{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:P4YPO6W67WTCAZT52WGU6OF7EM","short_pith_number":"pith:P4YPO6W6","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"},"canonical_sha256":"7f30f77adefda620667dd58d4f38bf23148410475684081300b2f91d32485f70","source":{"kind":"arxiv","id":"1405.3609","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3609","created_at":"2026-05-18T00:52:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3609v4","created_at":"2026-05-18T00:52:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3609","created_at":"2026-05-18T00:52:32Z"},{"alias_kind":"pith_short_12","alias_value":"P4YPO6W67WTC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P4YPO6W67WTCAZT5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P4YPO6W6","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:P4YPO6W67WTCAZT52WGU6OF7EM","target":"record","payload":{"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"},"canonical_sha256":"7f30f77adefda620667dd58d4f38bf23148410475684081300b2f91d32485f70","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"},"source_kind":"arxiv","source_id":"1405.3609","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GChnbKYeBtK10upyG20IuKZ2Ri2JR07T5LSGP05cpK2YyPGMzii3IumLRdMI8RqwadeQKfCejdNh26K3WbGGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:44:00.744498Z"},"content_sha256":"f2f7ddeec3e7e805801d67a6d0a30855bf1cdc1dfa999ca4204ecb819d564b9e","schema_version":"1.0","event_id":"sha256:f2f7ddeec3e7e805801d67a6d0a30855bf1cdc1dfa999ca4204ecb819d564b9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:P4YPO6W67WTCAZT52WGU6OF7EM","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4l6tDlRwieewL7H+iE/wH8nrnfrtf/JJk+fL1pk60DHMQfwnj5vUuDoyfkUoCxOqYdHEgVI9T8SbKLcxI5TRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:44:00.744877Z"},"content_sha256":"a400ec559656c9c7615f2f572093b00732e31c33a0051d6f18fc80504d633848","schema_version":"1.0","event_id":"sha256:a400ec559656c9c7615f2f572093b00732e31c33a0051d6f18fc80504d633848"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/bundle.json","state_url":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4YPO6W67WTCAZT52WGU6OF7EM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T14:44:00Z","links":{"resolver":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM","bundle":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/bundle.json","state":"https://pith.science/pith/P4YPO6W67WTCAZT52WGU6OF7EM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4YPO6W67WTCAZT52WGU6OF7EM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:P4YPO6W67WTCAZT52WGU6OF7EM","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":"16533275000a5abb0423fe923442f3ca06469f0dbd5be21e74550d1a8b79ada0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-14T18:21:44Z","title_canon_sha256":"ad87d3204ab0f89e72f9d99b607111ab96710a553e5eb88349821b3dc5846233"},"schema_version":"1.0","source":{"id":"1405.3609","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3609","created_at":"2026-05-18T00:52:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3609v4","created_at":"2026-05-18T00:52:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3609","created_at":"2026-05-18T00:52:32Z"},{"alias_kind":"pith_short_12","alias_value":"P4YPO6W67WTC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P4YPO6W67WTCAZT5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P4YPO6W6","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:a400ec559656c9c7615f2f572093b00732e31c33a0051d6f18fc80504d633848","target":"graph","created_at":"2026-05-18T00:52:32Z","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 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 $p_{\\rm c}=1-e^{-1}$ ","authors_text":"Jan M. Swart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-14T18:21:44Z","title":"A simple rank-based Markov chain with self-organized criticality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3609","kind":"arxiv","version":4},"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:f2f7ddeec3e7e805801d67a6d0a30855bf1cdc1dfa999ca4204ecb819d564b9e","target":"record","created_at":"2026-05-18T00:52:32Z","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":"16533275000a5abb0423fe923442f3ca06469f0dbd5be21e74550d1a8b79ada0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-14T18:21:44Z","title_canon_sha256":"ad87d3204ab0f89e72f9d99b607111ab96710a553e5eb88349821b3dc5846233"},"schema_version":"1.0","source":{"id":"1405.3609","kind":"arxiv","version":4}},"canonical_sha256":"7f30f77adefda620667dd58d4f38bf23148410475684081300b2f91d32485f70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f30f77adefda620667dd58d4f38bf23148410475684081300b2f91d32485f70","first_computed_at":"2026-05-18T00:52:32.904613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:32.904613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JVervktaOwqyfPc17lUlKhFSKo5HRICfGBlWF0wBoxZghv18+5f2yN0KHGmQiWrGbHBRiVSYARVqdOenEFB1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:32.905182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3609","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2f7ddeec3e7e805801d67a6d0a30855bf1cdc1dfa999ca4204ecb819d564b9e","sha256:a400ec559656c9c7615f2f572093b00732e31c33a0051d6f18fc80504d633848"],"state_sha256":"556e3da287cd9a25cba5e9ce7d29d4fe2bcba970eaeb35abdca8f85339a8bb1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6H4IJrFqVucghih0gT69C3qbosZebOpsHWh4I5aIzjzaWEsJ6tXoHHMSu6rZKMP5OqJNh5LLr7FxNRBiywbDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:44:00.748471Z","bundle_sha256":"75b2fe561380087c33b43fbbded1e15eee64ae836a8936a9fca4346ac4531350"}}