{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WXLNDOIMW67GPTQRTJWLLXV7CX","short_pith_number":"pith:WXLNDOIM","canonical_record":{"source":{"id":"1401.0099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-31T05:45:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e0323716c2d7d2af62fed5ea3e6528eb2be469027d25342e34f1877fe073571f","abstract_canon_sha256":"567eb9246b5a988c912a738b30de5618d3619444fc454ce22858169865c5e421"},"schema_version":"1.0"},"canonical_sha256":"b5d6d1b90cb7be67ce119a6cb5debf15cfa32ff470998ce8575378bf471dc76d","source":{"kind":"arxiv","id":"1401.0099","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0099","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0099v1","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0099","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"WXLNDOIMW67G","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WXLNDOIMW67GPTQR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WXLNDOIM","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WXLNDOIMW67GPTQRTJWLLXV7CX","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-31T05:45:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e0323716c2d7d2af62fed5ea3e6528eb2be469027d25342e34f1877fe073571f","abstract_canon_sha256":"567eb9246b5a988c912a738b30de5618d3619444fc454ce22858169865c5e421"},"schema_version":"1.0"},"canonical_sha256":"b5d6d1b90cb7be67ce119a6cb5debf15cfa32ff470998ce8575378bf471dc76d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:31.038715Z","signature_b64":"7UXQqjuB7GtOBm3IaooH7eUU8wDk+Q0F47TyUHlbiPu5yHJx2dGDieqVj7480BHEzcP+KpFrnm5XCxeQ61N6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5d6d1b90cb7be67ce119a6cb5debf15cfa32ff470998ce8575378bf471dc76d","last_reissued_at":"2026-05-18T03:03:31.038182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:31.038182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0099","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":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"35QS02BXtJzZIErLY/YmpKd8GGgzXq8OOqrzp8fmwlfxqPt24fLoyhPgCwYhXqgO2fLnYvuFGpYDpFJF1QvVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:17:09.200906Z"},"content_sha256":"95e53d7d6150e16ef97f3f82877679fe5c4e3d25747e46fbf0d72aa60a719255","schema_version":"1.0","event_id":"sha256:95e53d7d6150e16ef97f3f82877679fe5c4e3d25747e46fbf0d72aa60a719255"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WXLNDOIMW67GPTQRTJWLLXV7CX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants for maximally entangled vectors and unitary bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Ajit Iqbal Singh, Sibasish Ghosh","submitted_at":"2013-12-31T05:45:53Z","abstract_excerpt":"The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. Werner [{\\it J. Phys. A: Math. Gen.} {\\bf 34} (2001) 7081], relate it to local operations on maximally entangled vectors bases, find an invariant for equivalence classes in terms of certain commuting systems, and, relate it to mutually unbiased bases and Hadamard matrices. Illustrations are given in the context of latin squares and projective representations as well. Applications to quantum tomography are indicated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0099","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":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yREWuLu7H/6UxDzr44o1oAjy2l4YaOXHQliRa6Us9612p/ysnxkMlo3F5b4Ybkc5ym/4105Fp8Ny2Z+DYCWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:17:09.201574Z"},"content_sha256":"c36c9619dd47de0078e40de3739d885dc32d02e57c3621ae359401ed16baba77","schema_version":"1.0","event_id":"sha256:c36c9619dd47de0078e40de3739d885dc32d02e57c3621ae359401ed16baba77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WXLNDOIMW67GPTQRTJWLLXV7CX/bundle.json","state_url":"https://pith.science/pith/WXLNDOIMW67GPTQRTJWLLXV7CX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WXLNDOIMW67GPTQRTJWLLXV7CX/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":"2026-05-23T22:17:09Z","links":{"resolver":"https://pith.science/pith/WXLNDOIMW67GPTQRTJWLLXV7CX","bundle":"https://pith.science/pith/WXLNDOIMW67GPTQRTJWLLXV7CX/bundle.json","state":"https://pith.science/pith/WXLNDOIMW67GPTQRTJWLLXV7CX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WXLNDOIMW67GPTQRTJWLLXV7CX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WXLNDOIMW67GPTQRTJWLLXV7CX","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":"567eb9246b5a988c912a738b30de5618d3619444fc454ce22858169865c5e421","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-31T05:45:53Z","title_canon_sha256":"e0323716c2d7d2af62fed5ea3e6528eb2be469027d25342e34f1877fe073571f"},"schema_version":"1.0","source":{"id":"1401.0099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0099","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0099v1","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0099","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"WXLNDOIMW67G","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WXLNDOIMW67GPTQR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WXLNDOIM","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:c36c9619dd47de0078e40de3739d885dc32d02e57c3621ae359401ed16baba77","target":"graph","created_at":"2026-05-18T03:03:31Z","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":"The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. Werner [{\\it J. Phys. A: Math. Gen.} {\\bf 34} (2001) 7081], relate it to local operations on maximally entangled vectors bases, find an invariant for equivalence classes in terms of certain commuting systems, and, relate it to mutually unbiased bases and Hadamard matrices. Illustrations are given in the context of latin squares and projective representations as well. Applications to quantum tomography are indicated.","authors_text":"Ajit Iqbal Singh, Sibasish Ghosh","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-31T05:45:53Z","title":"Invariants for maximally entangled vectors and unitary bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0099","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":"sha256:95e53d7d6150e16ef97f3f82877679fe5c4e3d25747e46fbf0d72aa60a719255","target":"record","created_at":"2026-05-18T03:03:31Z","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":"567eb9246b5a988c912a738b30de5618d3619444fc454ce22858169865c5e421","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-31T05:45:53Z","title_canon_sha256":"e0323716c2d7d2af62fed5ea3e6528eb2be469027d25342e34f1877fe073571f"},"schema_version":"1.0","source":{"id":"1401.0099","kind":"arxiv","version":1}},"canonical_sha256":"b5d6d1b90cb7be67ce119a6cb5debf15cfa32ff470998ce8575378bf471dc76d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5d6d1b90cb7be67ce119a6cb5debf15cfa32ff470998ce8575378bf471dc76d","first_computed_at":"2026-05-18T03:03:31.038182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:31.038182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7UXQqjuB7GtOBm3IaooH7eUU8wDk+Q0F47TyUHlbiPu5yHJx2dGDieqVj7480BHEzcP+KpFrnm5XCxeQ61N6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:31.038715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95e53d7d6150e16ef97f3f82877679fe5c4e3d25747e46fbf0d72aa60a719255","sha256:c36c9619dd47de0078e40de3739d885dc32d02e57c3621ae359401ed16baba77"],"state_sha256":"1dec4e1594a4cd774233f92f9200f2d77ae8e8dd96e27c6dd0c508c5c2071588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WkR1nd5Cw5+AZJVwDawUmnoVdtWCdVtO/W/zyB7WehszFNd80tVEDj+A6U/o+kpinL1sUht/FMqApP65+gP5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T22:17:09.204901Z","bundle_sha256":"776f55dcf76d35abe099bf161049087ee27a1aceab93c27fc7b68356c2322917"}}