{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B6TAT2VRJBUCWXDNYCKJP5ZBKL","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":"d9df37acd564c1f76096d63251414c0d4b64cbcbf7978363e6a4e2c39d9f8096","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-20T15:28:05Z","title_canon_sha256":"e6ff331a639adee50a41714903d1289033579a9d3ee12c996e9add55b4f49dea"},"schema_version":"1.0","source":{"id":"1802.07150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07150","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07150v1","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07150","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"B6TAT2VRJBUC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B6TAT2VRJBUCWXDN","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B6TAT2VR","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:a4ed5356127615b16cb48fa8064033eaad064f031e89388e390f1141deb11582","target":"graph","created_at":"2026-05-18T00:22:53Z","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":"This survey article gives an elementary introduction to the algebraic approach to Markov process duality, as opposed to the pathwise approach. In the algebraic approach, a Markov generator is written as the sum of products of simpler operators, which each have a dual with respect to some duality function. We discuss at length the recent suggestion by Giardin\\`a, Redig, and others, that it may be a good idea to choose these simpler operators in such a way that they form an irreducible representation of some known Lie algebra. In particular, we collect the necessary background on representations","authors_text":"Anja Sturm, Florian V\\\"ollering, Jan M. Swart","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-20T15:28:05Z","title":"The Algebraic Approach to Duality: An Introduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07150","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":"sha256:773a45b154d03d4303928dd32b3f33ad8b0302e2e9702c437d6138246a140b63","target":"record","created_at":"2026-05-18T00:22:53Z","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":"d9df37acd564c1f76096d63251414c0d4b64cbcbf7978363e6a4e2c39d9f8096","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-20T15:28:05Z","title_canon_sha256":"e6ff331a639adee50a41714903d1289033579a9d3ee12c996e9add55b4f49dea"},"schema_version":"1.0","source":{"id":"1802.07150","kind":"arxiv","version":1}},"canonical_sha256":"0fa609eab148682b5c6dc09497f72152dffa4aacaecddadf2cb95728ca40e423","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fa609eab148682b5c6dc09497f72152dffa4aacaecddadf2cb95728ca40e423","first_computed_at":"2026-05-18T00:22:53.437926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:53.437926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KN6iXZW36pSu0dG8Y/S2RpFv3OpEj6/1H9CfuwsJBx/k7A4Q/NZI8+EZHNQMYZ9S6OaptrMCec39k/FhiWKcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:53.438485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:773a45b154d03d4303928dd32b3f33ad8b0302e2e9702c437d6138246a140b63","sha256:a4ed5356127615b16cb48fa8064033eaad064f031e89388e390f1141deb11582"],"state_sha256":"5bb085116ecd690b752d7e57782c97b82858484d408c859e03da039aa8e3e145"}