{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SY6RVM4QVUIL3BSEHHYKXT6B3Q","short_pith_number":"pith:SY6RVM4Q","canonical_record":{"source":{"id":"1703.07289","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T15:56:32Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8cfe2022bd0e1a1b4459973a4dd6b2ac62dd09bd6329729d26f954ce37abc74c","abstract_canon_sha256":"3936389f012d097892bf7ca0cbc00dc01de70e66af76d182750848b3d63dc296"},"schema_version":"1.0"},"canonical_sha256":"963d1ab390ad10bd864439f0abcfc1dc3c2e067fd7ddcef88817fa0bfb2fde11","source":{"kind":"arxiv","id":"1703.07289","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07289","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07289v2","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07289","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"SY6RVM4QVUIL","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SY6RVM4QVUIL3BSE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SY6RVM4Q","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SY6RVM4QVUIL3BSEHHYKXT6B3Q","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07289","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T15:56:32Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8cfe2022bd0e1a1b4459973a4dd6b2ac62dd09bd6329729d26f954ce37abc74c","abstract_canon_sha256":"3936389f012d097892bf7ca0cbc00dc01de70e66af76d182750848b3d63dc296"},"schema_version":"1.0"},"canonical_sha256":"963d1ab390ad10bd864439f0abcfc1dc3c2e067fd7ddcef88817fa0bfb2fde11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:56.696268Z","signature_b64":"hvJkL7bsmX/NzE9ZGphFvujSs8x4ohQqCL4lxN8uvM1aLBx34oGE3XH0PdvzkeMXdrQmc1lZmyonQAF2dU/ZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"963d1ab390ad10bd864439f0abcfc1dc3c2e067fd7ddcef88817fa0bfb2fde11","last_reissued_at":"2026-05-18T00:23:56.695580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:56.695580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07289","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":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"16kHEamJespPDIS2m9vhEBqBHT/6C2UD8jjcg+Xfh8TBhKQtGuBZt7uYSyeD0SWjP8g1Lhm6MSO2AEI3bmMbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:57:26.273001Z"},"content_sha256":"d9432bd3c256c2209f4d39a44efdaf01f7915f880420a9561e4092e9f9ecc3b3","schema_version":"1.0","event_id":"sha256:d9432bd3c256c2209f4d39a44efdaf01f7915f880420a9561e4092e9f9ecc3b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SY6RVM4QVUIL3BSEHHYKXT6B3Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing Asymptotic Randomization in Abelian Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.DS","authors_text":"Benjamin Hellouin de Menibus (IRIF), Guillaume Theyssier (I2M), Ville Salo","submitted_at":"2017-03-21T15:56:32Z","abstract_excerpt":"Abelian cellular automata (CA) are CA which are group endomorphisms of the full group shift when endowing the alphabet with an abelian group structure. A CA randomizes an initial probability measure if its iterated images weak *-converge towards the uniform Bernoulli measure (the Haar measure in this setting). We are interested in structural phenomena, i.e. randomization for a wide class of initial measures (under some mixing hypotheses). First, we prove that an abelian CA randomizes in Ces{\\`a}ro mean if and only if it has no soliton, i.e. a finite configuration whose time evolution remains b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07289","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":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1zPO5ROgqAPdcvF7ME3sNHkniGmgElF17NrCW+3TW/aqPgIJNlqlykSuSovZ6bGG5om3IYjNHKqhx5KXZhimCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:57:26.273741Z"},"content_sha256":"213c61380b8d99fc55362a98fb5ff61ac9fe0f58d433ab1d48aa48a89be3da6d","schema_version":"1.0","event_id":"sha256:213c61380b8d99fc55362a98fb5ff61ac9fe0f58d433ab1d48aa48a89be3da6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SY6RVM4QVUIL3BSEHHYKXT6B3Q/bundle.json","state_url":"https://pith.science/pith/SY6RVM4QVUIL3BSEHHYKXT6B3Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SY6RVM4QVUIL3BSEHHYKXT6B3Q/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":"2026-06-09T04:57:26Z","links":{"resolver":"https://pith.science/pith/SY6RVM4QVUIL3BSEHHYKXT6B3Q","bundle":"https://pith.science/pith/SY6RVM4QVUIL3BSEHHYKXT6B3Q/bundle.json","state":"https://pith.science/pith/SY6RVM4QVUIL3BSEHHYKXT6B3Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SY6RVM4QVUIL3BSEHHYKXT6B3Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SY6RVM4QVUIL3BSEHHYKXT6B3Q","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":"3936389f012d097892bf7ca0cbc00dc01de70e66af76d182750848b3d63dc296","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T15:56:32Z","title_canon_sha256":"8cfe2022bd0e1a1b4459973a4dd6b2ac62dd09bd6329729d26f954ce37abc74c"},"schema_version":"1.0","source":{"id":"1703.07289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07289","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07289v2","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07289","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"SY6RVM4QVUIL","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SY6RVM4QVUIL3BSE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SY6RVM4Q","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:213c61380b8d99fc55362a98fb5ff61ac9fe0f58d433ab1d48aa48a89be3da6d","target":"graph","created_at":"2026-05-18T00:23:56Z","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":"Abelian cellular automata (CA) are CA which are group endomorphisms of the full group shift when endowing the alphabet with an abelian group structure. A CA randomizes an initial probability measure if its iterated images weak *-converge towards the uniform Bernoulli measure (the Haar measure in this setting). We are interested in structural phenomena, i.e. randomization for a wide class of initial measures (under some mixing hypotheses). First, we prove that an abelian CA randomizes in Ces{\\`a}ro mean if and only if it has no soliton, i.e. a finite configuration whose time evolution remains b","authors_text":"Benjamin Hellouin de Menibus (IRIF), Guillaume Theyssier (I2M), Ville Salo","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T15:56:32Z","title":"Characterizing Asymptotic Randomization in Abelian Cellular Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07289","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:d9432bd3c256c2209f4d39a44efdaf01f7915f880420a9561e4092e9f9ecc3b3","target":"record","created_at":"2026-05-18T00:23:56Z","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":"3936389f012d097892bf7ca0cbc00dc01de70e66af76d182750848b3d63dc296","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T15:56:32Z","title_canon_sha256":"8cfe2022bd0e1a1b4459973a4dd6b2ac62dd09bd6329729d26f954ce37abc74c"},"schema_version":"1.0","source":{"id":"1703.07289","kind":"arxiv","version":2}},"canonical_sha256":"963d1ab390ad10bd864439f0abcfc1dc3c2e067fd7ddcef88817fa0bfb2fde11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"963d1ab390ad10bd864439f0abcfc1dc3c2e067fd7ddcef88817fa0bfb2fde11","first_computed_at":"2026-05-18T00:23:56.695580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:56.695580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvJkL7bsmX/NzE9ZGphFvujSs8x4ohQqCL4lxN8uvM1aLBx34oGE3XH0PdvzkeMXdrQmc1lZmyonQAF2dU/ZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:56.696268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9432bd3c256c2209f4d39a44efdaf01f7915f880420a9561e4092e9f9ecc3b3","sha256:213c61380b8d99fc55362a98fb5ff61ac9fe0f58d433ab1d48aa48a89be3da6d"],"state_sha256":"e603888ddb176879f8ecf3096570c0938efa43e56a07bb8394b564bd23a5fe0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q3+0pRLHx1TUOHvWy7OB+PSiB1AVfi6v3xqQ6hMdl3peMgD2Krr91klIWxtKsnPlwgORTB3YydLIFCjQ7ri+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:57:26.276531Z","bundle_sha256":"f652b578be38dba5b70c2cc2b7767a830465168227497ed9403043c73501296a"}}