{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:MKNEALPCJYPKEZXN43RESXN42P","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":"c4f835d5b1580a1e67acddbb29a73a711b30c91793b75dcb3bea389869eed605","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-03-07T10:44:40Z","title_canon_sha256":"d58e9ffa8919341c9571b4a5a67f12d3483aa8ded782af5d2fbb63c7cb921d49"},"schema_version":"1.0","source":{"id":"quant-ph/0603051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0603051","created_at":"2026-05-18T01:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0603051v2","created_at":"2026-05-18T01:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0603051","created_at":"2026-05-18T01:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"MKNEALPCJYPK","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MKNEALPCJYPKEZXN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MKNEALPC","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:70a43e77b90df7dfcca9341c111e2bc4a04d9c57b7f9c3d1dc13c232d4e8c4d3","target":"graph","created_at":"2026-05-18T01:37:57Z","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":"The paper deals with the projective line over the finite factor ring $R\\_{\\clubsuit} \\equiv$ GF(2)[$x$]/$<x^{3} - x>$. The line is endowed with 18 points, spanning the neighbourhoods of three pairwise distant points. As $R\\_{\\clubsuit}$ is not a local ring, the neighbour (or parallel) relation is not an equivalence relation so that the sets of neighbour points to two distant points overlap. There are nine neighbour points to any point of the line, forming three disjoint families under the reduction modulo either of two maximal ideals of the ring. Two of the families contain four points each an","authors_text":"Metod Saniga (ASTRINSTSAV), Michel Planat (FEMTO-ST)","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-03-07T10:44:40Z","title":"The Projective Line Over the Finite Quotient Ring GF(2)[$x$]/$< x^{3} - x>$ and Quantum Entanglement I. Theoretical Background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0603051","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":"sha256:2798f13120297504d7375a723d61c83aecc22288cec9f63eb3e1b21030680844","target":"record","created_at":"2026-05-18T01:37:57Z","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":"c4f835d5b1580a1e67acddbb29a73a711b30c91793b75dcb3bea389869eed605","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-03-07T10:44:40Z","title_canon_sha256":"d58e9ffa8919341c9571b4a5a67f12d3483aa8ded782af5d2fbb63c7cb921d49"},"schema_version":"1.0","source":{"id":"quant-ph/0603051","kind":"arxiv","version":2}},"canonical_sha256":"629a402de24e1ea266ede6e2495dbcd3c7db220cd83609668c0471b47a02c1f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"629a402de24e1ea266ede6e2495dbcd3c7db220cd83609668c0471b47a02c1f5","first_computed_at":"2026-05-18T01:37:57.099261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:57.099261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LKU+ACTo/RdMDaCC7g9Xn5+jxe2/OqByxcnZvJMUWcY1ZbrnAU/K7xFhhB0MST4XUwzHUr53/mBTE+a4r9ysAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:57.099809Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0603051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2798f13120297504d7375a723d61c83aecc22288cec9f63eb3e1b21030680844","sha256:70a43e77b90df7dfcca9341c111e2bc4a04d9c57b7f9c3d1dc13c232d4e8c4d3"],"state_sha256":"d9d7ca2e543299481aabbb0293a99b89f84f0d2393c35667bef5649e5ffe9ddf"}