{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:O24XT3DWMCP3U3MW2ZH63CNOC7","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":"d479265ca9a29474f1b24ac829f5d8233b831eb5ab77448eb488e9483b6c4e85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-09-24T12:27:07Z","title_canon_sha256":"d8ac26eec40b0be0c582e5f86f0b6958c58f5b19d5a43704269e64187d3bb37e"},"schema_version":"1.0","source":{"id":"1009.4820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4820","created_at":"2026-05-18T04:28:08Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4820v2","created_at":"2026-05-18T04:28:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4820","created_at":"2026-05-18T04:28:08Z"},{"alias_kind":"pith_short_12","alias_value":"O24XT3DWMCP3","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O24XT3DWMCP3U3MW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O24XT3DW","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:522b1e9f9eb66e4496dba6d9c67b9ace4c0f585bc865a6bf48dd1f001fbbb9ae","target":"graph","created_at":"2026-05-18T04:28:08Z","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 consider rational power series over an alphabet $\\Sigma$ with coefficients in a ordered commutative semiring $K$ and characterize them as the free ordered $K$-semialgebras in various classes of ordered $K$-semialgebras equipped with a star operation satisfying the least pre-fixed point rule and/or its dual. The results are generalizations of Kozen's axiomatization of regular languages.","authors_text":"Werner Kuich, Zoltan Esik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-09-24T12:27:07Z","title":"Free inductive K-semialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4820","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":"sha256:0ab92f9c3cf031591afd0d06438cfea6e8723cc3698723bf4e597225ea2ab99d","target":"record","created_at":"2026-05-18T04:28:08Z","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":"d479265ca9a29474f1b24ac829f5d8233b831eb5ab77448eb488e9483b6c4e85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-09-24T12:27:07Z","title_canon_sha256":"d8ac26eec40b0be0c582e5f86f0b6958c58f5b19d5a43704269e64187d3bb37e"},"schema_version":"1.0","source":{"id":"1009.4820","kind":"arxiv","version":2}},"canonical_sha256":"76b979ec76609fba6d96d64fed89ae17dc8bcfd8abd49649bff5bda8a4240d79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76b979ec76609fba6d96d64fed89ae17dc8bcfd8abd49649bff5bda8a4240d79","first_computed_at":"2026-05-18T04:28:08.052984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:08.052984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d26gVMIedDRk428c0KZXXoeykNDfWvJBm1jK87Wusd31NjtLqK5UuE9sT8rXJo6xXyGzO5eeq8d+Y5GdE814AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:08.053793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ab92f9c3cf031591afd0d06438cfea6e8723cc3698723bf4e597225ea2ab99d","sha256:522b1e9f9eb66e4496dba6d9c67b9ace4c0f585bc865a6bf48dd1f001fbbb9ae"],"state_sha256":"34370c9f0efd4937ceacb9a6822e8985d2e32b29d3ff2d60ab001cac5923c143"}