{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MVWTYZI2SH56GJEAILNF5QWD4B","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":"d6c3795ab3a7811814b5d4d93d2270ae8f9c1fed0b577ceaf78126cc912985a0","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-27T14:40:46Z","title_canon_sha256":"3bb53e05339923c84be2cfca27cfb61da48e84e7a5c5098a2a1130e6aabb5c3f"},"schema_version":"1.0","source":{"id":"1204.6229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6229","created_at":"2026-05-18T03:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6229v2","created_at":"2026-05-18T03:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6229","created_at":"2026-05-18T03:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"MVWTYZI2SH56","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MVWTYZI2SH56GJEA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MVWTYZI2","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:ee106adee517837cd6127b2dd1464c9527d2fc45e762dcba9ffc82d23a9fb13c","target":"graph","created_at":"2026-05-18T03:49:57Z","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":"A \"magic rectangle\" of eleven observables of four qubits, employed by Harvey and Chryssanthacopoulos (2008) to prove the Bell-Kochen-Specker theorem in a 16-dimensional Hilbert space, is given a neat finite-geometrical reinterpretation in terms of the structure of the symplectic polar space $W(7, 2)$ of the real four-qubit Pauli group. Each of the four sets of observables of cardinality five represents an elliptic quadric in the three-dimensional projective space of order two (PG$(3, 2)$) it spans, whereas the remaining set of cardinality four corresponds to an affine plane of order two. The f","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":"2012-04-27T14:40:46Z","title":"Finite Geometry Behind the Harvey-Chryssanthacopoulos Four-Qubit Magic Rectangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6229","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":"sha256:89c2b588aa25589b16bbcfcce07feca85bea714e853c1a0958929454d3ba79e7","target":"record","created_at":"2026-05-18T03:49:57Z","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":"d6c3795ab3a7811814b5d4d93d2270ae8f9c1fed0b577ceaf78126cc912985a0","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-27T14:40:46Z","title_canon_sha256":"3bb53e05339923c84be2cfca27cfb61da48e84e7a5c5098a2a1130e6aabb5c3f"},"schema_version":"1.0","source":{"id":"1204.6229","kind":"arxiv","version":2}},"canonical_sha256":"656d3c651a91fbe3248042da5ec2c3e04dc00fef3881ca2da739e6fafbd0558a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"656d3c651a91fbe3248042da5ec2c3e04dc00fef3881ca2da739e6fafbd0558a","first_computed_at":"2026-05-18T03:49:57.969404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:57.969404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bKDE4Iq/PhQq+kNKPDWjtCvm019r5QodfzCuMaD/ky8ui/UKdGJ8HHXHF9yqsUyL4//yGnWDxzQRBt7az1STBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:57.969845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89c2b588aa25589b16bbcfcce07feca85bea714e853c1a0958929454d3ba79e7","sha256:ee106adee517837cd6127b2dd1464c9527d2fc45e762dcba9ffc82d23a9fb13c"],"state_sha256":"8e1b32cef3432d2bd84284635d1530693aeffa1a796c232d06e18f36dd0d9271"}