{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:UKGGFQX4VY3JXKC2QGVRWJWXB6","short_pith_number":"pith:UKGGFQX4","canonical_record":{"source":{"id":"math/0512107","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2005-12-05T19:38:32Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"251e9c3a945bf205fcf01320f3a87b69c8e442a7540ef828ce3767a7a3930fca","abstract_canon_sha256":"858451ac93107a4e9ae47078deb76e676ddd7298fa4dd09c10d84300a753cb03"},"schema_version":"1.0"},"canonical_sha256":"a28c62c2fcae369ba85a81ab1b26d70f847cf7e292ac458825a7942a6f1d5ab3","source":{"kind":"arxiv","id":"math/0512107","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512107","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512107v1","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512107","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"UKGGFQX4VY3J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UKGGFQX4VY3JXKC2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UKGGFQX4","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:UKGGFQX4VY3JXKC2QGVRWJWXB6","target":"record","payload":{"canonical_record":{"source":{"id":"math/0512107","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2005-12-05T19:38:32Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"251e9c3a945bf205fcf01320f3a87b69c8e442a7540ef828ce3767a7a3930fca","abstract_canon_sha256":"858451ac93107a4e9ae47078deb76e676ddd7298fa4dd09c10d84300a753cb03"},"schema_version":"1.0"},"canonical_sha256":"a28c62c2fcae369ba85a81ab1b26d70f847cf7e292ac458825a7942a6f1d5ab3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:55.976811Z","signature_b64":"Dd597vrGJkPUaocBgBPPQaJnSOv9KqL7xzCC0O+VMQAQ40Xu/GbyPnAIuW9wfimk+RaMRuWlTnNHokVyyPPMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a28c62c2fcae369ba85a81ab1b26d70f847cf7e292ac458825a7942a6f1d5ab3","last_reissued_at":"2026-05-18T04:28:55.976188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:55.976188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0512107","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":"2026-05-18T04:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eJRLjXaBBqxwW65HqJqzWPzgxnPC26bp+ZMQ86mPlt7/CPqj9fsZ384EfSrgkfW+v7MIZYe+QhOC0zVlcHinCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:53:12.526999Z"},"content_sha256":"94df00eb6e002470ed718d18e5d18999b0f88999e5dd6802b6be733c16496c66","schema_version":"1.0","event_id":"sha256:94df00eb6e002470ed718d18e5d18999b0f88999e5dd6802b6be733c16496c66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:UKGGFQX4VY3JXKC2QGVRWJWXB6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"What can one reconstruct from the representation ring of a compact group?","license":"","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.GR","authors_text":"Zoltan Zimboras","submitted_at":"2005-12-05T19:38:32Z","abstract_excerpt":"It is well known that there exist non-isomorphic compact groups with isomorphic representation rings (fusion rules). Nevertheless, considerable structural information about the group can be reconstructed from its representation ring. We review these types of partial reconstruction theorems, including some recent results. In the Appendix a derivation of the Clebsch-Gordan series of SU(2) based only on information about the dimensions of the irreps is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512107","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":"2026-05-18T04:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYAl5Ch1jChXTkGHVNDSuHK1NaG2UXErD+GMyzZMjFalYtd0tfaaAoGztsrzrLdL9hYTS+snLvFLBqVHv9nCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:53:12.527349Z"},"content_sha256":"e935b7bc5a4e48bda202f2487912f0c1c56b5ea8f196687053a2a560ead301ce","schema_version":"1.0","event_id":"sha256:e935b7bc5a4e48bda202f2487912f0c1c56b5ea8f196687053a2a560ead301ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKGGFQX4VY3JXKC2QGVRWJWXB6/bundle.json","state_url":"https://pith.science/pith/UKGGFQX4VY3JXKC2QGVRWJWXB6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKGGFQX4VY3JXKC2QGVRWJWXB6/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":"2026-06-20T08:53:12Z","links":{"resolver":"https://pith.science/pith/UKGGFQX4VY3JXKC2QGVRWJWXB6","bundle":"https://pith.science/pith/UKGGFQX4VY3JXKC2QGVRWJWXB6/bundle.json","state":"https://pith.science/pith/UKGGFQX4VY3JXKC2QGVRWJWXB6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKGGFQX4VY3JXKC2QGVRWJWXB6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:UKGGFQX4VY3JXKC2QGVRWJWXB6","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":"858451ac93107a4e9ae47078deb76e676ddd7298fa4dd09c10d84300a753cb03","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"","primary_cat":"math.GR","submitted_at":"2005-12-05T19:38:32Z","title_canon_sha256":"251e9c3a945bf205fcf01320f3a87b69c8e442a7540ef828ce3767a7a3930fca"},"schema_version":"1.0","source":{"id":"math/0512107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512107","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512107v1","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512107","created_at":"2026-05-18T04:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"UKGGFQX4VY3J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UKGGFQX4VY3JXKC2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UKGGFQX4","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:e935b7bc5a4e48bda202f2487912f0c1c56b5ea8f196687053a2a560ead301ce","target":"graph","created_at":"2026-05-18T04:28:55Z","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":"It is well known that there exist non-isomorphic compact groups with isomorphic representation rings (fusion rules). Nevertheless, considerable structural information about the group can be reconstructed from its representation ring. We review these types of partial reconstruction theorems, including some recent results. In the Appendix a derivation of the Clebsch-Gordan series of SU(2) based only on information about the dimensions of the irreps is presented.","authors_text":"Zoltan Zimboras","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2005-12-05T19:38:32Z","title":"What can one reconstruct from the representation ring of a compact group?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512107","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":"sha256:94df00eb6e002470ed718d18e5d18999b0f88999e5dd6802b6be733c16496c66","target":"record","created_at":"2026-05-18T04:28:55Z","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":"858451ac93107a4e9ae47078deb76e676ddd7298fa4dd09c10d84300a753cb03","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"","primary_cat":"math.GR","submitted_at":"2005-12-05T19:38:32Z","title_canon_sha256":"251e9c3a945bf205fcf01320f3a87b69c8e442a7540ef828ce3767a7a3930fca"},"schema_version":"1.0","source":{"id":"math/0512107","kind":"arxiv","version":1}},"canonical_sha256":"a28c62c2fcae369ba85a81ab1b26d70f847cf7e292ac458825a7942a6f1d5ab3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a28c62c2fcae369ba85a81ab1b26d70f847cf7e292ac458825a7942a6f1d5ab3","first_computed_at":"2026-05-18T04:28:55.976188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:55.976188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dd597vrGJkPUaocBgBPPQaJnSOv9KqL7xzCC0O+VMQAQ40Xu/GbyPnAIuW9wfimk+RaMRuWlTnNHokVyyPPMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:55.976811Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94df00eb6e002470ed718d18e5d18999b0f88999e5dd6802b6be733c16496c66","sha256:e935b7bc5a4e48bda202f2487912f0c1c56b5ea8f196687053a2a560ead301ce"],"state_sha256":"78b4f470b21b9240c732ab001ce140db51dcece4bab6a4fbf014af677d230a8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3k6rLq+C3tkpg2rQB/+zs77RCX6t4QKm7Hhgq1d44WcigbKqXMgYtWqxFhT3wTlfa62cXRwTnyeCV6wHUSQCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:53:12.529245Z","bundle_sha256":"ea6a9a514980d37bec7511b2769e3d5d3955b3e7659ce070c61187aede3aefaa"}}