{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7OSUMYLV3YGJBYVE35U6FRBHVE","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":"16788cd88fa0bbda1d9aae8290e418df824e1ccee139cc04792a3484f1666a79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-02-13T15:44:43Z","title_canon_sha256":"24eb195bcfe0dc39841f58490cc2e196f0676ed22ee15a365289efba067edcd4"},"schema_version":"1.0","source":{"id":"1902.04957","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04957","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04957v1","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04957","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"7OSUMYLV3YGJ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7OSUMYLV3YGJBYVE","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7OSUMYLV","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:c6d4ddab690724c1897874b1713c58beef9e87e936a36598d9495516a1bd41fd","target":"graph","created_at":"2026-05-17T23:54:03Z","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":"Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations. Concatenation hierarchies have gathered a lot of interest since the 70s, thanks to an alternate logical definition: each concatenation hierarchy is the quantification alternation hierarchy within a variant of first-order logic over words.\n  Our goal is to understand such hierarchies. We look at two decision problems: membership and separation. For a class of languages","authors_text":"Marc Zeitoun, Thomas Place","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-02-13T15:44:43Z","title":"Separation and covering for group based concatenation hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04957","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":"sha256:661b77d3d1e33a56a1209d84d93d2a72179c44577545dacb426878132e4ad9b1","target":"record","created_at":"2026-05-17T23:54:03Z","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":"16788cd88fa0bbda1d9aae8290e418df824e1ccee139cc04792a3484f1666a79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-02-13T15:44:43Z","title_canon_sha256":"24eb195bcfe0dc39841f58490cc2e196f0676ed22ee15a365289efba067edcd4"},"schema_version":"1.0","source":{"id":"1902.04957","kind":"arxiv","version":1}},"canonical_sha256":"fba5466175de0c90e2a4df69e2c427a9267077c4cddeea400a1b2926c3a174d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fba5466175de0c90e2a4df69e2c427a9267077c4cddeea400a1b2926c3a174d5","first_computed_at":"2026-05-17T23:54:03.798076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:03.798076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mTo31Ot5mwY6bWizcAkRm7jSMQWRKS9OQMe4a/HfWtbfJ1CkV4ubW4f5gHxF1mFUqGB1cD/9JA9VTiaVgw6vBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:03.798543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.04957","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:661b77d3d1e33a56a1209d84d93d2a72179c44577545dacb426878132e4ad9b1","sha256:c6d4ddab690724c1897874b1713c58beef9e87e936a36598d9495516a1bd41fd"],"state_sha256":"95a401707ce7a5d23542a8a2b6e7593daab06ee136554db5ab3e113913cbee6b"}