{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CCWYBVTL5KBH4B7CC6GYAGEZZP","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":"004e681a484deea77e634a23e9636f48c61f15810a49bf40293735eb3b56e2ea","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-03-29T06:42:23Z","title_canon_sha256":"b85c08018fd531571632161eda4dfa300c8e17239803cfa033710a8bccebabf2"},"schema_version":"1.0","source":{"id":"1903.12369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12369","created_at":"2026-05-17T23:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12369v1","created_at":"2026-05-17T23:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12369","created_at":"2026-05-17T23:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"CCWYBVTL5KBH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CCWYBVTL5KBH4B7C","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CCWYBVTL","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:e515a11af2c38868b712f647f272707d8daff5195ce0dc3d59280936214ce3ca","target":"graph","created_at":"2026-05-17T23:45:27Z","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 show that the C*-algebras associated with synchronous games give rise to certain quantum families of maps between the input and output sets of the game. In particular situations (e.g. for graph endomorphism games) these quantum families have a natural quantum semigroup structure and if the condition of preservation of a natural state is added, they are in fact compact quantum groups.","authors_text":"Piotr M. So{\\l}tan","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-03-29T06:42:23Z","title":"Quantum Semigroups from Synchronous Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12369","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":"sha256:8e22ec71e9728f2a45c5dfabfb055cb0923ba4231d95abd874ee233b4fde4be3","target":"record","created_at":"2026-05-17T23:45:27Z","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":"004e681a484deea77e634a23e9636f48c61f15810a49bf40293735eb3b56e2ea","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-03-29T06:42:23Z","title_canon_sha256":"b85c08018fd531571632161eda4dfa300c8e17239803cfa033710a8bccebabf2"},"schema_version":"1.0","source":{"id":"1903.12369","kind":"arxiv","version":1}},"canonical_sha256":"10ad80d66bea827e07e2178d801899cbceffb9c28d537d041eaa6b75c2db7c60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10ad80d66bea827e07e2178d801899cbceffb9c28d537d041eaa6b75c2db7c60","first_computed_at":"2026-05-17T23:45:27.054454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:27.054454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H1IyqNahutOCY39RNibADlGiQJUTymDzPMQSpPBrBXMdzYWy/Cez3bHviqGo/wJNXxjvodFAUNhBJ4L7IfloCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:27.055038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.12369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e22ec71e9728f2a45c5dfabfb055cb0923ba4231d95abd874ee233b4fde4be3","sha256:e515a11af2c38868b712f647f272707d8daff5195ce0dc3d59280936214ce3ca"],"state_sha256":"5135f7811e4f2bcbccfe51809e3c7653ae6345f9371fe5250a5061f2b8a53f97"}