{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E7G5RKXZRLHSNNDDQYRW2J3CAD","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":"1af74bf4bd0a2492e1abdad09b58808ecafb74702630c125a60397bbf9c65aee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-14T09:56:19Z","title_canon_sha256":"3937b2e603494d8cf22719e82e21ec1c5a4a9fd85500713fc4484c86484d9c85"},"schema_version":"1.0","source":{"id":"1202.2977","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2977","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2977v4","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2977","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"E7G5RKXZRLHS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E7G5RKXZRLHSNNDD","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E7G5RKXZ","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:595fd13489d98a7e39b60c02baa80fc011799ce164ed23fa3c453e79a653c198","target":"graph","created_at":"2026-05-18T01:37:08Z","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":"Finding necessary and sufficient conditions for isomorphism between two semigroups of order-preserving transformations over an infinite domain with restricted range was an open problem in \\cite{FHQS}. In this paper, we show a proof strategy to answer that question.","authors_text":"Phichet Jitjankarn, Thitarie Rungratgasame","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-14T09:56:19Z","title":"A note on Isomorphism theorems for semigroups of order-preserving transformations with restricted range"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2977","kind":"arxiv","version":4},"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":"sha256:79dd4bf4b2bdfe3b1cef4925481bc2226e32c6c092d3db365fa5512096310292","target":"record","created_at":"2026-05-18T01:37:08Z","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":"1af74bf4bd0a2492e1abdad09b58808ecafb74702630c125a60397bbf9c65aee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-14T09:56:19Z","title_canon_sha256":"3937b2e603494d8cf22719e82e21ec1c5a4a9fd85500713fc4484c86484d9c85"},"schema_version":"1.0","source":{"id":"1202.2977","kind":"arxiv","version":4}},"canonical_sha256":"27cdd8aaf98acf26b46386236d276200dd2d6c3ed5b1438b8b46252ec9f12505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27cdd8aaf98acf26b46386236d276200dd2d6c3ed5b1438b8b46252ec9f12505","first_computed_at":"2026-05-18T01:37:08.257995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:08.257995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uzOI+99m8ueiYK5cYXqTY00u2qCdpLnXTGyGd+ouzxWYJ27mw1ypKN2vWDjV7xWTDPHyY9UbFrwHnpjpwKnfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:08.258770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2977","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79dd4bf4b2bdfe3b1cef4925481bc2226e32c6c092d3db365fa5512096310292","sha256:595fd13489d98a7e39b60c02baa80fc011799ce164ed23fa3c453e79a653c198"],"state_sha256":"2a535b1051bee29e5fec9e1c8d4a1b1e0a756099da31b9f4577a1f8f78becaad"}