{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:XEXBWFV3QDV4TJ435ADMOG6WMH","short_pith_number":"pith:XEXBWFV3","canonical_record":{"source":{"id":"cond-mat/0304288","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-04-11T21:01:30Z","cross_cats_sorted":[],"title_canon_sha256":"cd20c93a685d23a02b5b356105bfb08683acefdf1928b54c0c77b033f322ceea","abstract_canon_sha256":"f4990cd8861a0b01cf0274d83edd266ddb06c1d9d7e4bbb1ed7f311a56e07aac"},"schema_version":"1.0"},"canonical_sha256":"b92e1b16bb80ebc9a79be806c71bd661f4184aaa08e589137cd54833dfa5cb93","source":{"kind":"arxiv","id":"cond-mat/0304288","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0304288","created_at":"2026-05-18T01:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0304288v2","created_at":"2026-05-18T01:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0304288","created_at":"2026-05-18T01:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"XEXBWFV3QDV4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XEXBWFV3QDV4TJ43","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XEXBWFV3","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:XEXBWFV3QDV4TJ435ADMOG6WMH","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0304288","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-04-11T21:01:30Z","cross_cats_sorted":[],"title_canon_sha256":"cd20c93a685d23a02b5b356105bfb08683acefdf1928b54c0c77b033f322ceea","abstract_canon_sha256":"f4990cd8861a0b01cf0274d83edd266ddb06c1d9d7e4bbb1ed7f311a56e07aac"},"schema_version":"1.0"},"canonical_sha256":"b92e1b16bb80ebc9a79be806c71bd661f4184aaa08e589137cd54833dfa5cb93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:01.567770Z","signature_b64":"w6/37hO/YamOal+o5CCLNg9VKePz77fg+4JZOx+OLhy6kqziUP8jwYCUxvkxzMaECVyEZvMNJmk0DHBu281YBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b92e1b16bb80ebc9a79be806c71bd661f4184aaa08e589137cd54833dfa5cb93","last_reissued_at":"2026-05-18T01:40:01.567151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:01.567151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0304288","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":"2026-05-18T01:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDBwqx8YnqIGwrjhQ+B3as3ft36xeXpvsP5A1Ya1PaLyfv70wTUItGq8A6N5GzoJu8izcKMLBg2kwkarQ3BHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:29:11.525828Z"},"content_sha256":"7142c1e67785c9a7b14f182266db1f204e4d7fcd412dd9669a7628f0afa7559e","schema_version":"1.0","event_id":"sha256:7142c1e67785c9a7b14f182266db1f204e4d7fcd412dd9669a7628f0afa7559e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:XEXBWFV3QDV4TJ435ADMOG6WMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On singular probability densities generated by extremal dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Guilherme J. M. Garcia, Ronald Dickman","submitted_at":"2003-04-11T21:01:30Z","abstract_excerpt":"Extremal dynamics is the mechanism that drives the Bak-Sneppen model into a (self-organized) critical state, marked by a singular stationary probability density $p(x)$. With the aim of understanding this phenomenon, we study the BS model and several variants via mean-field theory and simulation. In all cases, we find that $p(x)$ is singular at one or more points, as a consequence of extremal dynamics. Furthermore we show that the extremal barrier $x_i$ always belongs to the `prohibited' interval, in which $p(x)=0$. Our simulations indicate that the Bak-Sneppen universality class is robust with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0304288","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":"2026-05-18T01:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTTntZtOT7rS6420jCkmd+y/qty9piIAs6UUmgqznVeHtCbfooC50GuFYV2Ip7Qr0+ehVwG67OqFqrTygxlCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:29:11.526426Z"},"content_sha256":"33de79652cce91e7f5c3bb4b037ae5638633d63c2d984adc0310e13929ac5ce8","schema_version":"1.0","event_id":"sha256:33de79652cce91e7f5c3bb4b037ae5638633d63c2d984adc0310e13929ac5ce8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XEXBWFV3QDV4TJ435ADMOG6WMH/bundle.json","state_url":"https://pith.science/pith/XEXBWFV3QDV4TJ435ADMOG6WMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XEXBWFV3QDV4TJ435ADMOG6WMH/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":"2026-05-31T07:29:11Z","links":{"resolver":"https://pith.science/pith/XEXBWFV3QDV4TJ435ADMOG6WMH","bundle":"https://pith.science/pith/XEXBWFV3QDV4TJ435ADMOG6WMH/bundle.json","state":"https://pith.science/pith/XEXBWFV3QDV4TJ435ADMOG6WMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XEXBWFV3QDV4TJ435ADMOG6WMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XEXBWFV3QDV4TJ435ADMOG6WMH","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":"f4990cd8861a0b01cf0274d83edd266ddb06c1d9d7e4bbb1ed7f311a56e07aac","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-04-11T21:01:30Z","title_canon_sha256":"cd20c93a685d23a02b5b356105bfb08683acefdf1928b54c0c77b033f322ceea"},"schema_version":"1.0","source":{"id":"cond-mat/0304288","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0304288","created_at":"2026-05-18T01:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0304288v2","created_at":"2026-05-18T01:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0304288","created_at":"2026-05-18T01:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"XEXBWFV3QDV4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XEXBWFV3QDV4TJ43","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XEXBWFV3","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:33de79652cce91e7f5c3bb4b037ae5638633d63c2d984adc0310e13929ac5ce8","target":"graph","created_at":"2026-05-18T01:40:01Z","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":"Extremal dynamics is the mechanism that drives the Bak-Sneppen model into a (self-organized) critical state, marked by a singular stationary probability density $p(x)$. With the aim of understanding this phenomenon, we study the BS model and several variants via mean-field theory and simulation. In all cases, we find that $p(x)$ is singular at one or more points, as a consequence of extremal dynamics. Furthermore we show that the extremal barrier $x_i$ always belongs to the `prohibited' interval, in which $p(x)=0$. Our simulations indicate that the Bak-Sneppen universality class is robust with","authors_text":"Guilherme J. M. Garcia, Ronald Dickman","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-04-11T21:01:30Z","title":"On singular probability densities generated by extremal dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0304288","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":"sha256:7142c1e67785c9a7b14f182266db1f204e4d7fcd412dd9669a7628f0afa7559e","target":"record","created_at":"2026-05-18T01:40:01Z","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":"f4990cd8861a0b01cf0274d83edd266ddb06c1d9d7e4bbb1ed7f311a56e07aac","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-04-11T21:01:30Z","title_canon_sha256":"cd20c93a685d23a02b5b356105bfb08683acefdf1928b54c0c77b033f322ceea"},"schema_version":"1.0","source":{"id":"cond-mat/0304288","kind":"arxiv","version":2}},"canonical_sha256":"b92e1b16bb80ebc9a79be806c71bd661f4184aaa08e589137cd54833dfa5cb93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b92e1b16bb80ebc9a79be806c71bd661f4184aaa08e589137cd54833dfa5cb93","first_computed_at":"2026-05-18T01:40:01.567151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:01.567151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w6/37hO/YamOal+o5CCLNg9VKePz77fg+4JZOx+OLhy6kqziUP8jwYCUxvkxzMaECVyEZvMNJmk0DHBu281YBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:01.567770Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0304288","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7142c1e67785c9a7b14f182266db1f204e4d7fcd412dd9669a7628f0afa7559e","sha256:33de79652cce91e7f5c3bb4b037ae5638633d63c2d984adc0310e13929ac5ce8"],"state_sha256":"5a91357561cc65cfe0781192e9d703a4606d5e5aec11f47e588d5c44deee9446"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+qyweaPCQUS2sTMxvG2pTaXN/Oml6gyFnB/27CTHN4mwdKguWIDD9nm4KEN9xtCCiMRpLCoUHiIrXqX1WUwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:29:11.530074Z","bundle_sha256":"009809164a850ecf2603056bd8d6fe4607f7ce0885a52893fa333c3bbc1e90be"}}