{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:O2RZRBNQHWUH7VY5FHOQA4KBQN","short_pith_number":"pith:O2RZRBNQ","canonical_record":{"source":{"id":"1102.3281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-16T10:02:16Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"7143e51807dc36ef14de91d746cfc6129528e19683eb4f9217d769aae427cc3a","abstract_canon_sha256":"d8e5b29dfb01e9286778cfd107d6991b4ef6b14022c1befebb489b5d4d71a35a"},"schema_version":"1.0"},"canonical_sha256":"76a39885b03da87fd71d29dd007141835c15848acc448ba7d546de8dff360c41","source":{"kind":"arxiv","id":"1102.3281","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3281","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3281v2","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3281","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"O2RZRBNQHWUH","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O2RZRBNQHWUH7VY5","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O2RZRBNQ","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:O2RZRBNQHWUH7VY5FHOQA4KBQN","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-16T10:02:16Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"7143e51807dc36ef14de91d746cfc6129528e19683eb4f9217d769aae427cc3a","abstract_canon_sha256":"d8e5b29dfb01e9286778cfd107d6991b4ef6b14022c1befebb489b5d4d71a35a"},"schema_version":"1.0"},"canonical_sha256":"76a39885b03da87fd71d29dd007141835c15848acc448ba7d546de8dff360c41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:02.327866Z","signature_b64":"oufOYQ7gJ4D7gYmYbXlgERcw1cx4y2xhk3dvU6TCeUY1av1agPyS+OEUM+KOcJ92r+1lUpaF1+wK3M+p8zA2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76a39885b03da87fd71d29dd007141835c15848acc448ba7d546de8dff360c41","last_reissued_at":"2026-05-18T04:23:02.327193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:02.327193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3281","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLnlt37OWyEWHi0MxcNyCR9+PEeImyvBXG8Hy2fLPKMBG339L9QSoz0PRH2XfBBKB1ecu2K6kJ2LR4fbkaB+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:55:56.446696Z"},"content_sha256":"a123da177baf97a17213f07c51c8bbda10c93a6e3dcacab0caf065860cd8da8d","schema_version":"1.0","event_id":"sha256:a123da177baf97a17213f07c51c8bbda10c93a6e3dcacab0caf065860cd8da8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:O2RZRBNQHWUH7VY5FHOQA4KBQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Sequence of Qubit-Qudit Pauli Groups as a Nested Structure of Doilies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"quant-ph","authors_text":"Metod Saniga, Michel Planat","submitted_at":"2011-02-16T10:02:16Z","abstract_excerpt":"Following the spirit of a recent work of one of the authors (J. Phys. A: Math. Theor. 44 (2011) 045301), the essential structure of the generalized Pauli group of a qubit-qu$d$it, where $d = 2^{k}$ and an integer $k \\geq 2$, is recast in the language of a finite geometry. A point of such geometry is represented by the maximum set of mutually commuting elements of the group and two distinct points are regarded as collinear if the corresponding sets have exactly $2^{k} - 1$ elements in common. The geometry comprises $2^{k} - 1$ copies of the generalized quadrangle of order two (\"the doily\") that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3281","kind":"arxiv","version":2},"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":"2026-05-18T04:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/iPwQYJEmGzUkwfYK4CWigKIZJMK1ciORESwGsd80y8ZE5Si8c0q7bU6X0aV1iD3UL+NuBs0OjIUEH6TWaIyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:55:56.447299Z"},"content_sha256":"7792bdac060374106a7697ce00ab75f6d1a37c985e03b0cab21548c3db89ec1d","schema_version":"1.0","event_id":"sha256:7792bdac060374106a7697ce00ab75f6d1a37c985e03b0cab21548c3db89ec1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2RZRBNQHWUH7VY5FHOQA4KBQN/bundle.json","state_url":"https://pith.science/pith/O2RZRBNQHWUH7VY5FHOQA4KBQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2RZRBNQHWUH7VY5FHOQA4KBQN/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":"2026-05-27T22:55:56Z","links":{"resolver":"https://pith.science/pith/O2RZRBNQHWUH7VY5FHOQA4KBQN","bundle":"https://pith.science/pith/O2RZRBNQHWUH7VY5FHOQA4KBQN/bundle.json","state":"https://pith.science/pith/O2RZRBNQHWUH7VY5FHOQA4KBQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2RZRBNQHWUH7VY5FHOQA4KBQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:O2RZRBNQHWUH7VY5FHOQA4KBQN","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":"d8e5b29dfb01e9286778cfd107d6991b4ef6b14022c1befebb489b5d4d71a35a","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-16T10:02:16Z","title_canon_sha256":"7143e51807dc36ef14de91d746cfc6129528e19683eb4f9217d769aae427cc3a"},"schema_version":"1.0","source":{"id":"1102.3281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3281","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3281v2","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3281","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"O2RZRBNQHWUH","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O2RZRBNQHWUH7VY5","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O2RZRBNQ","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:7792bdac060374106a7697ce00ab75f6d1a37c985e03b0cab21548c3db89ec1d","target":"graph","created_at":"2026-05-18T04:23:02Z","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":"Following the spirit of a recent work of one of the authors (J. Phys. A: Math. Theor. 44 (2011) 045301), the essential structure of the generalized Pauli group of a qubit-qu$d$it, where $d = 2^{k}$ and an integer $k \\geq 2$, is recast in the language of a finite geometry. A point of such geometry is represented by the maximum set of mutually commuting elements of the group and two distinct points are regarded as collinear if the corresponding sets have exactly $2^{k} - 1$ elements in common. The geometry comprises $2^{k} - 1$ copies of the generalized quadrangle of order two (\"the doily\") that","authors_text":"Metod Saniga, Michel Planat","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-16T10:02:16Z","title":"A Sequence of Qubit-Qudit Pauli Groups as a Nested Structure of Doilies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3281","kind":"arxiv","version":2},"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:a123da177baf97a17213f07c51c8bbda10c93a6e3dcacab0caf065860cd8da8d","target":"record","created_at":"2026-05-18T04:23:02Z","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":"d8e5b29dfb01e9286778cfd107d6991b4ef6b14022c1befebb489b5d4d71a35a","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-16T10:02:16Z","title_canon_sha256":"7143e51807dc36ef14de91d746cfc6129528e19683eb4f9217d769aae427cc3a"},"schema_version":"1.0","source":{"id":"1102.3281","kind":"arxiv","version":2}},"canonical_sha256":"76a39885b03da87fd71d29dd007141835c15848acc448ba7d546de8dff360c41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76a39885b03da87fd71d29dd007141835c15848acc448ba7d546de8dff360c41","first_computed_at":"2026-05-18T04:23:02.327193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:02.327193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oufOYQ7gJ4D7gYmYbXlgERcw1cx4y2xhk3dvU6TCeUY1av1agPyS+OEUM+KOcJ92r+1lUpaF1+wK3M+p8zA2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:02.327866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a123da177baf97a17213f07c51c8bbda10c93a6e3dcacab0caf065860cd8da8d","sha256:7792bdac060374106a7697ce00ab75f6d1a37c985e03b0cab21548c3db89ec1d"],"state_sha256":"07f36e953e09b2a6dca277abd2870af231da339bbe90c6dc921b37998d63d1c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xDlPkoD8mm0oSGAF3+5MGQj9c29lLXHZeieWh4pa6eR1dUwg30ffyPFfaogORaokohg9+7vgtZI/v5IHJPAVBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:55:56.450608Z","bundle_sha256":"1a4b41127c73db4fbc5d79c829b5f9f3ce9dcb5c4cbfcdea6f7181a1d5bfdb7b"}}