{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7P5PRFRZ3BDTCQSGPOWAQTVVT4","short_pith_number":"pith:7P5PRFRZ","canonical_record":{"source":{"id":"1601.05694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-21T16:17:42Z","cross_cats_sorted":[],"title_canon_sha256":"8bce2c6631e4bb8143f8642d2190a8962e58edc85c9db0a8c4079af4ffbab162","abstract_canon_sha256":"e8791e678070573fd6d2a0a8ef0a4c3639e0bafa80277fc225be8282f65b213e"},"schema_version":"1.0"},"canonical_sha256":"fbfaf89639d8473142467bac084eb59f1f91c190d5dc9de22ba8d2fe70832292","source":{"kind":"arxiv","id":"1601.05694","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05694","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05694v1","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05694","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"7P5PRFRZ3BDT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7P5PRFRZ3BDTCQSG","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7P5PRFRZ","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7P5PRFRZ3BDTCQSGPOWAQTVVT4","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-21T16:17:42Z","cross_cats_sorted":[],"title_canon_sha256":"8bce2c6631e4bb8143f8642d2190a8962e58edc85c9db0a8c4079af4ffbab162","abstract_canon_sha256":"e8791e678070573fd6d2a0a8ef0a4c3639e0bafa80277fc225be8282f65b213e"},"schema_version":"1.0"},"canonical_sha256":"fbfaf89639d8473142467bac084eb59f1f91c190d5dc9de22ba8d2fe70832292","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:23.632670Z","signature_b64":"86qNQUbG3HUvbcB9mb/QZ4yXtZwtxddxqheEqq7Hx8IafgzHMHOsNWt5L7614I6/5CvVOdJYE0gNEKwqjjfdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbfaf89639d8473142467bac084eb59f1f91c190d5dc9de22ba8d2fe70832292","last_reissued_at":"2026-05-18T00:52:23.632237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:23.632237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05694","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":"2026-05-18T00:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/Fl7l8On73OpBIgmb/5uakw9HAOTu2HqNuzGjmKvA/3BjQHRyEoHKbs/MZHe8Ba27swbL9/Eg3n/Gy3Ev/oBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:59:15.507669Z"},"content_sha256":"d629185f5e61786cc9166f178ca5fdbb535402b5d168e41597753f16e953a2fe","schema_version":"1.0","event_id":"sha256:d629185f5e61786cc9166f178ca5fdbb535402b5d168e41597753f16e953a2fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7P5PRFRZ3BDTCQSGPOWAQTVVT4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Finite Monoids of Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alonso Castillo-Ramirez, Maximilien Gadouleau","submitted_at":"2016-01-21T16:17:42Z","abstract_excerpt":"For any group $G$ and set $A$, a cellular automaton over $G$ and $A$ is a transformation $\\tau : A^G \\to A^G$ defined via a finite neighborhood $S \\subseteq G$ (called a memory set of $\\tau$) and a local function $\\mu : A^S \\to A$. In this paper, we assume that $G$ and $A$ are both finite and study various algebraic properties of the finite monoid $\\text{CA}(G,A)$ consisting of all cellular automata over $G$ and $A$. Let $\\text{ICA}(G;A)$ be the group of invertible cellular automata over $G$ and $A$. In the first part, using information on the conjugacy classes of subgroups of $G$, we give a d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05694","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":"2026-05-18T00:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UAIsY7DoI0c+oVIB7CGiZan5I3rNy2Pyo+Z959AFi2LlFnQsxHWNuFHhWf5cOOPUWSQPRBPVpAN+X/oSlYeFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:59:15.508104Z"},"content_sha256":"542d9615de6b9b2e59734ca6cfb2d1d7c8c6f5c7ddd98ca2bc800d08f05c94b1","schema_version":"1.0","event_id":"sha256:542d9615de6b9b2e59734ca6cfb2d1d7c8c6f5c7ddd98ca2bc800d08f05c94b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7P5PRFRZ3BDTCQSGPOWAQTVVT4/bundle.json","state_url":"https://pith.science/pith/7P5PRFRZ3BDTCQSGPOWAQTVVT4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7P5PRFRZ3BDTCQSGPOWAQTVVT4/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":"2026-05-31T03:59:15Z","links":{"resolver":"https://pith.science/pith/7P5PRFRZ3BDTCQSGPOWAQTVVT4","bundle":"https://pith.science/pith/7P5PRFRZ3BDTCQSGPOWAQTVVT4/bundle.json","state":"https://pith.science/pith/7P5PRFRZ3BDTCQSGPOWAQTVVT4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7P5PRFRZ3BDTCQSGPOWAQTVVT4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7P5PRFRZ3BDTCQSGPOWAQTVVT4","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":"e8791e678070573fd6d2a0a8ef0a4c3639e0bafa80277fc225be8282f65b213e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-21T16:17:42Z","title_canon_sha256":"8bce2c6631e4bb8143f8642d2190a8962e58edc85c9db0a8c4079af4ffbab162"},"schema_version":"1.0","source":{"id":"1601.05694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05694","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05694v1","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05694","created_at":"2026-05-18T00:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"7P5PRFRZ3BDT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7P5PRFRZ3BDTCQSG","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7P5PRFRZ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:542d9615de6b9b2e59734ca6cfb2d1d7c8c6f5c7ddd98ca2bc800d08f05c94b1","target":"graph","created_at":"2026-05-18T00:52:23Z","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":"For any group $G$ and set $A$, a cellular automaton over $G$ and $A$ is a transformation $\\tau : A^G \\to A^G$ defined via a finite neighborhood $S \\subseteq G$ (called a memory set of $\\tau$) and a local function $\\mu : A^S \\to A$. In this paper, we assume that $G$ and $A$ are both finite and study various algebraic properties of the finite monoid $\\text{CA}(G,A)$ consisting of all cellular automata over $G$ and $A$. Let $\\text{ICA}(G;A)$ be the group of invertible cellular automata over $G$ and $A$. In the first part, using information on the conjugacy classes of subgroups of $G$, we give a d","authors_text":"Alonso Castillo-Ramirez, Maximilien Gadouleau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-21T16:17:42Z","title":"On Finite Monoids of Cellular Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05694","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:d629185f5e61786cc9166f178ca5fdbb535402b5d168e41597753f16e953a2fe","target":"record","created_at":"2026-05-18T00:52:23Z","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":"e8791e678070573fd6d2a0a8ef0a4c3639e0bafa80277fc225be8282f65b213e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-01-21T16:17:42Z","title_canon_sha256":"8bce2c6631e4bb8143f8642d2190a8962e58edc85c9db0a8c4079af4ffbab162"},"schema_version":"1.0","source":{"id":"1601.05694","kind":"arxiv","version":1}},"canonical_sha256":"fbfaf89639d8473142467bac084eb59f1f91c190d5dc9de22ba8d2fe70832292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbfaf89639d8473142467bac084eb59f1f91c190d5dc9de22ba8d2fe70832292","first_computed_at":"2026-05-18T00:52:23.632237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:23.632237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86qNQUbG3HUvbcB9mb/QZ4yXtZwtxddxqheEqq7Hx8IafgzHMHOsNWt5L7614I6/5CvVOdJYE0gNEKwqjjfdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:23.632670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d629185f5e61786cc9166f178ca5fdbb535402b5d168e41597753f16e953a2fe","sha256:542d9615de6b9b2e59734ca6cfb2d1d7c8c6f5c7ddd98ca2bc800d08f05c94b1"],"state_sha256":"ccb06135af7cef961c5444a9731c4c22b3af23b89208d7606c02d80dc5d90783"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+mUaJBmTRNzJ3btsb9OCtp/5uXbSj7ANYAwE0ZHMfPLocTFvFArFdCtoxltMvXSs0KQnfFbITj8cWCVrL77DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:59:15.511257Z","bundle_sha256":"b22ab31f90b0e7ab266f24a8245ae551c4aa54058c9689fd73752f96128bcb3b"}}