{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DKECDOTYW2X6SFLPOX4SYD63WL","short_pith_number":"pith:DKECDOTY","canonical_record":{"source":{"id":"1307.0570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T01:32:37Z","cross_cats_sorted":[],"title_canon_sha256":"284128dfa714ae970f06ae1dcc8eeab9739b4e0da2a527362706c5bbae015139","abstract_canon_sha256":"c3dbf22815d72630e4ec51c9607447f3850abbc95cc2f15f77f697ee8acc2336"},"schema_version":"1.0"},"canonical_sha256":"1a8821ba78b6afe9156f75f92c0fdbb2e7a624a875872acfd5b55cb3428b193b","source":{"kind":"arxiv","id":"1307.0570","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0570","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0570v2","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0570","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"pith_short_12","alias_value":"DKECDOTYW2X6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DKECDOTYW2X6SFLP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DKECDOTY","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DKECDOTYW2X6SFLPOX4SYD63WL","target":"record","payload":{"canonical_record":{"source":{"id":"1307.0570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T01:32:37Z","cross_cats_sorted":[],"title_canon_sha256":"284128dfa714ae970f06ae1dcc8eeab9739b4e0da2a527362706c5bbae015139","abstract_canon_sha256":"c3dbf22815d72630e4ec51c9607447f3850abbc95cc2f15f77f697ee8acc2336"},"schema_version":"1.0"},"canonical_sha256":"1a8821ba78b6afe9156f75f92c0fdbb2e7a624a875872acfd5b55cb3428b193b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:00.822801Z","signature_b64":"MUCURsGdo3H9pEM/hAkPTDGKFeJEj0bZFgcMCvZJ7uKOYMrVQ1Yj6tfVFIbx2zMzVkGZz1dCTk4GC8scHSl1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a8821ba78b6afe9156f75f92c0fdbb2e7a624a875872acfd5b55cb3428b193b","last_reissued_at":"2026-05-18T01:49:00.822381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:00.822381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.0570","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TC2rxtz06pRVYgEBKjS2njSoW2LykcsUueuLlq/dlPTbIX/JNTEH5T2TcS+zHeN8cScPChtE+KBRHr5bokgOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:23:43.755338Z"},"content_sha256":"12b0e4e3fe687426e356c691da461b35c361b70b4fc1846ce5386e52a10c6171","schema_version":"1.0","event_id":"sha256:12b0e4e3fe687426e356c691da461b35c361b70b4fc1846ce5386e52a10c6171"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DKECDOTYW2X6SFLPOX4SYD63WL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Rank Driven Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. J. Prieto, J. J. P. Veerman","submitted_at":"2013-07-02T01:32:37Z","abstract_excerpt":"We investigate a class of models related to the Bak-Sneppen model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of \"complex behavior\" such as self-organized criticality that is often observed in physical and biological systems.\n  In this model, random fitnesses in $[0,1]$ are associated to agents located at the vertices of a graph $G$. Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others \\emph{with a priori given rank probabilities} are replaced by new agents with random"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0570","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KU21FPwpsUnhPcXx4dK3JOH+3oZ0dyNesu8MKQnJEz3hWBgFWBQa2NTZo9jf1LX12ZmBYVBF/P25QuwLQAWHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:23:43.755700Z"},"content_sha256":"b82b08182469e185e64c695d202979388c4a9a433392c75c6cdd25897acb92d0","schema_version":"1.0","event_id":"sha256:b82b08182469e185e64c695d202979388c4a9a433392c75c6cdd25897acb92d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKECDOTYW2X6SFLPOX4SYD63WL/bundle.json","state_url":"https://pith.science/pith/DKECDOTYW2X6SFLPOX4SYD63WL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKECDOTYW2X6SFLPOX4SYD63WL/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":"2026-06-25T09:23:43Z","links":{"resolver":"https://pith.science/pith/DKECDOTYW2X6SFLPOX4SYD63WL","bundle":"https://pith.science/pith/DKECDOTYW2X6SFLPOX4SYD63WL/bundle.json","state":"https://pith.science/pith/DKECDOTYW2X6SFLPOX4SYD63WL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKECDOTYW2X6SFLPOX4SYD63WL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DKECDOTYW2X6SFLPOX4SYD63WL","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":"c3dbf22815d72630e4ec51c9607447f3850abbc95cc2f15f77f697ee8acc2336","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T01:32:37Z","title_canon_sha256":"284128dfa714ae970f06ae1dcc8eeab9739b4e0da2a527362706c5bbae015139"},"schema_version":"1.0","source":{"id":"1307.0570","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0570","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0570v2","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0570","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"pith_short_12","alias_value":"DKECDOTYW2X6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DKECDOTYW2X6SFLP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DKECDOTY","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:b82b08182469e185e64c695d202979388c4a9a433392c75c6cdd25897acb92d0","target":"graph","created_at":"2026-05-18T01:49:00Z","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 investigate a class of models related to the Bak-Sneppen model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of \"complex behavior\" such as self-organized criticality that is often observed in physical and biological systems.\n  In this model, random fitnesses in $[0,1]$ are associated to agents located at the vertices of a graph $G$. Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others \\emph{with a priori given rank probabilities} are replaced by new agents with random","authors_text":"F. J. Prieto, J. J. P. Veerman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T01:32:37Z","title":"On Rank Driven Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0570","kind":"arxiv","version":2},"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":"sha256:12b0e4e3fe687426e356c691da461b35c361b70b4fc1846ce5386e52a10c6171","target":"record","created_at":"2026-05-18T01:49:00Z","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":"c3dbf22815d72630e4ec51c9607447f3850abbc95cc2f15f77f697ee8acc2336","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T01:32:37Z","title_canon_sha256":"284128dfa714ae970f06ae1dcc8eeab9739b4e0da2a527362706c5bbae015139"},"schema_version":"1.0","source":{"id":"1307.0570","kind":"arxiv","version":2}},"canonical_sha256":"1a8821ba78b6afe9156f75f92c0fdbb2e7a624a875872acfd5b55cb3428b193b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a8821ba78b6afe9156f75f92c0fdbb2e7a624a875872acfd5b55cb3428b193b","first_computed_at":"2026-05-18T01:49:00.822381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:00.822381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MUCURsGdo3H9pEM/hAkPTDGKFeJEj0bZFgcMCvZJ7uKOYMrVQ1Yj6tfVFIbx2zMzVkGZz1dCTk4GC8scHSl1DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:00.822801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0570","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12b0e4e3fe687426e356c691da461b35c361b70b4fc1846ce5386e52a10c6171","sha256:b82b08182469e185e64c695d202979388c4a9a433392c75c6cdd25897acb92d0"],"state_sha256":"c7f3d5010ee85a32f67562de5b808525441035290b96dc3ffb541839bb85b5be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EuOW/iCQh2rcx4zFI1othrJ9r4JRtjaezdMHDpryEvmSCDmZf5vy2JPHpa08MCTeF7DEVe2SNvckdKbTUO/9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:23:43.757642Z","bundle_sha256":"ff6678c980b71b949bfe620d7ff072b4c0099e904854466ce90bcf30feea7259"}}