{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3FNNXA2TGNXSH2NCPEB6BQAOFG","short_pith_number":"pith:3FNNXA2T","canonical_record":{"source":{"id":"1011.5119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2010-11-23T14:47:11Z","cross_cats_sorted":["cs.DC","cs.DM","math.CO","math.PR"],"title_canon_sha256":"f4423b2006d71a86602e7ba2223f489ffaa4cd8cc8289c91067bcaca8dba8aaa","abstract_canon_sha256":"7091a1385ba6f36717980b5399de744325fba465b877e4905ba19a6f6cb01a7a"},"schema_version":"1.0"},"canonical_sha256":"d95adb8353336f23e9a27903e0c00e29af3b08bb92c351f744c5ea768554d8ef","source":{"kind":"arxiv","id":"1011.5119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5119","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5119v1","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5119","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"3FNNXA2TGNXS","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3FNNXA2TGNXSH2NC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3FNNXA2T","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3FNNXA2TGNXSH2NCPEB6BQAOFG","target":"record","payload":{"canonical_record":{"source":{"id":"1011.5119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2010-11-23T14:47:11Z","cross_cats_sorted":["cs.DC","cs.DM","math.CO","math.PR"],"title_canon_sha256":"f4423b2006d71a86602e7ba2223f489ffaa4cd8cc8289c91067bcaca8dba8aaa","abstract_canon_sha256":"7091a1385ba6f36717980b5399de744325fba465b877e4905ba19a6f6cb01a7a"},"schema_version":"1.0"},"canonical_sha256":"d95adb8353336f23e9a27903e0c00e29af3b08bb92c351f744c5ea768554d8ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:54.778094Z","signature_b64":"hW1QFEaBE3mFGnFSEvhyoKFpcehPlJwkYoBDZSEA6mfgXnscI/6uyiTL5ta1KWKtq1YEgaNSLwP6+iCnndzeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d95adb8353336f23e9a27903e0c00e29af3b08bb92c351f744c5ea768554d8ef","last_reissued_at":"2026-05-18T04:34:54.777700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:54.777700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.5119","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":"2026-05-18T04:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6nhRiB4UEMM1kPiyKUKSTVKHW8Jfg1dIP+JHD/JVdOAQoZmXCqEE2NAqj3NrXlLxcK+xUFhyNN6ys6NBFpfiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:01:13.103958Z"},"content_sha256":"572b06dd80891138d1c4041838bffe77161cc52168a2bc3349afdd04e668c30e","schema_version":"1.0","event_id":"sha256:572b06dd80891138d1c4041838bffe77161cc52168a2bc3349afdd04e668c30e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3FNNXA2TGNXSH2NCPEB6BQAOFG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Minority on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.DM","math.CO","math.PR"],"primary_cat":"nlin.CG","authors_text":"Damien Regnault, Eric Thierry1, Jean-Baptiste Rouquier","submitted_at":"2010-11-23T14:47:11Z","abstract_excerpt":"Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical Minority rule. Minority has been well-studied for synchronous updates and is thus a reasonable choice to begin with. Yet, beyond its apparent simplicity, this rule yields complex behaviors when asynchronism is introduced. We investigate the transitory part as well as the asymptotic behavior of the dynamics under full asyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5119","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":""},"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":"2026-05-18T04:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lcf6GiL4zfXtfOLWxb9DuSFOGFWDRTkHURjjEIbwfgM53PJfqQCbJX/OzUUo5nwd1b7iS3w+Qs7hr4jpFezIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:01:13.104695Z"},"content_sha256":"64feb2532763c96143859ccb779c66517555d6536fffc680880991ad649e6ca8","schema_version":"1.0","event_id":"sha256:64feb2532763c96143859ccb779c66517555d6536fffc680880991ad649e6ca8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FNNXA2TGNXSH2NCPEB6BQAOFG/bundle.json","state_url":"https://pith.science/pith/3FNNXA2TGNXSH2NCPEB6BQAOFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FNNXA2TGNXSH2NCPEB6BQAOFG/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":"2026-05-25T17:01:13Z","links":{"resolver":"https://pith.science/pith/3FNNXA2TGNXSH2NCPEB6BQAOFG","bundle":"https://pith.science/pith/3FNNXA2TGNXSH2NCPEB6BQAOFG/bundle.json","state":"https://pith.science/pith/3FNNXA2TGNXSH2NCPEB6BQAOFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FNNXA2TGNXSH2NCPEB6BQAOFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3FNNXA2TGNXSH2NCPEB6BQAOFG","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":"7091a1385ba6f36717980b5399de744325fba465b877e4905ba19a6f6cb01a7a","cross_cats_sorted":["cs.DC","cs.DM","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2010-11-23T14:47:11Z","title_canon_sha256":"f4423b2006d71a86602e7ba2223f489ffaa4cd8cc8289c91067bcaca8dba8aaa"},"schema_version":"1.0","source":{"id":"1011.5119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5119","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5119v1","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5119","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"3FNNXA2TGNXS","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3FNNXA2TGNXSH2NC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3FNNXA2T","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:64feb2532763c96143859ccb779c66517555d6536fffc680880991ad649e6ca8","target":"graph","created_at":"2026-05-18T04:34:54Z","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":"Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical Minority rule. Minority has been well-studied for synchronous updates and is thus a reasonable choice to begin with. Yet, beyond its apparent simplicity, this rule yields complex behaviors when asynchronism is introduced. We investigate the transitory part as well as the asymptotic behavior of the dynamics under full asyn","authors_text":"Damien Regnault, Eric Thierry1, Jean-Baptiste Rouquier","cross_cats":["cs.DC","cs.DM","math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2010-11-23T14:47:11Z","title":"Stochastic Minority on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5119","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":"sha256:572b06dd80891138d1c4041838bffe77161cc52168a2bc3349afdd04e668c30e","target":"record","created_at":"2026-05-18T04:34:54Z","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":"7091a1385ba6f36717980b5399de744325fba465b877e4905ba19a6f6cb01a7a","cross_cats_sorted":["cs.DC","cs.DM","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2010-11-23T14:47:11Z","title_canon_sha256":"f4423b2006d71a86602e7ba2223f489ffaa4cd8cc8289c91067bcaca8dba8aaa"},"schema_version":"1.0","source":{"id":"1011.5119","kind":"arxiv","version":1}},"canonical_sha256":"d95adb8353336f23e9a27903e0c00e29af3b08bb92c351f744c5ea768554d8ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d95adb8353336f23e9a27903e0c00e29af3b08bb92c351f744c5ea768554d8ef","first_computed_at":"2026-05-18T04:34:54.777700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:54.777700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hW1QFEaBE3mFGnFSEvhyoKFpcehPlJwkYoBDZSEA6mfgXnscI/6uyiTL5ta1KWKtq1YEgaNSLwP6+iCnndzeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:54.778094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:572b06dd80891138d1c4041838bffe77161cc52168a2bc3349afdd04e668c30e","sha256:64feb2532763c96143859ccb779c66517555d6536fffc680880991ad649e6ca8"],"state_sha256":"3624ade1030178445c948c0c8ef73e65ab882b0b6786392e314a97feb6258bbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"37V7IrlMWw2mR01TC8ogQhSHgEL+YebNujsvppI96q+NFMhOCuDkecMEpGGosgJU6Ip3vHQA+Z+eGNUmnUKsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:01:13.108855Z","bundle_sha256":"e030ae4b8ec3683c392b7ac539e2c6f42e65409334a691971bce10d1ca5f4ad7"}}