{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:OJI4VBYNP2UK6ZK4VEA3US5BAB","short_pith_number":"pith:OJI4VBYN","canonical_record":{"source":{"id":"0704.3406","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-25T16:35:14Z","cross_cats_sorted":["cond-mat.dis-nn","q-bio.MN"],"title_canon_sha256":"68ab7adb42f5fbebda9fd18f1c23ee6349531972dcf908f3d7dd7b231ab42c27","abstract_canon_sha256":"4f9c8cd7bd526535b9e455e26408bf82a80be7c3747838632bad6517c364b3ed"},"schema_version":"1.0"},"canonical_sha256":"7251ca870d7ea8af655ca901ba4ba1007bca0f5a0b2ee9e50c955ed435e54fe3","source":{"kind":"arxiv","id":"0704.3406","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3406","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3406v1","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3406","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"OJI4VBYNP2UK","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"pith_short_16","alias_value":"OJI4VBYNP2UK6ZK4","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"pith_short_8","alias_value":"OJI4VBYN","created_at":"2026-07-04T15:03:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:OJI4VBYNP2UK6ZK4VEA3US5BAB","target":"record","payload":{"canonical_record":{"source":{"id":"0704.3406","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-25T16:35:14Z","cross_cats_sorted":["cond-mat.dis-nn","q-bio.MN"],"title_canon_sha256":"68ab7adb42f5fbebda9fd18f1c23ee6349531972dcf908f3d7dd7b231ab42c27","abstract_canon_sha256":"4f9c8cd7bd526535b9e455e26408bf82a80be7c3747838632bad6517c364b3ed"},"schema_version":"1.0"},"canonical_sha256":"7251ca870d7ea8af655ca901ba4ba1007bca0f5a0b2ee9e50c955ed435e54fe3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:03:07.612406Z","signature_b64":"GR4Z2j0LBRnetG3ibXAAy1BgUEeq7S0fb8993JwyBFqb3B4zkVemZXUkP1lq5Snsnon46CDI4kS+RfwGyJ6NBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7251ca870d7ea8af655ca901ba4ba1007bca0f5a0b2ee9e50c955ed435e54fe3","last_reissued_at":"2026-07-04T15:03:07.612001Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:03:07.612001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.3406","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHKMyrc4CC8HbYjOTWPniR/RpdggFfWBFPMR8sfgWVtqPaWXLD7+GmHfPRVXWzQNzUCwzbTZv7g2IQRpWDm5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:13:51.852088Z"},"content_sha256":"c7a0937e6e4e0b29ccde45debbeadee74ee71cf94a4605bef94f2840d164567e","schema_version":"1.0","event_id":"sha256:c7a0937e6e4e0b29ccde45debbeadee74ee71cf94a4605bef94f2840d164567e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:OJI4VBYNP2UK6ZK4VEA3US5BAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation of external regulation and asynchronous dynamics in random Boolean networks","license":"","headline":"","cross_cats":["cond-mat.dis-nn","q-bio.MN"],"primary_cat":"cond-mat.stat-mech","authors_text":"Andrea Pagnani, Hamed Mahmoudi, Martin Weigt, Riccardo Zecchina","submitted_at":"2007-04-25T16:35:14Z","abstract_excerpt":"Boolean Networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level of understanding of asynchronous updates schemes is still very poor. In this paper we study the propagation of external information given by regulatory input variables into a random Boolean network. We compute both analytically and numerically the time evolution and the asymptotic behavior of this propagation of external regulation (PER). In particular, this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3406","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0704.3406/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXOzqfS0KT+QLq13Or6NREC1v7r60LQw6Z7Tj7SfXOzeZQK7uUi2tubOQsNQC0mZAuXogfAf9ddm3mfCjOpjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:13:51.852598Z"},"content_sha256":"49e0d60eb9d57a60ea6c5f69c66383bd339d9a736f9e4fd6676c2d39e017f5b8","schema_version":"1.0","event_id":"sha256:49e0d60eb9d57a60ea6c5f69c66383bd339d9a736f9e4fd6676c2d39e017f5b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJI4VBYNP2UK6ZK4VEA3US5BAB/bundle.json","state_url":"https://pith.science/pith/OJI4VBYNP2UK6ZK4VEA3US5BAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJI4VBYNP2UK6ZK4VEA3US5BAB/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":"2026-08-05T21:13:51Z","links":{"resolver":"https://pith.science/pith/OJI4VBYNP2UK6ZK4VEA3US5BAB","bundle":"https://pith.science/pith/OJI4VBYNP2UK6ZK4VEA3US5BAB/bundle.json","state":"https://pith.science/pith/OJI4VBYNP2UK6ZK4VEA3US5BAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJI4VBYNP2UK6ZK4VEA3US5BAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:OJI4VBYNP2UK6ZK4VEA3US5BAB","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":"4f9c8cd7bd526535b9e455e26408bf82a80be7c3747838632bad6517c364b3ed","cross_cats_sorted":["cond-mat.dis-nn","q-bio.MN"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-25T16:35:14Z","title_canon_sha256":"68ab7adb42f5fbebda9fd18f1c23ee6349531972dcf908f3d7dd7b231ab42c27"},"schema_version":"1.0","source":{"id":"0704.3406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3406","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3406v1","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3406","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"OJI4VBYNP2UK","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"pith_short_16","alias_value":"OJI4VBYNP2UK6ZK4","created_at":"2026-07-04T15:03:07Z"},{"alias_kind":"pith_short_8","alias_value":"OJI4VBYN","created_at":"2026-07-04T15:03:07Z"}],"graph_snapshots":[{"event_id":"sha256:49e0d60eb9d57a60ea6c5f69c66383bd339d9a736f9e4fd6676c2d39e017f5b8","target":"graph","created_at":"2026-07-04T15:03:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0704.3406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Boolean Networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level of understanding of asynchronous updates schemes is still very poor. In this paper we study the propagation of external information given by regulatory input variables into a random Boolean network. We compute both analytically and numerically the time evolution and the asymptotic behavior of this propagation of external regulation (PER). In particular, this","authors_text":"Andrea Pagnani, Hamed Mahmoudi, Martin Weigt, Riccardo Zecchina","cross_cats":["cond-mat.dis-nn","q-bio.MN"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-25T16:35:14Z","title":"Propagation of external regulation and asynchronous dynamics in random Boolean networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3406","kind":"arxiv","version":1},"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:c7a0937e6e4e0b29ccde45debbeadee74ee71cf94a4605bef94f2840d164567e","target":"record","created_at":"2026-07-04T15:03:07Z","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":"4f9c8cd7bd526535b9e455e26408bf82a80be7c3747838632bad6517c364b3ed","cross_cats_sorted":["cond-mat.dis-nn","q-bio.MN"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-25T16:35:14Z","title_canon_sha256":"68ab7adb42f5fbebda9fd18f1c23ee6349531972dcf908f3d7dd7b231ab42c27"},"schema_version":"1.0","source":{"id":"0704.3406","kind":"arxiv","version":1}},"canonical_sha256":"7251ca870d7ea8af655ca901ba4ba1007bca0f5a0b2ee9e50c955ed435e54fe3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7251ca870d7ea8af655ca901ba4ba1007bca0f5a0b2ee9e50c955ed435e54fe3","first_computed_at":"2026-07-04T15:03:07.612001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:03:07.612001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GR4Z2j0LBRnetG3ibXAAy1BgUEeq7S0fb8993JwyBFqb3B4zkVemZXUkP1lq5Snsnon46CDI4kS+RfwGyJ6NBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:03:07.612406Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a0937e6e4e0b29ccde45debbeadee74ee71cf94a4605bef94f2840d164567e","sha256:49e0d60eb9d57a60ea6c5f69c66383bd339d9a736f9e4fd6676c2d39e017f5b8"],"state_sha256":"1ce42351b66848b0c0ff6a175dc7bee970fa328b8196d4fbe9344ad695aba6b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7wQ27lBaekDHG4VcOLQGEYpDtQxIzFmO4ljPYXfH44/rJU3hvwLXxBq58iFr9lV1cPIoS6vtXA3DZ/tvJaTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T21:13:51.857618Z","bundle_sha256":"f1c333308a4554e56803debef83f24a68ab3796577e4ff60819f77dff540ebf1"}}