{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ENWGH4XGM2CSAIIGD3WC26TV3D","short_pith_number":"pith:ENWGH4XG","canonical_record":{"source":{"id":"1710.06123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-17T06:51:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2b55854a1e52b526bd6933f4ebc532085e2fb4eeee7b9cd37e33ecc720ba9776","abstract_canon_sha256":"1fe9d8b8057807a184dd9632b5187b40a201a8ceb90a47924f822ca6d78b151f"},"schema_version":"1.0"},"canonical_sha256":"236c63f2e666852021061eec2d7a75d8ee16d0f953305f6efa0774547f47f1a9","source":{"kind":"arxiv","id":"1710.06123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06123","created_at":"2026-05-18T00:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06123v1","created_at":"2026-05-18T00:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06123","created_at":"2026-05-18T00:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"ENWGH4XGM2CS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ENWGH4XGM2CSAIIG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ENWGH4XG","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ENWGH4XGM2CSAIIGD3WC26TV3D","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-17T06:51:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2b55854a1e52b526bd6933f4ebc532085e2fb4eeee7b9cd37e33ecc720ba9776","abstract_canon_sha256":"1fe9d8b8057807a184dd9632b5187b40a201a8ceb90a47924f822ca6d78b151f"},"schema_version":"1.0"},"canonical_sha256":"236c63f2e666852021061eec2d7a75d8ee16d0f953305f6efa0774547f47f1a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:37.660613Z","signature_b64":"j0WudzTfF//RUjtpdkNAXQkgyM3Tq/gQai2+oOR4MWvXnS2+WHaEb026AcZPkDUTgAkubEJkjXyzhT++PFnnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"236c63f2e666852021061eec2d7a75d8ee16d0f953305f6efa0774547f47f1a9","last_reissued_at":"2026-05-18T00:32:37.659974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:37.659974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06123","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":"2026-05-18T00:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UaHiBOpZ8mMXw9TT1CKrAlWo6NHF95yCjNr4AgIXP5g1IzWyhs1mvWr6QxD4f0D9vWpElgqnPsRqZGsQbIEoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:58:32.283809Z"},"content_sha256":"02017b26fe062b0c4702e58576cbc113a6f4fbe39e184673f2acea06da06c779","schema_version":"1.0","event_id":"sha256:02017b26fe062b0c4702e58576cbc113a6f4fbe39e184673f2acea06da06c779"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ENWGH4XGM2CSAIIGD3WC26TV3D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A theorem for random Fourier series on compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Sang-Gyun Youn","submitted_at":"2017-10-17T06:51:30Z","abstract_excerpt":"Helgason showed that a given measure $f\\in M(G)$ on a compact group $G$ should be in $L^2(G)$ automatically if all random Fourier series of $f$ are in $M(G)$. We explore a natural analogue of the theorem in the framework of compact quantum groups and apply the obtained results to study complete representability problem for convolution algebras of compact quantum groups as an operator algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06123","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":""},"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":"2026-05-18T00:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCr9KfsIk/qhJAMQw/mkc+NErgRKP+ImPpK7yiIE1RjEOgyzj/rYLC0pzYf3fp3uvweyAlmX+SzDC2EhvvniCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:58:32.284150Z"},"content_sha256":"475c6185c6a9e46347bc28a6643c4481610228795254ceb9a29eb3e0ee523843","schema_version":"1.0","event_id":"sha256:475c6185c6a9e46347bc28a6643c4481610228795254ceb9a29eb3e0ee523843"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ENWGH4XGM2CSAIIGD3WC26TV3D/bundle.json","state_url":"https://pith.science/pith/ENWGH4XGM2CSAIIGD3WC26TV3D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ENWGH4XGM2CSAIIGD3WC26TV3D/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":"2026-06-28T14:58:32Z","links":{"resolver":"https://pith.science/pith/ENWGH4XGM2CSAIIGD3WC26TV3D","bundle":"https://pith.science/pith/ENWGH4XGM2CSAIIGD3WC26TV3D/bundle.json","state":"https://pith.science/pith/ENWGH4XGM2CSAIIGD3WC26TV3D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ENWGH4XGM2CSAIIGD3WC26TV3D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ENWGH4XGM2CSAIIGD3WC26TV3D","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":"1fe9d8b8057807a184dd9632b5187b40a201a8ceb90a47924f822ca6d78b151f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-17T06:51:30Z","title_canon_sha256":"2b55854a1e52b526bd6933f4ebc532085e2fb4eeee7b9cd37e33ecc720ba9776"},"schema_version":"1.0","source":{"id":"1710.06123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06123","created_at":"2026-05-18T00:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06123v1","created_at":"2026-05-18T00:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06123","created_at":"2026-05-18T00:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"ENWGH4XGM2CS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ENWGH4XGM2CSAIIG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ENWGH4XG","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:475c6185c6a9e46347bc28a6643c4481610228795254ceb9a29eb3e0ee523843","target":"graph","created_at":"2026-05-18T00:32:37Z","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":"Helgason showed that a given measure $f\\in M(G)$ on a compact group $G$ should be in $L^2(G)$ automatically if all random Fourier series of $f$ are in $M(G)$. We explore a natural analogue of the theorem in the framework of compact quantum groups and apply the obtained results to study complete representability problem for convolution algebras of compact quantum groups as an operator algebra.","authors_text":"Sang-Gyun Youn","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-17T06:51:30Z","title":"A theorem for random Fourier series on compact quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06123","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":"sha256:02017b26fe062b0c4702e58576cbc113a6f4fbe39e184673f2acea06da06c779","target":"record","created_at":"2026-05-18T00:32:37Z","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":"1fe9d8b8057807a184dd9632b5187b40a201a8ceb90a47924f822ca6d78b151f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-17T06:51:30Z","title_canon_sha256":"2b55854a1e52b526bd6933f4ebc532085e2fb4eeee7b9cd37e33ecc720ba9776"},"schema_version":"1.0","source":{"id":"1710.06123","kind":"arxiv","version":1}},"canonical_sha256":"236c63f2e666852021061eec2d7a75d8ee16d0f953305f6efa0774547f47f1a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"236c63f2e666852021061eec2d7a75d8ee16d0f953305f6efa0774547f47f1a9","first_computed_at":"2026-05-18T00:32:37.659974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:37.659974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j0WudzTfF//RUjtpdkNAXQkgyM3Tq/gQai2+oOR4MWvXnS2+WHaEb026AcZPkDUTgAkubEJkjXyzhT++PFnnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:37.660613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02017b26fe062b0c4702e58576cbc113a6f4fbe39e184673f2acea06da06c779","sha256:475c6185c6a9e46347bc28a6643c4481610228795254ceb9a29eb3e0ee523843"],"state_sha256":"9afd3bfc037d61ade833e29b46d98f7a6570cb73981ba3dd1966f15c86a4c092"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJeOoAb41h86uBRrp5Ycz3nB4pt+F0QxwX4K4jw3t0+E6k8RUA/mPJV0I3h9VAWTXf5jKp7gngmQPNC4kqMKDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T14:58:32.286185Z","bundle_sha256":"e636f31da88809a2e0143e07d48722b12a60bf8b14b0ce4ef32065aa04992776"}}