{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:PWPR6RNEMHV3K3FGT5LWEDOGMD","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":"afa76b258eb0df76e31e46b6361fc10b4c77748ebac40035329c8575596275fa","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"cs.LO","submitted_at":"2006-09-08T08:51:33Z","title_canon_sha256":"7d3b3f0d52f8dae31762c6bac6ec362be57408d14016111381b5a092c91008fd"},"schema_version":"1.0","source":{"id":"cs/0609040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0609040","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0609040v2","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0609040","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"PWPR6RNEMHV3","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"PWPR6RNEMHV3K3FG","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"PWPR6RNE","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:2e4da995785f47949d9aff689ad4c08fcf2bab86e1293df1f4f8ecfabe227068","target":"graph","created_at":"2026-05-18T00:53:03Z","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":"Denotational semantics can be based on algebras with additional structure (order, metric, etc.) which makes it possible to interpret recursive specifications. It was the idea of Elgot to base denotational semantics on iterative theories instead, i.e., theories in which abstract recursive specifications are required to have unique solutions. Later Bloom and Esik studied iteration theories and iteration algebras in which a specified solution has to obey certain axioms. We propose so-called Elgot algebras as a convenient structure for semantics in the present paper. An Elgot algebra is an algebra","authors_text":"Jiri Adamek, Jiri Velebil, Stefan Milius","cross_cats":["math.CT"],"headline":"","license":"","primary_cat":"cs.LO","submitted_at":"2006-09-08T08:51:33Z","title":"Elgot Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0609040","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":"sha256:413b9a6806cc9bed7f7aa56838989e7f08374b7c75acb5be1c1b026ed6de2b03","target":"record","created_at":"2026-05-18T00:53:03Z","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":"afa76b258eb0df76e31e46b6361fc10b4c77748ebac40035329c8575596275fa","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"cs.LO","submitted_at":"2006-09-08T08:51:33Z","title_canon_sha256":"7d3b3f0d52f8dae31762c6bac6ec362be57408d14016111381b5a092c91008fd"},"schema_version":"1.0","source":{"id":"cs/0609040","kind":"arxiv","version":2}},"canonical_sha256":"7d9f1f45a461ebb56ca69f57620dc660e65cff2a66dd45b1bf58ab57ceaa1fac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d9f1f45a461ebb56ca69f57620dc660e65cff2a66dd45b1bf58ab57ceaa1fac","first_computed_at":"2026-05-18T00:53:03.334755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:03.334755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZkjSFLI9EPbBjMR46U2vRnGg/+GR6lC6hQ4N0YnMl+JUNnBJOhcQIdPmUfmgYLj/EMIWJB0qqLpnCQY1NvJTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:03.335457Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0609040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:413b9a6806cc9bed7f7aa56838989e7f08374b7c75acb5be1c1b026ed6de2b03","sha256:2e4da995785f47949d9aff689ad4c08fcf2bab86e1293df1f4f8ecfabe227068"],"state_sha256":"3cdb27e98953e81ebea4dd575c0e461b794aa3f8693e8c4c51d140bfdd931a92"}