{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:P4YPO6W67WTCAZT52WGU6OF7EM","short_pith_number":"pith:P4YPO6W6","schema_version":"1.0","canonical_sha256":"7f30f77adefda620667dd58d4f38bf23148410475684081300b2f91d32485f70","source":{"kind":"arxiv","id":"1405.3609","version":4},"attestation_state":"computed","paper":{"title":"A simple rank-based Markov chain with self-organized criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan M. Swart","submitted_at":"2014-05-14T18:21:44Z","abstract_excerpt":"We introduce a self-reinforced point processes on the unit interval that appears to exhibit self-organized criticality, somewhat reminiscent of the well-known Bak-Sneppen model. The process takes values in the finite subsets of the unit interval and evolves according to the following rules. In each time step, a particle is added at a uniformly chosen position, independent of the particles that are already present. If there are any particles to the left of the newly arrived particle, then the left-most of these is removed. We show that all particles arriving to the left of $p_{\\rm c}=1-e^{-1}$ "},"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":"1405.3609","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-14T18:21:44Z","cross_cats_sorted":[],"title_canon_sha256":"ad87d3204ab0f89e72f9d99b607111ab96710a553e5eb88349821b3dc5846233","abstract_canon_sha256":"16533275000a5abb0423fe923442f3ca06469f0dbd5be21e74550d1a8b79ada0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:32.905182Z","signature_b64":"JVervktaOwqyfPc17lUlKhFSKo5HRICfGBlWF0wBoxZghv18+5f2yN0KHGmQiWrGbHBRiVSYARVqdOenEFB1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f30f77adefda620667dd58d4f38bf23148410475684081300b2f91d32485f70","last_reissued_at":"2026-05-18T00:52:32.904613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:32.904613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A simple rank-based Markov chain with self-organized criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan M. Swart","submitted_at":"2014-05-14T18:21:44Z","abstract_excerpt":"We introduce a self-reinforced point processes on the unit interval that appears to exhibit self-organized criticality, somewhat reminiscent of the well-known Bak-Sneppen model. The process takes values in the finite subsets of the unit interval and evolves according to the following rules. In each time step, a particle is added at a uniformly chosen position, independent of the particles that are already present. If there are any particles to the left of the newly arrived particle, then the left-most of these is removed. We show that all particles arriving to the left of $p_{\\rm c}=1-e^{-1}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3609","kind":"arxiv","version":4},"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":"1405.3609","created_at":"2026-05-18T00:52:32.904696+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.3609v4","created_at":"2026-05-18T00:52:32.904696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3609","created_at":"2026-05-18T00:52:32.904696+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4YPO6W67WTC","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4YPO6W67WTCAZT5","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4YPO6W6","created_at":"2026-05-18T12:28:43.426989+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/P4YPO6W67WTCAZT52WGU6OF7EM","json":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM.json","graph_json":"https://pith.science/api/pith-number/P4YPO6W67WTCAZT52WGU6OF7EM/graph.json","events_json":"https://pith.science/api/pith-number/P4YPO6W67WTCAZT52WGU6OF7EM/events.json","paper":"https://pith.science/paper/P4YPO6W6"},"agent_actions":{"view_html":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM","download_json":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM.json","view_paper":"https://pith.science/paper/P4YPO6W6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.3609&json=true","fetch_graph":"https://pith.science/api/pith-number/P4YPO6W67WTCAZT52WGU6OF7EM/graph.json","fetch_events":"https://pith.science/api/pith-number/P4YPO6W67WTCAZT52WGU6OF7EM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/action/storage_attestation","attest_author":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/action/author_attestation","sign_citation":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/action/citation_signature","submit_replication":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/action/replication_record"}},"created_at":"2026-05-18T00:52:32.904696+00:00","updated_at":"2026-05-18T00:52:32.904696+00:00"}