{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3MNQQ5EOGLK2UYP6IBGUXBOWKU","short_pith_number":"pith:3MNQQ5EO","canonical_record":{"source":{"id":"1001.5470","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-01-29T20:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"ccc4e1d473087dae41311a2a5673ef734bf311381855f407b79862cb54ab9bc6","abstract_canon_sha256":"1281187d7b1ef10cf8d6e14cc4054ddffa3a35a0fd3db121f5c25b8acfa99f97"},"schema_version":"1.0"},"canonical_sha256":"db1b08748e32d5aa61fe404d4b85d6550fc92a8ed1df2bb251710eb842782a76","source":{"kind":"arxiv","id":"1001.5470","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5470","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5470v2","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5470","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"3MNQQ5EOGLK2","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3MNQQ5EOGLK2UYP6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3MNQQ5EO","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3MNQQ5EOGLK2UYP6IBGUXBOWKU","target":"record","payload":{"canonical_record":{"source":{"id":"1001.5470","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-01-29T20:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"ccc4e1d473087dae41311a2a5673ef734bf311381855f407b79862cb54ab9bc6","abstract_canon_sha256":"1281187d7b1ef10cf8d6e14cc4054ddffa3a35a0fd3db121f5c25b8acfa99f97"},"schema_version":"1.0"},"canonical_sha256":"db1b08748e32d5aa61fe404d4b85d6550fc92a8ed1df2bb251710eb842782a76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:02.610278Z","signature_b64":"cwKb2l1hSy494fUXFVjxWj5quPaplPGSC2ADKSa5ZcTTmEKFsQzDno0SV2GGItwLTm+/gVSh2WmXh5YNMR+8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db1b08748e32d5aa61fe404d4b85d6550fc92a8ed1df2bb251710eb842782a76","last_reissued_at":"2026-05-18T04:42:02.609792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:02.609792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.5470","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":"2026-05-18T04:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2ca0ZX0JOdSQzfU4SZacreyMHEcezlFfrikLEmz6hbfATB1dJYHWPFlJ6VM5V/clZLKTQQ4hTsLiJw6NOV+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:32:02.460854Z"},"content_sha256":"b21e1aa44fa7b70a0da5484dd4287e80da57fb40ce6a1ad272e1e927e710d535","schema_version":"1.0","event_id":"sha256:b21e1aa44fa7b70a0da5484dd4287e80da57fb40ce6a1ad272e1e927e710d535"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3MNQQ5EOGLK2UYP6IBGUXBOWKU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Directional Dynamics along Arbitrary Curves in Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Guillaume Theyssier (LAMA), Martin Delacourt (LIF), Mathieu Sablik (LATP), Victor Poupet (LIF)","submitted_at":"2010-01-29T20:14:33Z","abstract_excerpt":"This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule (temporal action) and the shift map (spacial action): qualitative behaviours inherited from topological dynamics (equicontinuity, sensitivity, expansivity) are thus considered along arbitrary curves in space-time. The main contributions of the paper concern equicontinuous dynamics which can be connected to the notion of consequences of a word. We show that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5470","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":"2026-05-18T04:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sq+nwnw3sybxBwxb4W11nV+3C1s4BqC/mHI+wizzed2/cdHI0v8Z4FCZT3qEQIOpb6nSfdX7Q99xnxKptmOpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:32:02.461203Z"},"content_sha256":"4af7faedc5c4d0c6e9afb811849ca165b3f93793a8055dbe2c1d00fab1576bf8","schema_version":"1.0","event_id":"sha256:4af7faedc5c4d0c6e9afb811849ca165b3f93793a8055dbe2c1d00fab1576bf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3MNQQ5EOGLK2UYP6IBGUXBOWKU/bundle.json","state_url":"https://pith.science/pith/3MNQQ5EOGLK2UYP6IBGUXBOWKU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3MNQQ5EOGLK2UYP6IBGUXBOWKU/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":"2026-07-01T02:32:02Z","links":{"resolver":"https://pith.science/pith/3MNQQ5EOGLK2UYP6IBGUXBOWKU","bundle":"https://pith.science/pith/3MNQQ5EOGLK2UYP6IBGUXBOWKU/bundle.json","state":"https://pith.science/pith/3MNQQ5EOGLK2UYP6IBGUXBOWKU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3MNQQ5EOGLK2UYP6IBGUXBOWKU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3MNQQ5EOGLK2UYP6IBGUXBOWKU","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":"1281187d7b1ef10cf8d6e14cc4054ddffa3a35a0fd3db121f5c25b8acfa99f97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-01-29T20:14:33Z","title_canon_sha256":"ccc4e1d473087dae41311a2a5673ef734bf311381855f407b79862cb54ab9bc6"},"schema_version":"1.0","source":{"id":"1001.5470","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5470","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5470v2","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5470","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"3MNQQ5EOGLK2","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3MNQQ5EOGLK2UYP6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3MNQQ5EO","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:4af7faedc5c4d0c6e9afb811849ca165b3f93793a8055dbe2c1d00fab1576bf8","target":"graph","created_at":"2026-05-18T04:42:02Z","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":"This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule (temporal action) and the shift map (spacial action): qualitative behaviours inherited from topological dynamics (equicontinuity, sensitivity, expansivity) are thus considered along arbitrary curves in space-time. The main contributions of the paper concern equicontinuous dynamics which can be connected to the notion of consequences of a word. We show that ","authors_text":"Guillaume Theyssier (LAMA), Martin Delacourt (LIF), Mathieu Sablik (LATP), Victor Poupet (LIF)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-01-29T20:14:33Z","title":"Directional Dynamics along Arbitrary Curves in Cellular Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5470","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:b21e1aa44fa7b70a0da5484dd4287e80da57fb40ce6a1ad272e1e927e710d535","target":"record","created_at":"2026-05-18T04:42:02Z","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":"1281187d7b1ef10cf8d6e14cc4054ddffa3a35a0fd3db121f5c25b8acfa99f97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-01-29T20:14:33Z","title_canon_sha256":"ccc4e1d473087dae41311a2a5673ef734bf311381855f407b79862cb54ab9bc6"},"schema_version":"1.0","source":{"id":"1001.5470","kind":"arxiv","version":2}},"canonical_sha256":"db1b08748e32d5aa61fe404d4b85d6550fc92a8ed1df2bb251710eb842782a76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db1b08748e32d5aa61fe404d4b85d6550fc92a8ed1df2bb251710eb842782a76","first_computed_at":"2026-05-18T04:42:02.609792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:02.609792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cwKb2l1hSy494fUXFVjxWj5quPaplPGSC2ADKSa5ZcTTmEKFsQzDno0SV2GGItwLTm+/gVSh2WmXh5YNMR+8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:02.610278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.5470","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b21e1aa44fa7b70a0da5484dd4287e80da57fb40ce6a1ad272e1e927e710d535","sha256:4af7faedc5c4d0c6e9afb811849ca165b3f93793a8055dbe2c1d00fab1576bf8"],"state_sha256":"866d23408880e2fba005258c7e126dfb6e0e70590fa36e3c88f36ef6b6a9d04e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YxHFjRu6cY8KhIH6eofQUYyXyh2C6lmZjbeQp6bEXMVgyc/br6XhWY0fI1WKWcdZvbxHZcd535b5EDQH2CjbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T02:32:02.463213Z","bundle_sha256":"7c5362b84891df3fc1b61d63bec4414e05ea73885d6c3751bb7e5846f0955d06"}}