{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R5TYBRHZB2HYECR7GJJO4YLTLO","short_pith_number":"pith:R5TYBRHZ","canonical_record":{"source":{"id":"1704.00716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2017-04-03T17:57:49Z","cross_cats_sorted":[],"title_canon_sha256":"d4ec7fabc84cbee399b501a764bc43cff9d964379bc24ccc96eda3296825e100","abstract_canon_sha256":"cfdfbdea7d08c70fac33d4dfaecaa8cf597ef6f100d44756ff55ea3ddaf9f555"},"schema_version":"1.0"},"canonical_sha256":"8f6780c4f90e8f820a3f3252ee61735bb7c0f612fe4c617eab206fdfd936bf50","source":{"kind":"arxiv","id":"1704.00716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00716","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00716v1","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00716","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"R5TYBRHZB2HY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R5TYBRHZB2HYECR7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R5TYBRHZ","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R5TYBRHZB2HYECR7GJJO4YLTLO","target":"record","payload":{"canonical_record":{"source":{"id":"1704.00716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2017-04-03T17:57:49Z","cross_cats_sorted":[],"title_canon_sha256":"d4ec7fabc84cbee399b501a764bc43cff9d964379bc24ccc96eda3296825e100","abstract_canon_sha256":"cfdfbdea7d08c70fac33d4dfaecaa8cf597ef6f100d44756ff55ea3ddaf9f555"},"schema_version":"1.0"},"canonical_sha256":"8f6780c4f90e8f820a3f3252ee61735bb7c0f612fe4c617eab206fdfd936bf50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:21.506627Z","signature_b64":"nHIEJi6nBC5sWpXAO95l1h3/vpuaLN80qL0dAp2perLedKNTJsAzxiv9j6gewOj2S6Yx94UnUmn25t7YegDDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f6780c4f90e8f820a3f3252ee61735bb7c0f612fe4c617eab206fdfd936bf50","last_reissued_at":"2026-05-18T00:47:21.506059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:21.506059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.00716","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":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6PmqbOO16t2gU6zlXZFKWQVbbEdLNODOvgKCO/ru9u9crog6wRW0A/SxLmuw1UByfvc1X+T7dJ/CeMiYaqgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:45:26.652605Z"},"content_sha256":"2f654459fd9b0fca2dab7c675b7cf2eeef553d423f0ea2451c31ff53c86c4c6c","schema_version":"1.0","event_id":"sha256:2f654459fd9b0fca2dab7c675b7cf2eeef553d423f0ea2451c31ff53c86c4c6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R5TYBRHZB2HYECR7GJJO4YLTLO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CG","authors_text":"Henryk Fuk\\'s, Joel Midgley-Volpato","submitted_at":"2017-04-03T17:57:49Z","abstract_excerpt":"In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also calculated densities of 0, 1 and 2 after n iterations of this rule, using finite state machines to conjecture patterns present in preimage sets. Here, we re-derive the same formulae in a rigorous way, without resorting to any semi-empirical methods. This is done by analysing the behaviour of continuous clusters of symbols and by considering their interactions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00716","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":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GBxuXG6MqK35eWTZ1emmSR3YkOajzM3RprwX0RJU+C/iritSOFm9SKKl3Jf8aBHVxnc+R/k1qKDDPEFhb8gJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:45:26.653352Z"},"content_sha256":"4685f68b0b978f016de09765fb43958500b506429483099d4df2d9dbd229a786","schema_version":"1.0","event_id":"sha256:4685f68b0b978f016de09765fb43958500b506429483099d4df2d9dbd229a786"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R5TYBRHZB2HYECR7GJJO4YLTLO/bundle.json","state_url":"https://pith.science/pith/R5TYBRHZB2HYECR7GJJO4YLTLO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R5TYBRHZB2HYECR7GJJO4YLTLO/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":"2026-06-09T02:45:26Z","links":{"resolver":"https://pith.science/pith/R5TYBRHZB2HYECR7GJJO4YLTLO","bundle":"https://pith.science/pith/R5TYBRHZB2HYECR7GJJO4YLTLO/bundle.json","state":"https://pith.science/pith/R5TYBRHZB2HYECR7GJJO4YLTLO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R5TYBRHZB2HYECR7GJJO4YLTLO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R5TYBRHZB2HYECR7GJJO4YLTLO","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":"cfdfbdea7d08c70fac33d4dfaecaa8cf597ef6f100d44756ff55ea3ddaf9f555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2017-04-03T17:57:49Z","title_canon_sha256":"d4ec7fabc84cbee399b501a764bc43cff9d964379bc24ccc96eda3296825e100"},"schema_version":"1.0","source":{"id":"1704.00716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00716","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00716v1","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00716","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"R5TYBRHZB2HY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R5TYBRHZB2HYECR7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R5TYBRHZ","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:4685f68b0b978f016de09765fb43958500b506429483099d4df2d9dbd229a786","target":"graph","created_at":"2026-05-18T00:47:21Z","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":"In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also calculated densities of 0, 1 and 2 after n iterations of this rule, using finite state machines to conjecture patterns present in preimage sets. Here, we re-derive the same formulae in a rigorous way, without resorting to any semi-empirical methods. This is done by analysing the behaviour of continuous clusters of symbols and by considering their interactions.","authors_text":"Henryk Fuk\\'s, Joel Midgley-Volpato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2017-04-03T17:57:49Z","title":"An example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00716","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":"sha256:2f654459fd9b0fca2dab7c675b7cf2eeef553d423f0ea2451c31ff53c86c4c6c","target":"record","created_at":"2026-05-18T00:47:21Z","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":"cfdfbdea7d08c70fac33d4dfaecaa8cf597ef6f100d44756ff55ea3ddaf9f555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2017-04-03T17:57:49Z","title_canon_sha256":"d4ec7fabc84cbee399b501a764bc43cff9d964379bc24ccc96eda3296825e100"},"schema_version":"1.0","source":{"id":"1704.00716","kind":"arxiv","version":1}},"canonical_sha256":"8f6780c4f90e8f820a3f3252ee61735bb7c0f612fe4c617eab206fdfd936bf50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f6780c4f90e8f820a3f3252ee61735bb7c0f612fe4c617eab206fdfd936bf50","first_computed_at":"2026-05-18T00:47:21.506059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:21.506059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nHIEJi6nBC5sWpXAO95l1h3/vpuaLN80qL0dAp2perLedKNTJsAzxiv9j6gewOj2S6Yx94UnUmn25t7YegDDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:21.506627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f654459fd9b0fca2dab7c675b7cf2eeef553d423f0ea2451c31ff53c86c4c6c","sha256:4685f68b0b978f016de09765fb43958500b506429483099d4df2d9dbd229a786"],"state_sha256":"12fc64968e4e216068894465d7c2b115a3b14025cfb05179e42ed36293cc6033"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DSfDk/FaG43YtBml+CJxPrh+RZCG4h9uWnDkonA5pAe5wf7GOiehCNY5FQ86wSt80RlZvO0KD9tmOjcStEJ/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:45:26.656893Z","bundle_sha256":"d232709107473a844e9312c179d2a55233ed1c827944d62e78942d85fc57bcc1"}}