{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5HN5I7R46LWU6MKAZZQI2OEJZZ","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":"d4fb0ee44b582bf3ee4e630009550c11bd25edd019a1f4ad333203692be97bdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-03T17:59:19Z","title_canon_sha256":"d78d6ecdc74aad79425e617afcf0958080a3a6be109890aa11698b7df8b0b639"},"schema_version":"1.0","source":{"id":"1608.01268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01268","created_at":"2026-05-18T01:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01268v1","created_at":"2026-05-18T01:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01268","created_at":"2026-05-18T01:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"5HN5I7R46LWU","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5HN5I7R46LWU6MKA","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5HN5I7R4","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:89aec12b2c804a2a4cefcce1ffb21be2d1df16f7e51cb800a76ddb4e5ccb1403","target":"graph","created_at":"2026-05-18T01:09:56Z","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":"We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\\varTheta(n^2)$, where $n$ is the number of states of the automaton. This disproves a conjecture that every subset in a strongly connected synchronizing automaton is $cn$-extendable, for some constant $c$, and in particular, shows that the cubic upper bound on the length of the shortest reset words cannot be improved generally by means of the extension method. A detailed analysis sh","authors_text":"Andrzej Kisielewicz, Marek Szyku{\\l}a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-03T17:59:19Z","title":"Synchronizing Automata with Extremal Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01268","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":"sha256:5aa4cdaaec7a9bd4c128f72e67ca983ff54aa8b0f93f32ea814ac4f99febc0fa","target":"record","created_at":"2026-05-18T01:09:56Z","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":"d4fb0ee44b582bf3ee4e630009550c11bd25edd019a1f4ad333203692be97bdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-03T17:59:19Z","title_canon_sha256":"d78d6ecdc74aad79425e617afcf0958080a3a6be109890aa11698b7df8b0b639"},"schema_version":"1.0","source":{"id":"1608.01268","kind":"arxiv","version":1}},"canonical_sha256":"e9dbd47e3cf2ed4f3140ce608d3889ce6445eab598f91e352ae3662ec1b25d49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9dbd47e3cf2ed4f3140ce608d3889ce6445eab598f91e352ae3662ec1b25d49","first_computed_at":"2026-05-18T01:09:56.017119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:56.017119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1CBwGSa3g3dJPK+LJNf9ot9yFuGnfDyodiuXUW9PvpuCvvsVWcJrKH6lUdL26WJelPU5/flTZze+Uf0/TH3PAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:56.017858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aa4cdaaec7a9bd4c128f72e67ca983ff54aa8b0f93f32ea814ac4f99febc0fa","sha256:89aec12b2c804a2a4cefcce1ffb21be2d1df16f7e51cb800a76ddb4e5ccb1403"],"state_sha256":"dae4ddfcc77685c24762452fe3f02f85e31176c5acbf4aa492940ba289589e78"}