{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:DPR2UVQQOSPC6YTWINIKUSRTKO","short_pith_number":"pith:DPR2UVQQ","schema_version":"1.0","canonical_sha256":"1be3aa5610749e2f62764350aa4a3353aa9c7df460cf34a2729154bcc0c2d722","source":{"kind":"arxiv","id":"1006.0121","version":2},"attestation_state":"computed","paper":{"title":"Small-scale behaviour in deterministic reaction models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel ben-Avraham, Paolo Politi","submitted_at":"2010-06-01T12:10:31Z","abstract_excerpt":"In a recent paper published in this journal [J. Phys. A: Math. Theor. 42 (2009) 495004] we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power \\alpha of their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z)=z^{\\beta(\\alpha)} for small z and \\beta(\\alpha)>\\alpha. We can now prove analytically that in the strict limit of z\\to 0, \\beta=\\alpha for \\alpha>0, corresponding to the mean-field result, and we compute the length scale where mean-f"},"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":"1006.0121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-06-01T12:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"570a8587b763de84d02bf7b096815e3b2bca81458b55d60f5cde66d026d9134d","abstract_canon_sha256":"8e02313e02752a35cfe97e6cf68493bdbe51c67177134d1d1c802230e5a809df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:24.852404Z","signature_b64":"+zrMtcWrr6ge9/aSyanJy7BxGcyXqqRuSlZJGnsx5CYhj0W3jD5rXETZSN39kON7L7kA4vNmdJlQFSVGlBi8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be3aa5610749e2f62764350aa4a3353aa9c7df460cf34a2729154bcc0c2d722","last_reissued_at":"2026-05-18T04:41:24.851752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:24.851752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small-scale behaviour in deterministic reaction models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel ben-Avraham, Paolo Politi","submitted_at":"2010-06-01T12:10:31Z","abstract_excerpt":"In a recent paper published in this journal [J. Phys. A: Math. Theor. 42 (2009) 495004] we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power \\alpha of their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z)=z^{\\beta(\\alpha)} for small z and \\beta(\\alpha)>\\alpha. We can now prove analytically that in the strict limit of z\\to 0, \\beta=\\alpha for \\alpha>0, corresponding to the mean-field result, and we compute the length scale where mean-f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0121","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":"1006.0121","created_at":"2026-05-18T04:41:24.851854+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.0121v2","created_at":"2026-05-18T04:41:24.851854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0121","created_at":"2026-05-18T04:41:24.851854+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPR2UVQQOSPC","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPR2UVQQOSPC6YTW","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPR2UVQQ","created_at":"2026-05-18T12:26:06.534383+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/DPR2UVQQOSPC6YTWINIKUSRTKO","json":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO.json","graph_json":"https://pith.science/api/pith-number/DPR2UVQQOSPC6YTWINIKUSRTKO/graph.json","events_json":"https://pith.science/api/pith-number/DPR2UVQQOSPC6YTWINIKUSRTKO/events.json","paper":"https://pith.science/paper/DPR2UVQQ"},"agent_actions":{"view_html":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO","download_json":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO.json","view_paper":"https://pith.science/paper/DPR2UVQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.0121&json=true","fetch_graph":"https://pith.science/api/pith-number/DPR2UVQQOSPC6YTWINIKUSRTKO/graph.json","fetch_events":"https://pith.science/api/pith-number/DPR2UVQQOSPC6YTWINIKUSRTKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO/action/storage_attestation","attest_author":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO/action/author_attestation","sign_citation":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO/action/citation_signature","submit_replication":"https://pith.science/pith/DPR2UVQQOSPC6YTWINIKUSRTKO/action/replication_record"}},"created_at":"2026-05-18T04:41:24.851854+00:00","updated_at":"2026-05-18T04:41:24.851854+00:00"}