{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VBBALMV25KHVVMKOV5AJSELQXZ","short_pith_number":"pith:VBBALMV2","canonical_record":{"source":{"id":"1504.00169","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-04-01T10:10:05Z","cross_cats_sorted":["cs.CC","cs.DM","math.GR"],"title_canon_sha256":"ed2701165234accb69379d8e7b56efbd033d56541bfe8bced61179285ca39b0d","abstract_canon_sha256":"e5c960d5c98f54590c6d79f6eb5d219ef11056dc49d533059de6f003fdb062a6"},"schema_version":"1.0"},"canonical_sha256":"a84205b2baea8f5ab14eaf40991170be62e8b194fbdcbe18701331b2a53374b2","source":{"kind":"arxiv","id":"1504.00169","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00169","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00169v3","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00169","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"VBBALMV25KHV","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VBBALMV25KHVVMKO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VBBALMV2","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VBBALMV25KHVVMKOV5AJSELQXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00169","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-04-01T10:10:05Z","cross_cats_sorted":["cs.CC","cs.DM","math.GR"],"title_canon_sha256":"ed2701165234accb69379d8e7b56efbd033d56541bfe8bced61179285ca39b0d","abstract_canon_sha256":"e5c960d5c98f54590c6d79f6eb5d219ef11056dc49d533059de6f003fdb062a6"},"schema_version":"1.0"},"canonical_sha256":"a84205b2baea8f5ab14eaf40991170be62e8b194fbdcbe18701331b2a53374b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:43.835571Z","signature_b64":"fYkzZb06ZIbFFl1RxCBvyXu+HDtZ9+9V4fbgVNn25ZQzboDCbmuh+GgcfUZsHqErOFMQ5wuqbsDqHFcq0pr4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a84205b2baea8f5ab14eaf40991170be62e8b194fbdcbe18701331b2a53374b2","last_reissued_at":"2026-05-18T00:21:43.834905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:43.834905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00169","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yoviR3+wzwb/FEudBvmxcitxBQyLTfBieHtWB30HmwxFU7zeQ3WzrP2zO0ejtxYNIzL62RMl3Z+1vbN3O58jCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:58:53.609929Z"},"content_sha256":"0f0d2ec8dfebe8df2d53f468b6128dfa1aafbc27711909c0dcc181f9cfebb92f","schema_version":"1.0","event_id":"sha256:0f0d2ec8dfebe8df2d53f468b6128dfa1aafbc27711909c0dcc181f9cfebb92f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VBBALMV25KHVVMKOV5AJSELQXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete Simulation of Automata Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.GR"],"primary_cat":"cs.FL","authors_text":"Alonso Castillo-Ramirez, Florian Bridoux, Maximilien Gadouleau","submitted_at":"2015-04-01T10:10:05Z","abstract_excerpt":"Consider a finite set $A$ and an integer $n \\geq 1$. This paper studies the concept of complete simulation in the context of semigroups of transformations of $A^n$, also known as finite state-homogeneous automata networks. For $m \\geq n$, a transformation of $A^m$ is \\emph{$n$-complete of size $m$} if it may simulate every transformation of $A^n$ by updating one coordinate (or register) at a time. Using tools from memoryless computation, it is established that there is no $n$-complete transformation of size $n$, but there is such a transformation of size $n+1$. By studying the the time of simu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00169","kind":"arxiv","version":3},"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":"2026-05-18T00:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hgLIk8MFscFmWoexS+ZB0FjxvukuP9MNTXuY7lfuTl6KFGfa5BqA5k23MlMIjm+OmMQaPryE0g1aqPjfiwDgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:58:53.610600Z"},"content_sha256":"233f4214220a03dc48d55ff68ab260581da873de224ccf3b2d7802880aaa516d","schema_version":"1.0","event_id":"sha256:233f4214220a03dc48d55ff68ab260581da873de224ccf3b2d7802880aaa516d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBBALMV25KHVVMKOV5AJSELQXZ/bundle.json","state_url":"https://pith.science/pith/VBBALMV25KHVVMKOV5AJSELQXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBBALMV25KHVVMKOV5AJSELQXZ/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":"2026-05-31T03:58:53Z","links":{"resolver":"https://pith.science/pith/VBBALMV25KHVVMKOV5AJSELQXZ","bundle":"https://pith.science/pith/VBBALMV25KHVVMKOV5AJSELQXZ/bundle.json","state":"https://pith.science/pith/VBBALMV25KHVVMKOV5AJSELQXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBBALMV25KHVVMKOV5AJSELQXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VBBALMV25KHVVMKOV5AJSELQXZ","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":"e5c960d5c98f54590c6d79f6eb5d219ef11056dc49d533059de6f003fdb062a6","cross_cats_sorted":["cs.CC","cs.DM","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-04-01T10:10:05Z","title_canon_sha256":"ed2701165234accb69379d8e7b56efbd033d56541bfe8bced61179285ca39b0d"},"schema_version":"1.0","source":{"id":"1504.00169","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00169","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00169v3","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00169","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"VBBALMV25KHV","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VBBALMV25KHVVMKO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VBBALMV2","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:233f4214220a03dc48d55ff68ab260581da873de224ccf3b2d7802880aaa516d","target":"graph","created_at":"2026-05-18T00:21:43Z","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":"Consider a finite set $A$ and an integer $n \\geq 1$. This paper studies the concept of complete simulation in the context of semigroups of transformations of $A^n$, also known as finite state-homogeneous automata networks. For $m \\geq n$, a transformation of $A^m$ is \\emph{$n$-complete of size $m$} if it may simulate every transformation of $A^n$ by updating one coordinate (or register) at a time. Using tools from memoryless computation, it is established that there is no $n$-complete transformation of size $n$, but there is such a transformation of size $n+1$. By studying the the time of simu","authors_text":"Alonso Castillo-Ramirez, Florian Bridoux, Maximilien Gadouleau","cross_cats":["cs.CC","cs.DM","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-04-01T10:10:05Z","title":"Complete Simulation of Automata Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00169","kind":"arxiv","version":3},"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":"sha256:0f0d2ec8dfebe8df2d53f468b6128dfa1aafbc27711909c0dcc181f9cfebb92f","target":"record","created_at":"2026-05-18T00:21:43Z","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":"e5c960d5c98f54590c6d79f6eb5d219ef11056dc49d533059de6f003fdb062a6","cross_cats_sorted":["cs.CC","cs.DM","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-04-01T10:10:05Z","title_canon_sha256":"ed2701165234accb69379d8e7b56efbd033d56541bfe8bced61179285ca39b0d"},"schema_version":"1.0","source":{"id":"1504.00169","kind":"arxiv","version":3}},"canonical_sha256":"a84205b2baea8f5ab14eaf40991170be62e8b194fbdcbe18701331b2a53374b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a84205b2baea8f5ab14eaf40991170be62e8b194fbdcbe18701331b2a53374b2","first_computed_at":"2026-05-18T00:21:43.834905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:43.834905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fYkzZb06ZIbFFl1RxCBvyXu+HDtZ9+9V4fbgVNn25ZQzboDCbmuh+GgcfUZsHqErOFMQ5wuqbsDqHFcq0pr4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:43.835571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00169","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f0d2ec8dfebe8df2d53f468b6128dfa1aafbc27711909c0dcc181f9cfebb92f","sha256:233f4214220a03dc48d55ff68ab260581da873de224ccf3b2d7802880aaa516d"],"state_sha256":"11a45f8adbee35a738ef855991aa754c7747b2d4fecf70cc5192a884199dd803"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2B6NSQiK3ofAgDPKMn/hfXGU0SA3iCtuFKhfwSbkL6ChjR0dXDnyB/SK0l0jhaFLB16DgutVP82ZWIpv2aoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:58:53.614589Z","bundle_sha256":"c3f799e00e99a36ee9cb37672f11813dde48ffb24f289c963eb4f4249a184da5"}}