{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:POAURFBYF3YFSEE27KR6K6Q66P","short_pith_number":"pith:POAURFBY","canonical_record":{"source":{"id":"2011.03867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-11-07T23:14:59Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"164a0aab19ccb0c2f0e2dc31c20ac8039c95fb442a0f282d9d038253cc4a237c","abstract_canon_sha256":"06abe7e8ea9f6ac1bc3bc87f08bad70ac5e6efd9d879d0eccd919896efea8279"},"schema_version":"1.0"},"canonical_sha256":"7b814894382ef059109afaa3e57a1ef3dda57c304e988d5fc9982aa1ba56a805","source":{"kind":"arxiv","id":"2011.03867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.03867","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"2011.03867v1","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.03867","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"POAURFBYF3YF","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"pith_short_16","alias_value":"POAURFBYF3YFSEE2","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"pith_short_8","alias_value":"POAURFBY","created_at":"2026-07-05T01:49:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:POAURFBYF3YFSEE27KR6K6Q66P","target":"record","payload":{"canonical_record":{"source":{"id":"2011.03867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-11-07T23:14:59Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"164a0aab19ccb0c2f0e2dc31c20ac8039c95fb442a0f282d9d038253cc4a237c","abstract_canon_sha256":"06abe7e8ea9f6ac1bc3bc87f08bad70ac5e6efd9d879d0eccd919896efea8279"},"schema_version":"1.0"},"canonical_sha256":"7b814894382ef059109afaa3e57a1ef3dda57c304e988d5fc9982aa1ba56a805","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:49:59.989061Z","signature_b64":"ep6kf2BJzO+PrfAmRnRe7YXfPB7KdvmGTkCo9aFP6mG07z3ESYtkd9yUO9BweFzIFO7QxMrbk8LW0QirL87aBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b814894382ef059109afaa3e57a1ef3dda57c304e988d5fc9982aa1ba56a805","last_reissued_at":"2026-07-05T01:49:59.988639Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:49:59.988639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.03867","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4BApZEzA2j9ak2tNfDDgAnUdaUB4uYpMCFAI8j+a/IMdNvGwJcX3/Tb4QFRQML81q3+MD1XxzEDOUd+/ireDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T13:41:33.904967Z"},"content_sha256":"270c33c234e9f106d7d668ec97fd3275ad93933336cd738438b179828043350e","schema_version":"1.0","event_id":"sha256:270c33c234e9f106d7d668ec97fd3275ad93933336cd738438b179828043350e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:POAURFBYF3YFSEE27KR6K6Q66P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-local games and quantum symmetries of quantum metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Kari Eifler","submitted_at":"2020-11-07T23:14:59Z","abstract_excerpt":"We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries between two quantum metric spaces, and we show that if a pair of quantum metric spaces are algebraically quantum isometric, then their quantum isometry groups are monoidally equivalent. Motivated by the recent work on the graph isomorphism game, we introduce a new two-player non-local game called the metric isometry game, where players can win classically if and only if the metric spaces are isometri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03867","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.03867/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sICKW3QLOTl6ZA0Crwyf0kDl9fcSxFn2iK+Nfm0P0U2lzGoyPoaLWPOEInYxgNZhXCvfydDZ0gW4I2nHF1BfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T13:41:33.905522Z"},"content_sha256":"d46dff5b37ca29256e2393982e39765e1a176aa36cc25d1a3ea5e024c7abb09a","schema_version":"1.0","event_id":"sha256:d46dff5b37ca29256e2393982e39765e1a176aa36cc25d1a3ea5e024c7abb09a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/POAURFBYF3YFSEE27KR6K6Q66P/bundle.json","state_url":"https://pith.science/pith/POAURFBYF3YFSEE27KR6K6Q66P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/POAURFBYF3YFSEE27KR6K6Q66P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T13:41:33Z","links":{"resolver":"https://pith.science/pith/POAURFBYF3YFSEE27KR6K6Q66P","bundle":"https://pith.science/pith/POAURFBYF3YFSEE27KR6K6Q66P/bundle.json","state":"https://pith.science/pith/POAURFBYF3YFSEE27KR6K6Q66P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/POAURFBYF3YFSEE27KR6K6Q66P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:POAURFBYF3YFSEE27KR6K6Q66P","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":"06abe7e8ea9f6ac1bc3bc87f08bad70ac5e6efd9d879d0eccd919896efea8279","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-11-07T23:14:59Z","title_canon_sha256":"164a0aab19ccb0c2f0e2dc31c20ac8039c95fb442a0f282d9d038253cc4a237c"},"schema_version":"1.0","source":{"id":"2011.03867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.03867","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"2011.03867v1","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.03867","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"POAURFBYF3YF","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"pith_short_16","alias_value":"POAURFBYF3YFSEE2","created_at":"2026-07-05T01:49:59Z"},{"alias_kind":"pith_short_8","alias_value":"POAURFBY","created_at":"2026-07-05T01:49:59Z"}],"graph_snapshots":[{"event_id":"sha256:d46dff5b37ca29256e2393982e39765e1a176aa36cc25d1a3ea5e024c7abb09a","target":"graph","created_at":"2026-07-05T01:49:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.03867/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries between two quantum metric spaces, and we show that if a pair of quantum metric spaces are algebraically quantum isometric, then their quantum isometry groups are monoidally equivalent. Motivated by the recent work on the graph isomorphism game, we introduce a new two-player non-local game called the metric isometry game, where players can win classically if and only if the metric spaces are isometri","authors_text":"Kari Eifler","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-11-07T23:14:59Z","title":"Non-local games and quantum symmetries of quantum metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03867","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":"sha256:270c33c234e9f106d7d668ec97fd3275ad93933336cd738438b179828043350e","target":"record","created_at":"2026-07-05T01:49:59Z","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":"06abe7e8ea9f6ac1bc3bc87f08bad70ac5e6efd9d879d0eccd919896efea8279","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-11-07T23:14:59Z","title_canon_sha256":"164a0aab19ccb0c2f0e2dc31c20ac8039c95fb442a0f282d9d038253cc4a237c"},"schema_version":"1.0","source":{"id":"2011.03867","kind":"arxiv","version":1}},"canonical_sha256":"7b814894382ef059109afaa3e57a1ef3dda57c304e988d5fc9982aa1ba56a805","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b814894382ef059109afaa3e57a1ef3dda57c304e988d5fc9982aa1ba56a805","first_computed_at":"2026-07-05T01:49:59.988639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:49:59.988639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ep6kf2BJzO+PrfAmRnRe7YXfPB7KdvmGTkCo9aFP6mG07z3ESYtkd9yUO9BweFzIFO7QxMrbk8LW0QirL87aBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:49:59.989061Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.03867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:270c33c234e9f106d7d668ec97fd3275ad93933336cd738438b179828043350e","sha256:d46dff5b37ca29256e2393982e39765e1a176aa36cc25d1a3ea5e024c7abb09a"],"state_sha256":"b83a6a835cb4e712eda9b38e557a287481fcfb885d3043bd491bfb51cb600b82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opcAPqFGZptU9QqQPaZPZmDTUuSAcqM9JS0pyimvn78XZoV9yNO/jy9LJ5+D7d8UhXi4EHw2ExvuMaQzTs83AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T13:41:33.908359Z","bundle_sha256":"b1b0d34aab9063aa717309bb803d78e505380d6a45aef88fcb0a5c3cdc68d9b7"}}