{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5WTW57OKZZJWTRL5VZEHL72FND","short_pith_number":"pith:5WTW57OK","canonical_record":{"source":{"id":"1512.03696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-11T16:24:03Z","cross_cats_sorted":["cs.FL","nlin.CG"],"title_canon_sha256":"d21e55d042bf101b90a0bde16262808b288eb4ddfa723538495dc5d8dd98bb38","abstract_canon_sha256":"8ad5a62ce426526996fa4439b65ab2bfa427bc53c627991c4bc28cf576f0fd65"},"schema_version":"1.0"},"canonical_sha256":"eda76efdcace5369c57dae4875ff4568f44f6b21a5e4296979b61df44e0246b4","source":{"kind":"arxiv","id":"1512.03696","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03696","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03696v2","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03696","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"5WTW57OKZZJW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5WTW57OKZZJWTRL5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5WTW57OK","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5WTW57OKZZJWTRL5VZEHL72FND","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-11T16:24:03Z","cross_cats_sorted":["cs.FL","nlin.CG"],"title_canon_sha256":"d21e55d042bf101b90a0bde16262808b288eb4ddfa723538495dc5d8dd98bb38","abstract_canon_sha256":"8ad5a62ce426526996fa4439b65ab2bfa427bc53c627991c4bc28cf576f0fd65"},"schema_version":"1.0"},"canonical_sha256":"eda76efdcace5369c57dae4875ff4568f44f6b21a5e4296979b61df44e0246b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:29.804628Z","signature_b64":"70lLo+qsr9FA+3/cQ9eA7N/zS6nUZfII3vI0ORQ7rmVLFNpJlRjhFrTSbScIRFrmyfysbOFUF5j7hEf0J+unAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eda76efdcace5369c57dae4875ff4568f44f6b21a5e4296979b61df44e0246b4","last_reissued_at":"2026-05-18T00:50:29.803938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:29.803938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03696","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":"2026-05-18T00:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61hiJBcmx24dL+Eofjvk+TPuZTOD0AWr3SdtSxwn2Uai8Hpl0uKoT4cUZZvmnFjmF0T8pMH/wHv3FQxwI4BNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:29:41.018223Z"},"content_sha256":"1f65c1b18120a85697a23ebc474310c5ae08ff677da26163c5853858e85ed5f4","schema_version":"1.0","event_id":"sha256:1f65c1b18120a85697a23ebc474310c5ae08ff677da26163c5853858e85ed5f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5WTW57OKZZJWTRL5VZEHL72FND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterisation of limit measures of higher-dimensional cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","nlin.CG"],"primary_cat":"math.DS","authors_text":"Benjamin Hellouin de Menibus, Martin Delacourt","submitted_at":"2015-12-11T16:24:03Z","abstract_excerpt":"We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular automaton, and consider the (set of) limit probability measure(s) as time tends to infinity. In this paper, we prove that limit measures that can be reached by higher-dimensional cellular automata are completely characterised by computability conditions, as in the one-dimensional case. This implies that cellular automata have the same variety and complexity of typic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03696","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":"2026-05-18T00:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNh0kcRWciy4ZHFSXsCrDLZ7ngMGq2lZtux2ZgWCfGD1MIoaFcQY0w7P1tEMDXwMGifUrWR2cMpTce/ffnDZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:29:41.018587Z"},"content_sha256":"99d8db76b918caa9fca534e62e684da0bb2c23a071fa5ad543ece6dc96523ea3","schema_version":"1.0","event_id":"sha256:99d8db76b918caa9fca534e62e684da0bb2c23a071fa5ad543ece6dc96523ea3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5WTW57OKZZJWTRL5VZEHL72FND/bundle.json","state_url":"https://pith.science/pith/5WTW57OKZZJWTRL5VZEHL72FND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5WTW57OKZZJWTRL5VZEHL72FND/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":"2026-06-30T23:29:41Z","links":{"resolver":"https://pith.science/pith/5WTW57OKZZJWTRL5VZEHL72FND","bundle":"https://pith.science/pith/5WTW57OKZZJWTRL5VZEHL72FND/bundle.json","state":"https://pith.science/pith/5WTW57OKZZJWTRL5VZEHL72FND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5WTW57OKZZJWTRL5VZEHL72FND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5WTW57OKZZJWTRL5VZEHL72FND","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":"8ad5a62ce426526996fa4439b65ab2bfa427bc53c627991c4bc28cf576f0fd65","cross_cats_sorted":["cs.FL","nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-11T16:24:03Z","title_canon_sha256":"d21e55d042bf101b90a0bde16262808b288eb4ddfa723538495dc5d8dd98bb38"},"schema_version":"1.0","source":{"id":"1512.03696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03696","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03696v2","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03696","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"5WTW57OKZZJW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5WTW57OKZZJWTRL5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5WTW57OK","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:99d8db76b918caa9fca534e62e684da0bb2c23a071fa5ad543ece6dc96523ea3","target":"graph","created_at":"2026-05-18T00:50:29Z","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":"We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular automaton, and consider the (set of) limit probability measure(s) as time tends to infinity. In this paper, we prove that limit measures that can be reached by higher-dimensional cellular automata are completely characterised by computability conditions, as in the one-dimensional case. This implies that cellular automata have the same variety and complexity of typic","authors_text":"Benjamin Hellouin de Menibus, Martin Delacourt","cross_cats":["cs.FL","nlin.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-11T16:24:03Z","title":"Characterisation of limit measures of higher-dimensional cellular automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03696","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":"sha256:1f65c1b18120a85697a23ebc474310c5ae08ff677da26163c5853858e85ed5f4","target":"record","created_at":"2026-05-18T00:50:29Z","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":"8ad5a62ce426526996fa4439b65ab2bfa427bc53c627991c4bc28cf576f0fd65","cross_cats_sorted":["cs.FL","nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-11T16:24:03Z","title_canon_sha256":"d21e55d042bf101b90a0bde16262808b288eb4ddfa723538495dc5d8dd98bb38"},"schema_version":"1.0","source":{"id":"1512.03696","kind":"arxiv","version":2}},"canonical_sha256":"eda76efdcace5369c57dae4875ff4568f44f6b21a5e4296979b61df44e0246b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eda76efdcace5369c57dae4875ff4568f44f6b21a5e4296979b61df44e0246b4","first_computed_at":"2026-05-18T00:50:29.803938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:29.803938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"70lLo+qsr9FA+3/cQ9eA7N/zS6nUZfII3vI0ORQ7rmVLFNpJlRjhFrTSbScIRFrmyfysbOFUF5j7hEf0J+unAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:29.804628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f65c1b18120a85697a23ebc474310c5ae08ff677da26163c5853858e85ed5f4","sha256:99d8db76b918caa9fca534e62e684da0bb2c23a071fa5ad543ece6dc96523ea3"],"state_sha256":"d407e1915b44ff48d0ad414ec87daeb4268641879cff4f33e767d1235ddcba85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ytdhw/IvXvoL9U/7iwL4qNt35C5rjjuTsHxifDqnwlSUnoibxuThssc71/gnFS0ISzCUpM9PIsjf5qjjVjVHDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:29:41.020767Z","bundle_sha256":"5836403d669cccb553eb600db51f8ff715bb34a7e67b9917bfe4212460d1b808"}}