch_graph":"https://pith.science/api/pith-number/ISSZBMA7773OJSFEAHGBVT6TB6/graph.json","fetch_events":"https://pith.science/api/pith-number/ISSZBMA7773OJSFEAHGBVT6TB6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6/action/storage_attestation","attest_author":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6/action/author_attestation","sign_citation":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6/action/citation_signature","submit_replication":"https://pith.science/pith/ISSZBMA7773OJSFEAHGBVT6TB6/action/replication_record"}},"created_at":"2026-05-18T01:26:18.364825+00:00","updated_at":"2026-05-18T01:26:18.364825+00:00"}