{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3ARFSIYGNANCHNT76NEL4EOGZT","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":"661a53ac246a5c72115cd7c438ca7d21279b85361ada1bd2ebc7006a62660eb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-19T06:32:57Z","title_canon_sha256":"c5e57458b610102ed240e18b5aa617b2300dcc3775faadf8ff4754f64b519983"},"schema_version":"1.0","source":{"id":"1701.05309","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05309","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05309v1","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05309","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"3ARFSIYGNANC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3ARFSIYGNANCHNT7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3ARFSIYG","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:2080e1117241fd89fa1ace94c66e0e13f22e6ed6a214baba051599427f2fcf60","target":"graph","created_at":"2026-05-18T00:52:12Z","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":"In this paper we study twisted algebras of multiplier Hopf ($^*$-)algebras which generalize all kinds of smash products such as generalized smash products, twisted smash products, diagonal crossed products, L-R-smash products, two-sided crossed products and two-sided smash products for the ordinary Hopf algebras appeared in [P-O].","authors_text":"Shuanhong Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-19T06:32:57Z","title":"Twisted Algebras of Multiplier Hopf ($^*$-)algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05309","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":"sha256:7e3ff5c9ba62b5fe9037553e98ea33db6869140176f1bf9421873fd3c5f69a24","target":"record","created_at":"2026-05-18T00:52:12Z","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":"661a53ac246a5c72115cd7c438ca7d21279b85361ada1bd2ebc7006a62660eb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-19T06:32:57Z","title_canon_sha256":"c5e57458b610102ed240e18b5aa617b2300dcc3775faadf8ff4754f64b519983"},"schema_version":"1.0","source":{"id":"1701.05309","kind":"arxiv","version":1}},"canonical_sha256":"d822592306681a23b67ff348be11c6ccfa8c5019d93abfddc6a191e33f1e424a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d822592306681a23b67ff348be11c6ccfa8c5019d93abfddc6a191e33f1e424a","first_computed_at":"2026-05-18T00:52:12.700203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:12.700203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+d3sf1b92Umr4IsdVawjs5mwkfQHxRb6kliSp08b3kx3TbrxCcyASZJy3+FV3ejViheNrqbdrIYC3Z4DinwDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:12.700854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05309","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e3ff5c9ba62b5fe9037553e98ea33db6869140176f1bf9421873fd3c5f69a24","sha256:2080e1117241fd89fa1ace94c66e0e13f22e6ed6a214baba051599427f2fcf60"],"state_sha256":"26ee79b2dc33d831e19125f32f01040e56c6d6ba2bc975e493f10b0293b3b955"}