{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZD6TBO5NPZ66YD3XY66MTKLV3L","short_pith_number":"pith:ZD6TBO5N","canonical_record":{"source":{"id":"1506.06653","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-06-22T15:35:51Z","cross_cats_sorted":[],"title_canon_sha256":"4737d9d46b0d318415be2fc595fa78a2a0d249e53ae0c68e587a6cac96685763","abstract_canon_sha256":"69e73c8bfb33e570b2f0d3d6d5d4a7e66a2f15c5e9dfe4ced4261ef1af7de44f"},"schema_version":"1.0"},"canonical_sha256":"c8fd30bbad7e7dec0f77c7bcc9a975dac45ed38acdb1ab0209596aa8eefee3d7","source":{"kind":"arxiv","id":"1506.06653","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06653","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06653v2","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06653","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"ZD6TBO5NPZ66","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZD6TBO5NPZ66YD3X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZD6TBO5N","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZD6TBO5NPZ66YD3XY66MTKLV3L","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06653","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-06-22T15:35:51Z","cross_cats_sorted":[],"title_canon_sha256":"4737d9d46b0d318415be2fc595fa78a2a0d249e53ae0c68e587a6cac96685763","abstract_canon_sha256":"69e73c8bfb33e570b2f0d3d6d5d4a7e66a2f15c5e9dfe4ced4261ef1af7de44f"},"schema_version":"1.0"},"canonical_sha256":"c8fd30bbad7e7dec0f77c7bcc9a975dac45ed38acdb1ab0209596aa8eefee3d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:29.506245Z","signature_b64":"k5pT++t6LY2xO8dLlp3JpeQ5uF5v/2bCte+12LPs/Q/VNauSLj/kYxoMKRDfks+D9F65d4nQVoIOAEMzEvCADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8fd30bbad7e7dec0f77c7bcc9a975dac45ed38acdb1ab0209596aa8eefee3d7","last_reissued_at":"2026-05-18T01:20:29.505615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:29.505615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06653","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":"2026-05-18T01:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWTP2yRccmAFOnozaZ1gwzNK+Yh8ISf0Tdj7rB/hhxaPG33UWd5kGxIbSZYC0NZID3Dnvc2ccOWvyvqrjn0NCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:46:55.709331Z"},"content_sha256":"f965b060307171b0678f6d9a5f1c39740da090c6dc520fb7394cdaf1b7deb61b","schema_version":"1.0","event_id":"sha256:f965b060307171b0678f6d9a5f1c39740da090c6dc520fb7394cdaf1b7deb61b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZD6TBO5NPZ66YD3XY66MTKLV3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving two-dimensional density classification problem with two probabilistic cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CG","authors_text":"Henryk Fuk\\'s","submitted_at":"2015-06-22T15:35:51Z","abstract_excerpt":"The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which classifies binary strings according to their densities. If, however, in place of simple cells one uses agents which change their behaviour from one rule to another after a fixed number of iterations, the classification can be performed by the traffic rule 184 and the majority rule 232. This two-rule solution cannot be easily generalized to two (or higher) dimensions, because it c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06653","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":"2026-05-18T01:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umqYL1SplmK+ycHAoEoKqDF8BZ4SW4s25PC3zu7Pmg61kLYFDchifnABCMeMV6Rn7PNb3BFD9zwAd6nhppgADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:46:55.710057Z"},"content_sha256":"13f8748c45396d86f238b64745f4253229b08ba2343c69cd652c7de871a9d99a","schema_version":"1.0","event_id":"sha256:13f8748c45396d86f238b64745f4253229b08ba2343c69cd652c7de871a9d99a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZD6TBO5NPZ66YD3XY66MTKLV3L/bundle.json","state_url":"https://pith.science/pith/ZD6TBO5NPZ66YD3XY66MTKLV3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZD6TBO5NPZ66YD3XY66MTKLV3L/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":"2026-06-09T05:46:55Z","links":{"resolver":"https://pith.science/pith/ZD6TBO5NPZ66YD3XY66MTKLV3L","bundle":"https://pith.science/pith/ZD6TBO5NPZ66YD3XY66MTKLV3L/bundle.json","state":"https://pith.science/pith/ZD6TBO5NPZ66YD3XY66MTKLV3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZD6TBO5NPZ66YD3XY66MTKLV3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZD6TBO5NPZ66YD3XY66MTKLV3L","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":"69e73c8bfb33e570b2f0d3d6d5d4a7e66a2f15c5e9dfe4ced4261ef1af7de44f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-06-22T15:35:51Z","title_canon_sha256":"4737d9d46b0d318415be2fc595fa78a2a0d249e53ae0c68e587a6cac96685763"},"schema_version":"1.0","source":{"id":"1506.06653","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06653","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06653v2","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06653","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"ZD6TBO5NPZ66","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZD6TBO5NPZ66YD3X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZD6TBO5N","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:13f8748c45396d86f238b64745f4253229b08ba2343c69cd652c7de871a9d99a","target":"graph","created_at":"2026-05-18T01:20:29Z","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":"The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which classifies binary strings according to their densities. If, however, in place of simple cells one uses agents which change their behaviour from one rule to another after a fixed number of iterations, the classification can be performed by the traffic rule 184 and the majority rule 232. This two-rule solution cannot be easily generalized to two (or higher) dimensions, because it c","authors_text":"Henryk Fuk\\'s","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-06-22T15:35:51Z","title":"Solving two-dimensional density classification problem with two probabilistic cellular automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06653","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:f965b060307171b0678f6d9a5f1c39740da090c6dc520fb7394cdaf1b7deb61b","target":"record","created_at":"2026-05-18T01:20:29Z","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":"69e73c8bfb33e570b2f0d3d6d5d4a7e66a2f15c5e9dfe4ced4261ef1af7de44f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-06-22T15:35:51Z","title_canon_sha256":"4737d9d46b0d318415be2fc595fa78a2a0d249e53ae0c68e587a6cac96685763"},"schema_version":"1.0","source":{"id":"1506.06653","kind":"arxiv","version":2}},"canonical_sha256":"c8fd30bbad7e7dec0f77c7bcc9a975dac45ed38acdb1ab0209596aa8eefee3d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8fd30bbad7e7dec0f77c7bcc9a975dac45ed38acdb1ab0209596aa8eefee3d7","first_computed_at":"2026-05-18T01:20:29.505615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:29.505615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k5pT++t6LY2xO8dLlp3JpeQ5uF5v/2bCte+12LPs/Q/VNauSLj/kYxoMKRDfks+D9F65d4nQVoIOAEMzEvCADA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:29.506245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06653","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f965b060307171b0678f6d9a5f1c39740da090c6dc520fb7394cdaf1b7deb61b","sha256:13f8748c45396d86f238b64745f4253229b08ba2343c69cd652c7de871a9d99a"],"state_sha256":"f887f205afb6c23bad5291c991cd7e52694bd164a8cfd6449293d13066342808"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/bMfH59rdBwMNp3A2Y/Hbl/5ERfo4zZNFRvmVSXqLUtcmSLENjwxuitk9FmYT4MWv5oB68jg7FKgaURj7hVQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:46:55.714867Z","bundle_sha256":"2a347ece3a134ccce9b9115ce107d65c77da28e2a17064e383fc4f6dcd018592"}}