{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YRR3OHG4HCTRBFDHW7RW5PJYEJ","short_pith_number":"pith:YRR3OHG4","canonical_record":{"source":{"id":"1405.2169","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T08:31:54Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"3191f5345a010091cb297bff2bd7199ba1adaaf5de9720a16ab76a0fc8a26757","abstract_canon_sha256":"b6fa0914223a9fb3e1cc11f7e96450e59ea50a2a22edd23e491acd5327a0cf7c"},"schema_version":"1.0"},"canonical_sha256":"c463b71cdc38a7109467b7e36ebd382254392f1b3bc4a0630654b2ad1a95839e","source":{"kind":"arxiv","id":"1405.2169","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2169","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2169v3","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2169","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"YRR3OHG4HCTR","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YRR3OHG4HCTRBFDH","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YRR3OHG4","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YRR3OHG4HCTRBFDHW7RW5PJYEJ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2169","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T08:31:54Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"3191f5345a010091cb297bff2bd7199ba1adaaf5de9720a16ab76a0fc8a26757","abstract_canon_sha256":"b6fa0914223a9fb3e1cc11f7e96450e59ea50a2a22edd23e491acd5327a0cf7c"},"schema_version":"1.0"},"canonical_sha256":"c463b71cdc38a7109467b7e36ebd382254392f1b3bc4a0630654b2ad1a95839e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:15.802432Z","signature_b64":"hYAW8tUM0F97paORlo/ESzlDlmVQ7XSag+MrZDsiWqRp45+s5oYofRGvmCN51tJmV+cmYpMtHN2GK7CmAZOqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c463b71cdc38a7109467b7e36ebd382254392f1b3bc4a0630654b2ad1a95839e","last_reissued_at":"2026-05-18T01:43:15.801769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:15.801769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2169","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/9hNeSTh3dwaFrWv75FD3a+W5sabTRIgkyYd4v6WFcoXIg6gfjCbFkRP74Hsq34W15k9p73NGwKLT0B7FiUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:17:36.795223Z"},"content_sha256":"12e088beb54115f47a531737d90f7726fc97782e3c65b2a8ae3a10a5da4cc754","schema_version":"1.0","event_id":"sha256:12e088beb54115f47a531737d90f7726fc97782e3c65b2a8ae3a10a5da4cc754"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YRR3OHG4HCTRBFDHW7RW5PJYEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit constructions of unitary transformations between equivalent irreducible representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.RT","authors_text":"Marek Mozrzymas, Micha{\\l} Horodecki, Micha{\\l} Studzi\\'nski","submitted_at":"2014-05-09T08:31:54Z","abstract_excerpt":"Irreducible representations (irreps) of a finite group $G$ are equivalent if there exists a similarity transformation between them. In this paper, we describe an explicit algorithm for constructing this transformation between a pair of equivalent irreps, assuming we are given an algorithm to compute the matrix elements of these irreps. Along the way, we derive a generalization of the classical orthogonality relations for matrix elements of irreps of finite groups. We give an explicit form of such unitary matrices for the important case of conjugated Young-Yamanouchi representations, when our g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2169","kind":"arxiv","version":3},"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":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmizHXatLzeGTSYPzq+xfTzSb1EMmAb7q9Hqfast6fBsQlc1j58q5MKRKEDotfU4SDmLp9BAIo4Ud5fjtbEXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:17:36.795956Z"},"content_sha256":"652ccaed22885b6aba570e0866e1f7fa63e560d1c1f3af2a9e8dcd321974e57b","schema_version":"1.0","event_id":"sha256:652ccaed22885b6aba570e0866e1f7fa63e560d1c1f3af2a9e8dcd321974e57b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YRR3OHG4HCTRBFDHW7RW5PJYEJ/bundle.json","state_url":"https://pith.science/pith/YRR3OHG4HCTRBFDHW7RW5PJYEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YRR3OHG4HCTRBFDHW7RW5PJYEJ/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":"2026-06-08T05:17:36Z","links":{"resolver":"https://pith.science/pith/YRR3OHG4HCTRBFDHW7RW5PJYEJ","bundle":"https://pith.science/pith/YRR3OHG4HCTRBFDHW7RW5PJYEJ/bundle.json","state":"https://pith.science/pith/YRR3OHG4HCTRBFDHW7RW5PJYEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YRR3OHG4HCTRBFDHW7RW5PJYEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YRR3OHG4HCTRBFDHW7RW5PJYEJ","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":"b6fa0914223a9fb3e1cc11f7e96450e59ea50a2a22edd23e491acd5327a0cf7c","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T08:31:54Z","title_canon_sha256":"3191f5345a010091cb297bff2bd7199ba1adaaf5de9720a16ab76a0fc8a26757"},"schema_version":"1.0","source":{"id":"1405.2169","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2169","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2169v3","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2169","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"YRR3OHG4HCTR","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YRR3OHG4HCTRBFDH","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YRR3OHG4","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:652ccaed22885b6aba570e0866e1f7fa63e560d1c1f3af2a9e8dcd321974e57b","target":"graph","created_at":"2026-05-18T01:43:15Z","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":"Irreducible representations (irreps) of a finite group $G$ are equivalent if there exists a similarity transformation between them. In this paper, we describe an explicit algorithm for constructing this transformation between a pair of equivalent irreps, assuming we are given an algorithm to compute the matrix elements of these irreps. Along the way, we derive a generalization of the classical orthogonality relations for matrix elements of irreps of finite groups. We give an explicit form of such unitary matrices for the important case of conjugated Young-Yamanouchi representations, when our g","authors_text":"Marek Mozrzymas, Micha{\\l} Horodecki, Micha{\\l} Studzi\\'nski","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T08:31:54Z","title":"Explicit constructions of unitary transformations between equivalent irreducible representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2169","kind":"arxiv","version":3},"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":"sha256:12e088beb54115f47a531737d90f7726fc97782e3c65b2a8ae3a10a5da4cc754","target":"record","created_at":"2026-05-18T01:43:15Z","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":"b6fa0914223a9fb3e1cc11f7e96450e59ea50a2a22edd23e491acd5327a0cf7c","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T08:31:54Z","title_canon_sha256":"3191f5345a010091cb297bff2bd7199ba1adaaf5de9720a16ab76a0fc8a26757"},"schema_version":"1.0","source":{"id":"1405.2169","kind":"arxiv","version":3}},"canonical_sha256":"c463b71cdc38a7109467b7e36ebd382254392f1b3bc4a0630654b2ad1a95839e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c463b71cdc38a7109467b7e36ebd382254392f1b3bc4a0630654b2ad1a95839e","first_computed_at":"2026-05-18T01:43:15.801769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:15.801769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hYAW8tUM0F97paORlo/ESzlDlmVQ7XSag+MrZDsiWqRp45+s5oYofRGvmCN51tJmV+cmYpMtHN2GK7CmAZOqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:15.802432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2169","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12e088beb54115f47a531737d90f7726fc97782e3c65b2a8ae3a10a5da4cc754","sha256:652ccaed22885b6aba570e0866e1f7fa63e560d1c1f3af2a9e8dcd321974e57b"],"state_sha256":"0cb51943526dc5b168f9fd5a81235e8f66978ac2304aabb55916433258840b4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iI6aj7L/K1krHlCzixsOPVVvcxfGkR/43BaT8fpCaO5GEJ/FzP7ubLbchNscPrI2TLhvHBYDvinAgOls9TeaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T05:17:36.799858Z","bundle_sha256":"ba2c43be200d1f92f5aa42275bcfc76504e84440f0cb0f8f19adc38158049d49"}}