{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4AR5T64INTWDKLKEG3OBLJIFC5","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":"250ebf0ad3ee3b1d0ca41d9d41563a2a4141de14f96ac25d1469fae87b230e40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-07-14T08:37:56Z","title_canon_sha256":"ee903553ca9c201f5e2cdeb50cd54cd3c3cd6faa5de1aa6c96b09b915448e655"},"schema_version":"1.0","source":{"id":"1607.04031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04031","created_at":"2026-05-18T01:11:04Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04031v1","created_at":"2026-05-18T01:11:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04031","created_at":"2026-05-18T01:11:04Z"},{"alias_kind":"pith_short_12","alias_value":"4AR5T64INTWD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4AR5T64INTWDKLKE","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4AR5T64I","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:aeb7368d442f2a9844773fb071c300173aed054c97e42456b2878c16947fab1b","target":"graph","created_at":"2026-05-18T01:11:04Z","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 improve some results relative to the state complexity of the multiple catenation described by Gao and Yu. In particular we nearly divide by 2 the size of the alphabet needed for witnesses. We also give some refinements to the algebraic expression of the state complexity, which is especially complex with this operation. We obtain these results by using peculiar DFAs defined by Brzozowski.","authors_text":"Bruno Patrou, Jean-Gabriel Luque, Pascal Caron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-07-14T08:37:56Z","title":"State complexity of multiple catenation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04031","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":"sha256:5d944f325fe186113bdf0780b01ee24648c8f57c54ea53a7eeb875f03472c440","target":"record","created_at":"2026-05-18T01:11:04Z","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":"250ebf0ad3ee3b1d0ca41d9d41563a2a4141de14f96ac25d1469fae87b230e40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-07-14T08:37:56Z","title_canon_sha256":"ee903553ca9c201f5e2cdeb50cd54cd3c3cd6faa5de1aa6c96b09b915448e655"},"schema_version":"1.0","source":{"id":"1607.04031","kind":"arxiv","version":1}},"canonical_sha256":"e023d9fb886cec352d4436dc15a505174a70ad3edc19cf89211297cbf5375aec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e023d9fb886cec352d4436dc15a505174a70ad3edc19cf89211297cbf5375aec","first_computed_at":"2026-05-18T01:11:04.277449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:04.277449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hupS4iyszKcRkn/zU+ypi68tZP7Sx7qVOjsuLqLuRRFASrHftY6tRkMSJFyxh0FE0Dw7QhcDGBBDZ8kHBtbiBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:04.278059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d944f325fe186113bdf0780b01ee24648c8f57c54ea53a7eeb875f03472c440","sha256:aeb7368d442f2a9844773fb071c300173aed054c97e42456b2878c16947fab1b"],"state_sha256":"f1d5857f09cdbc278caaf58421ccd9548b3ed102f5721f3628f25d74a06aceb0"}