{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YQZBFMZZ46PHBOI4TORW5FVUGR","short_pith_number":"pith:YQZBFMZZ","canonical_record":{"source":{"id":"1605.02001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T16:42:19Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"2f479268ea2d84ce2f29b96b739b0d458df85d33759af2de2ddc2a1fd05ff119","abstract_canon_sha256":"c6da96ecdce2e656b85e94a4d109c12ccff31ee70b3ffba03ff1ccd0be6155af"},"schema_version":"1.0"},"canonical_sha256":"c43212b339e79e70b91c9ba36e96b43478f89de9ed0e27ae0ab85b0398705c24","source":{"kind":"arxiv","id":"1605.02001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02001","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02001v1","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02001","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"YQZBFMZZ46PH","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YQZBFMZZ46PHBOI4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YQZBFMZZ","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YQZBFMZZ46PHBOI4TORW5FVUGR","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T16:42:19Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"2f479268ea2d84ce2f29b96b739b0d458df85d33759af2de2ddc2a1fd05ff119","abstract_canon_sha256":"c6da96ecdce2e656b85e94a4d109c12ccff31ee70b3ffba03ff1ccd0be6155af"},"schema_version":"1.0"},"canonical_sha256":"c43212b339e79e70b91c9ba36e96b43478f89de9ed0e27ae0ab85b0398705c24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:01.331626Z","signature_b64":"eVJeRDnbstU8BW96ooWoBumYeGG6o+JevwgyALdwD8drSd/XUY9byTw96HrR64aRkD37jH0RMl+rzR0F5AYECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c43212b339e79e70b91c9ba36e96b43478f89de9ed0e27ae0ab85b0398705c24","last_reissued_at":"2026-05-18T00:50:01.330947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:01.330947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02001","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":"2026-05-18T00:50:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dRZyhSleMzs4JgR5aU6iv1pKeZl+hd70PpW9QjRgYBelx84qgTRg448OL+E2HEbFPKxkhSxl4xFV35XNDNQhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:31:46.246244Z"},"content_sha256":"25d894a3146701a285022d3a40af6dccb45824c0e571e9bb437f62b388137b36","schema_version":"1.0","event_id":"sha256:25d894a3146701a285022d3a40af6dccb45824c0e571e9bb437f62b388137b36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YQZBFMZZ46PHBOI4TORW5FVUGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Veldkamp Spaces: From (Dynkin) Diagrams to (Pauli) Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.CO","authors_text":"Frederic Holweck, Metod Saniga, Petr Pracna","submitted_at":"2016-05-06T16:42:19Z","abstract_excerpt":"Regarding a Dynkin diagram as a specific point-line incidence structure (where each line has just two points), one can associate with it a Veldkamp space. Focusing on extended Dynkin diagrams of type $\\widetilde{D}_n$, $4 \\leq n \\leq 8$, it is shown that the corresponding Veldkamp space always contains a distinguished copy of the projective space PG$(3,2)$. Proper labelling of the vertices of the diagram (for $4 \\leq n \\leq 7$) by particular elements of the two-qubit Pauli group establishes a bijection between the 15 elements of the group and the 15 points of the PG$(3,2)$. The bijection is su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02001","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":"2026-05-18T00:50:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O0LMIKmhOHcT8t80pfTayyZSSd/u9kw3BYoJWGIrDNg0MBinF6G0P3dS4/dAeV8YEccBl95/HDLIV6/e3n4eBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:31:46.246615Z"},"content_sha256":"030f08894b47e85607f9fb3ab1e14bde58f9241e11041071d45d73e597d9242e","schema_version":"1.0","event_id":"sha256:030f08894b47e85607f9fb3ab1e14bde58f9241e11041071d45d73e597d9242e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQZBFMZZ46PHBOI4TORW5FVUGR/bundle.json","state_url":"https://pith.science/pith/YQZBFMZZ46PHBOI4TORW5FVUGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQZBFMZZ46PHBOI4TORW5FVUGR/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":"2026-06-01T07:31:46Z","links":{"resolver":"https://pith.science/pith/YQZBFMZZ46PHBOI4TORW5FVUGR","bundle":"https://pith.science/pith/YQZBFMZZ46PHBOI4TORW5FVUGR/bundle.json","state":"https://pith.science/pith/YQZBFMZZ46PHBOI4TORW5FVUGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQZBFMZZ46PHBOI4TORW5FVUGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YQZBFMZZ46PHBOI4TORW5FVUGR","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":"c6da96ecdce2e656b85e94a4d109c12ccff31ee70b3ffba03ff1ccd0be6155af","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T16:42:19Z","title_canon_sha256":"2f479268ea2d84ce2f29b96b739b0d458df85d33759af2de2ddc2a1fd05ff119"},"schema_version":"1.0","source":{"id":"1605.02001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02001","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02001v1","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02001","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"YQZBFMZZ46PH","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YQZBFMZZ46PHBOI4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YQZBFMZZ","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:030f08894b47e85607f9fb3ab1e14bde58f9241e11041071d45d73e597d9242e","target":"graph","created_at":"2026-05-18T00:50:01Z","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":"Regarding a Dynkin diagram as a specific point-line incidence structure (where each line has just two points), one can associate with it a Veldkamp space. Focusing on extended Dynkin diagrams of type $\\widetilde{D}_n$, $4 \\leq n \\leq 8$, it is shown that the corresponding Veldkamp space always contains a distinguished copy of the projective space PG$(3,2)$. Proper labelling of the vertices of the diagram (for $4 \\leq n \\leq 7$) by particular elements of the two-qubit Pauli group establishes a bijection between the 15 elements of the group and the 15 points of the PG$(3,2)$. The bijection is su","authors_text":"Frederic Holweck, Metod Saniga, Petr Pracna","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T16:42:19Z","title":"Veldkamp Spaces: From (Dynkin) Diagrams to (Pauli) Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02001","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":"sha256:25d894a3146701a285022d3a40af6dccb45824c0e571e9bb437f62b388137b36","target":"record","created_at":"2026-05-18T00:50:01Z","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":"c6da96ecdce2e656b85e94a4d109c12ccff31ee70b3ffba03ff1ccd0be6155af","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T16:42:19Z","title_canon_sha256":"2f479268ea2d84ce2f29b96b739b0d458df85d33759af2de2ddc2a1fd05ff119"},"schema_version":"1.0","source":{"id":"1605.02001","kind":"arxiv","version":1}},"canonical_sha256":"c43212b339e79e70b91c9ba36e96b43478f89de9ed0e27ae0ab85b0398705c24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c43212b339e79e70b91c9ba36e96b43478f89de9ed0e27ae0ab85b0398705c24","first_computed_at":"2026-05-18T00:50:01.330947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:01.330947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eVJeRDnbstU8BW96ooWoBumYeGG6o+JevwgyALdwD8drSd/XUY9byTw96HrR64aRkD37jH0RMl+rzR0F5AYECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:01.331626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25d894a3146701a285022d3a40af6dccb45824c0e571e9bb437f62b388137b36","sha256:030f08894b47e85607f9fb3ab1e14bde58f9241e11041071d45d73e597d9242e"],"state_sha256":"12b577d363e49714e0be507a22b1cde8b75174e9ed39bc52be4b6b1fd1ac8dc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wz6AFJ/+QRnc3cBQN4AcuJ9qQwmFegvILbXoiHJfYq3FxwrifLIrvJ+Pnj6CWRAZcIdYQAAfZBH7i3cgc6rGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:31:46.248687Z","bundle_sha256":"03fb01648ee1e0841b2a02231598f59332f7f61767cbef3232b8d2166672d24b"}}