{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DNZTR4Y5CN7UFCFLFS4DT77R6Q","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":"6de745e8fc5f08ad9a3d9cd613a507038d710c7eb55e55303d5f69bf28a05e66","cross_cats_sorted":["math.MG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-28T12:45:05Z","title_canon_sha256":"3f768cef4248f39699af69d8e8f57963a253c2b0912a2889cdcad945145e54e3"},"schema_version":"1.0","source":{"id":"1205.6099","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6099","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6099v4","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6099","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"DNZTR4Y5CN7U","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DNZTR4Y5CN7UFCFL","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DNZTR4Y5","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:5d61e4ff75f32e072359812fd5a541e75ad1ffa0e1583491c5614a681785bc89","target":"graph","created_at":"2026-05-18T02:18:13Z","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 formulate a definition of isometric action of a compact quantum group (CQG) on a compact metric space, generalizing Banica's definition for finite metric spaces. For metric spaces $(X,d)$ which can be isometrically embedded in some Euclidean space, we prove the existence of a universal object in the category of the compact quantum groups acting isometrically on $(X,d)$. In fact, our existence theorem applies to a larger class, namely for any compact metric space $(X,d)$ which admits a one-to-one continuous map $f : X \\raro \\IR^n$ for some $n$ such that $d_0(f(x),f(y))=\\phi(d(x,y))$ (where $","authors_text":"Debashish Goswami","cross_cats":["math.MG","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-28T12:45:05Z","title":"Existence and examples of quantum isometry group for a class of compact metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6099","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:ad59040d9ea8392d13b38cb653f6cff1b49fe2dcb4789b4e88b8c97c946f52d5","target":"record","created_at":"2026-05-18T02:18:13Z","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":"6de745e8fc5f08ad9a3d9cd613a507038d710c7eb55e55303d5f69bf28a05e66","cross_cats_sorted":["math.MG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-28T12:45:05Z","title_canon_sha256":"3f768cef4248f39699af69d8e8f57963a253c2b0912a2889cdcad945145e54e3"},"schema_version":"1.0","source":{"id":"1205.6099","kind":"arxiv","version":4}},"canonical_sha256":"1b7338f31d137f4288ab2cb839fff1f43c2c54b8784fee01d95f25042b78d4f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b7338f31d137f4288ab2cb839fff1f43c2c54b8784fee01d95f25042b78d4f9","first_computed_at":"2026-05-18T02:18:13.887227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:13.887227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aREHSiThoB8T8rKmaE/9vIaIVBIiXtutueuT+BOqpqi+zMfi/ikiL0iY/NJyMk2SL2nEZqq4GnefZFWv9hGwDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:13.887589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6099","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad59040d9ea8392d13b38cb653f6cff1b49fe2dcb4789b4e88b8c97c946f52d5","sha256:5d61e4ff75f32e072359812fd5a541e75ad1ffa0e1583491c5614a681785bc89"],"state_sha256":"ccf514453ddb458e730022280ab6c37c36c7fe4f68c1944e278b5eada604e622"}