{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QNWFAZXNTBUZCG3KRG7O4UTSOZ","short_pith_number":"pith:QNWFAZXN","canonical_record":{"source":{"id":"1605.01426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-05-04T20:27:16Z","cross_cats_sorted":[],"title_canon_sha256":"2d07d7290aad42220493637ddddefba8ccdfc0db638d2c301f62f9b48de10e7a","abstract_canon_sha256":"465d67c00c44111dc21fa7e643034192b5de5ff948370b19ce4aa35ae0114d65"},"schema_version":"1.0"},"canonical_sha256":"836c5066ed9869911b6a89beee5272766c31cdaba1963c8602edc5b8c8dc869c","source":{"kind":"arxiv","id":"1605.01426","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01426","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01426v1","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01426","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"QNWFAZXNTBUZ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNWFAZXNTBUZCG3K","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNWFAZXN","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QNWFAZXNTBUZCG3KRG7O4UTSOZ","target":"record","payload":{"canonical_record":{"source":{"id":"1605.01426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-05-04T20:27:16Z","cross_cats_sorted":[],"title_canon_sha256":"2d07d7290aad42220493637ddddefba8ccdfc0db638d2c301f62f9b48de10e7a","abstract_canon_sha256":"465d67c00c44111dc21fa7e643034192b5de5ff948370b19ce4aa35ae0114d65"},"schema_version":"1.0"},"canonical_sha256":"836c5066ed9869911b6a89beee5272766c31cdaba1963c8602edc5b8c8dc869c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:21.024311Z","signature_b64":"MD2t9pBXWfyAYwvkG45opKro+3YG5j2hcVl8rUMRJePP1lwucYdF4mOPmhWBzstB8Q4KBXLqxASaq1nWZ4mmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"836c5066ed9869911b6a89beee5272766c31cdaba1963c8602edc5b8c8dc869c","last_reissued_at":"2026-05-18T00:46:21.023975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:21.023975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.01426","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":"2026-05-18T00:46:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zEIqo7BXKZZCMz8Sfkvs9qON4Ug6WCRXiVaMEllwc8dl2CJorR7VDskgX4yg9GjEc03vSe9357qoiCHeDpJYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:04:20.305263Z"},"content_sha256":"5a79a7ea5837b9e944dee03338e7b3d0cecd2f948b4d800d4655bc4bea15b796","schema_version":"1.0","event_id":"sha256:5a79a7ea5837b9e944dee03338e7b3d0cecd2f948b4d800d4655bc4bea15b796"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QNWFAZXNTBUZCG3KRG7O4UTSOZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sporadic SICs and the Normed Division Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Blake C. Stacey","submitted_at":"2016-05-04T20:27:16Z","abstract_excerpt":"Recently, Zhu classified all the SIC-POVMs whose symmetry groups act doubly transitively. Lattices of integers in the complex numbers, the quaternions and the octonions yield the key parts of these symmetry groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01426","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":"2026-05-18T00:46:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kIqHwislPlVJ12oWLnX/U47mvcP17el5vEHO3Dhwol1PwXfXp1MRcr3t10sw29fdU+16twxp7NG8DnA225muDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:04:20.305628Z"},"content_sha256":"8d9a1c8b7dc68fdf103859b1762632bbb6a41a5272265ae0fe70c661277f55a4","schema_version":"1.0","event_id":"sha256:8d9a1c8b7dc68fdf103859b1762632bbb6a41a5272265ae0fe70c661277f55a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNWFAZXNTBUZCG3KRG7O4UTSOZ/bundle.json","state_url":"https://pith.science/pith/QNWFAZXNTBUZCG3KRG7O4UTSOZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNWFAZXNTBUZCG3KRG7O4UTSOZ/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":"2026-06-20T02:04:20Z","links":{"resolver":"https://pith.science/pith/QNWFAZXNTBUZCG3KRG7O4UTSOZ","bundle":"https://pith.science/pith/QNWFAZXNTBUZCG3KRG7O4UTSOZ/bundle.json","state":"https://pith.science/pith/QNWFAZXNTBUZCG3KRG7O4UTSOZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNWFAZXNTBUZCG3KRG7O4UTSOZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QNWFAZXNTBUZCG3KRG7O4UTSOZ","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":"465d67c00c44111dc21fa7e643034192b5de5ff948370b19ce4aa35ae0114d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-05-04T20:27:16Z","title_canon_sha256":"2d07d7290aad42220493637ddddefba8ccdfc0db638d2c301f62f9b48de10e7a"},"schema_version":"1.0","source":{"id":"1605.01426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01426","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01426v1","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01426","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"QNWFAZXNTBUZ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNWFAZXNTBUZCG3K","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNWFAZXN","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:8d9a1c8b7dc68fdf103859b1762632bbb6a41a5272265ae0fe70c661277f55a4","target":"graph","created_at":"2026-05-18T00:46:21Z","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":"Recently, Zhu classified all the SIC-POVMs whose symmetry groups act doubly transitively. Lattices of integers in the complex numbers, the quaternions and the octonions yield the key parts of these symmetry groups.","authors_text":"Blake C. Stacey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-05-04T20:27:16Z","title":"Sporadic SICs and the Normed Division Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01426","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":"sha256:5a79a7ea5837b9e944dee03338e7b3d0cecd2f948b4d800d4655bc4bea15b796","target":"record","created_at":"2026-05-18T00:46:21Z","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":"465d67c00c44111dc21fa7e643034192b5de5ff948370b19ce4aa35ae0114d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-05-04T20:27:16Z","title_canon_sha256":"2d07d7290aad42220493637ddddefba8ccdfc0db638d2c301f62f9b48de10e7a"},"schema_version":"1.0","source":{"id":"1605.01426","kind":"arxiv","version":1}},"canonical_sha256":"836c5066ed9869911b6a89beee5272766c31cdaba1963c8602edc5b8c8dc869c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"836c5066ed9869911b6a89beee5272766c31cdaba1963c8602edc5b8c8dc869c","first_computed_at":"2026-05-18T00:46:21.023975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:21.023975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MD2t9pBXWfyAYwvkG45opKro+3YG5j2hcVl8rUMRJePP1lwucYdF4mOPmhWBzstB8Q4KBXLqxASaq1nWZ4mmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:21.024311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a79a7ea5837b9e944dee03338e7b3d0cecd2f948b4d800d4655bc4bea15b796","sha256:8d9a1c8b7dc68fdf103859b1762632bbb6a41a5272265ae0fe70c661277f55a4"],"state_sha256":"5f2250442a133da7e0df0da91a0d51a3713fd3e18e7659daea338e7c7315df05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/dRdGeSfnCVmdrcoDeKHwXVSpe3C5ch6h8bYXrbdAT8wB7yTnXi/s0eLoOLfXOEQ+vNkwV5t19DR2IP/bQIFBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:04:20.307567Z","bundle_sha256":"81f7450cbc21a74590b8e6483c92e99dc0411ee96021c4d868d14bc785fe0112"}}