{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A5YW7PXP3NZOJTBA6AXOUBCKZP","short_pith_number":"pith:A5YW7PXP","canonical_record":{"source":{"id":"1609.04420","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-14T20:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"cd341500f3103f3a38cb23c3f18252a7191ea751556797d6475fd6fd19ab5f33","abstract_canon_sha256":"43f728e6ef0f13943c5a0e9789d0cdb32a9d853c81490157f5667157b4456b62"},"schema_version":"1.0"},"canonical_sha256":"07716fbeefdb72e4cc20f02eea044acbceec243327d7d18ae9f4bc1490d26337","source":{"kind":"arxiv","id":"1609.04420","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04420","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04420v4","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04420","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"A5YW7PXP3NZO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A5YW7PXP3NZOJTBA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A5YW7PXP","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A5YW7PXP3NZOJTBA6AXOUBCKZP","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04420","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-14T20:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"cd341500f3103f3a38cb23c3f18252a7191ea751556797d6475fd6fd19ab5f33","abstract_canon_sha256":"43f728e6ef0f13943c5a0e9789d0cdb32a9d853c81490157f5667157b4456b62"},"schema_version":"1.0"},"canonical_sha256":"07716fbeefdb72e4cc20f02eea044acbceec243327d7d18ae9f4bc1490d26337","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:41.135495Z","signature_b64":"x/WajAkGf9N6e/EXAwGSULhVV7XM25Wjrnxh//ONBSAoVnb/PQj0kxLji13+tXKHap/LaXS6GKTykcJm0RHYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07716fbeefdb72e4cc20f02eea044acbceec243327d7d18ae9f4bc1490d26337","last_reissued_at":"2026-05-18T00:40:41.134746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:41.134746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04420","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":"2026-05-18T00:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fT/gvsNxyuUYwD4w2vrb8lmWWU//EILzok/14Jnk5mICxlzKO48NH1q/9OXknatKsh6NB8oYS9x8BIk4KV/QBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:24:04.117562Z"},"content_sha256":"cf87da03e8f28aff9ebe6949c6b78ed48ad416c99cee24d9c5dcf6a74227aca3","schema_version":"1.0","event_id":"sha256:cf87da03e8f28aff9ebe6949c6b78ed48ad416c99cee24d9c5dcf6a74227aca3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A5YW7PXP3NZOJTBA6AXOUBCKZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Local Version of the Bak-Sneppen Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Iddo Ben-Ari, Roger W. C. Silva","submitted_at":"2016-09-14T20:05:48Z","abstract_excerpt":"A major difficulty in studying the Bak-Sneppen model is in effectively comparing it with well-understood models. This stems from the use of two geometries: complete graph geometry to locate the global fitness minimizer, and graph geometry to replace the species in the neighborhood of the minimizer. We present a variant in which only the graph geometry is used. This allows to obtain the stationary distribution through random walk dynamics. We use this to show that for constant-degree graphs, the stationary fitness distribution converges to an IID law as the number of vertices tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04420","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":"2026-05-18T00:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJ2FvS/UYLnPqE98cWwSDh/id/FRGkI5cLSjU9Hc1LVrJWO1Hb5R/P/oRKHGo7O96hsQsOi5M/zV5F3mr4ROCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:24:04.117961Z"},"content_sha256":"faed603c1f5b7a110be830c606760be07b921e434e5d3471dc9eab40ea5d9579","schema_version":"1.0","event_id":"sha256:faed603c1f5b7a110be830c606760be07b921e434e5d3471dc9eab40ea5d9579"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5YW7PXP3NZOJTBA6AXOUBCKZP/bundle.json","state_url":"https://pith.science/pith/A5YW7PXP3NZOJTBA6AXOUBCKZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5YW7PXP3NZOJTBA6AXOUBCKZP/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":"2026-06-02T19:24:04Z","links":{"resolver":"https://pith.science/pith/A5YW7PXP3NZOJTBA6AXOUBCKZP","bundle":"https://pith.science/pith/A5YW7PXP3NZOJTBA6AXOUBCKZP/bundle.json","state":"https://pith.science/pith/A5YW7PXP3NZOJTBA6AXOUBCKZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5YW7PXP3NZOJTBA6AXOUBCKZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A5YW7PXP3NZOJTBA6AXOUBCKZP","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":"43f728e6ef0f13943c5a0e9789d0cdb32a9d853c81490157f5667157b4456b62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-14T20:05:48Z","title_canon_sha256":"cd341500f3103f3a38cb23c3f18252a7191ea751556797d6475fd6fd19ab5f33"},"schema_version":"1.0","source":{"id":"1609.04420","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04420","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04420v4","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04420","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"A5YW7PXP3NZO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A5YW7PXP3NZOJTBA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A5YW7PXP","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:faed603c1f5b7a110be830c606760be07b921e434e5d3471dc9eab40ea5d9579","target":"graph","created_at":"2026-05-18T00:40:41Z","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":"A major difficulty in studying the Bak-Sneppen model is in effectively comparing it with well-understood models. This stems from the use of two geometries: complete graph geometry to locate the global fitness minimizer, and graph geometry to replace the species in the neighborhood of the minimizer. We present a variant in which only the graph geometry is used. This allows to obtain the stationary distribution through random walk dynamics. We use this to show that for constant-degree graphs, the stationary fitness distribution converges to an IID law as the number of vertices tends to infinity.","authors_text":"Iddo Ben-Ari, Roger W. C. Silva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-14T20:05:48Z","title":"On a Local Version of the Bak-Sneppen Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04420","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:cf87da03e8f28aff9ebe6949c6b78ed48ad416c99cee24d9c5dcf6a74227aca3","target":"record","created_at":"2026-05-18T00:40:41Z","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":"43f728e6ef0f13943c5a0e9789d0cdb32a9d853c81490157f5667157b4456b62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-14T20:05:48Z","title_canon_sha256":"cd341500f3103f3a38cb23c3f18252a7191ea751556797d6475fd6fd19ab5f33"},"schema_version":"1.0","source":{"id":"1609.04420","kind":"arxiv","version":4}},"canonical_sha256":"07716fbeefdb72e4cc20f02eea044acbceec243327d7d18ae9f4bc1490d26337","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07716fbeefdb72e4cc20f02eea044acbceec243327d7d18ae9f4bc1490d26337","first_computed_at":"2026-05-18T00:40:41.134746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:41.134746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x/WajAkGf9N6e/EXAwGSULhVV7XM25Wjrnxh//ONBSAoVnb/PQj0kxLji13+tXKHap/LaXS6GKTykcJm0RHYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:41.135495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04420","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf87da03e8f28aff9ebe6949c6b78ed48ad416c99cee24d9c5dcf6a74227aca3","sha256:faed603c1f5b7a110be830c606760be07b921e434e5d3471dc9eab40ea5d9579"],"state_sha256":"d13657a223910bc470a0a6d54f47bdaa6d0a0d099deee6326582d8c9199099ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXt7RQlBZeEsjJdgeqVR3Jy7wNVU7lHzFFaB5DLt5X3gPmmL3k/E9VuvuX6Mopt9vf7XQMkfRbth5zqqPm1mAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:24:04.120124Z","bundle_sha256":"1a5c6e70ffadb7d19009ba2005e492034611d08464c491cf858c55a6ef4c32b6"}}