{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HFOGVCCEJUK6PVVR7ZA5JLJSYP","short_pith_number":"pith:HFOGVCCE","schema_version":"1.0","canonical_sha256":"395c6a88444d15e7d6b1fe41d4ad32c3c2b160b6555dc8f1bd78d75c978108fd","source":{"kind":"arxiv","id":"1711.11028","version":3},"attestation_state":"computed","paper":{"title":"Formation of large-scale random structure by competitive erosion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Lionel Levine, Shirshendu Ganguly, Sourav Sarkar","submitted_at":"2017-11-29T18:56:20Z","abstract_excerpt":"We study the following one-dimensional model of annihilating particles. Beginning with all sites of $\\mathbb{Z}$ uncolored, a blue particle performs simple random walk from $0$ until it reaches a nonzero red or uncolored site, and turns that site blue; then, a red particle performs simple random walk from $0$ until it reaches a nonzero blue or uncolored site, and turns that site red. We prove that after $n$ blue and $n$ red particles alternately perform such walks, the total number of colored sites is of order $n^{1/4}$. The resulting random color configuration, after rescaling by $n^{1/4}$ an"},"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":"1711.11028","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-29T18:56:20Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"b73d54f626b8e4a0823bd789c4c4aed9549526b4680f3aaefe61e2b4b70ff99f","abstract_canon_sha256":"7b191152e8e27544b6e0c777a85d19c5cd41ebe56aaea120990032954ef48bfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:41.420936Z","signature_b64":"Qjfq/cXF5hS2D0iNoRAayPeflbC4TbfXMkxHnKje446MJwDKbI9CY715S8e8Sr5HXg5pEt7cTazduqL5m8d3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"395c6a88444d15e7d6b1fe41d4ad32c3c2b160b6555dc8f1bd78d75c978108fd","last_reissued_at":"2026-05-18T00:19:41.420258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:41.420258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formation of large-scale random structure by competitive erosion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Lionel Levine, Shirshendu Ganguly, Sourav Sarkar","submitted_at":"2017-11-29T18:56:20Z","abstract_excerpt":"We study the following one-dimensional model of annihilating particles. Beginning with all sites of $\\mathbb{Z}$ uncolored, a blue particle performs simple random walk from $0$ until it reaches a nonzero red or uncolored site, and turns that site blue; then, a red particle performs simple random walk from $0$ until it reaches a nonzero blue or uncolored site, and turns that site red. We prove that after $n$ blue and $n$ red particles alternately perform such walks, the total number of colored sites is of order $n^{1/4}$. The resulting random color configuration, after rescaling by $n^{1/4}$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11028","kind":"arxiv","version":3},"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":"1711.11028","created_at":"2026-05-18T00:19:41.420373+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.11028v3","created_at":"2026-05-18T00:19:41.420373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11028","created_at":"2026-05-18T00:19:41.420373+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFOGVCCEJUK6","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFOGVCCEJUK6PVVR","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFOGVCCE","created_at":"2026-05-18T12:31:18.294218+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/HFOGVCCEJUK6PVVR7ZA5JLJSYP","json":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP.json","graph_json":"https://pith.science/api/pith-number/HFOGVCCEJUK6PVVR7ZA5JLJSYP/graph.json","events_json":"https://pith.science/api/pith-number/HFOGVCCEJUK6PVVR7ZA5JLJSYP/events.json","paper":"https://pith.science/paper/HFOGVCCE"},"agent_actions":{"view_html":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP","download_json":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP.json","view_paper":"https://pith.science/paper/HFOGVCCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.11028&json=true","fetch_graph":"https://pith.science/api/pith-number/HFOGVCCEJUK6PVVR7ZA5JLJSYP/graph.json","fetch_events":"https://pith.science/api/pith-number/HFOGVCCEJUK6PVVR7ZA5JLJSYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP/action/storage_attestation","attest_author":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP/action/author_attestation","sign_citation":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP/action/citation_signature","submit_replication":"https://pith.science/pith/HFOGVCCEJUK6PVVR7ZA5JLJSYP/action/replication_record"}},"created_at":"2026-05-18T00:19:41.420373+00:00","updated_at":"2026-05-18T00:19:41.420373+00:00"}