{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KG5XPS27E6N5SHOITUXDIVHFSW","short_pith_number":"pith:KG5XPS27","schema_version":"1.0","canonical_sha256":"51bb77cb5f279bd91dc89d2e3454e595a312a93ec4b8c573a64322d735365f9e","source":{"kind":"arxiv","id":"1509.03618","version":3},"attestation_state":"computed","paper":{"title":"A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP","math.RA","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander Ma, Manuel Reyes, Michael Ben-Zvi","submitted_at":"2015-09-11T19:18:15Z","abstract_excerpt":"We investigate the possibility of constructing Kochen-Specker uncolorable sets of idempotent matrices whose entries lie in various rings, including the rational numbers, the integers, and finite fields. Most notably, we show that there is no Kochen-Specker coloring of the $n \\times n$ idempotent integer matrices for $n \\geq 3$, thereby illustrating that Kochen-Specker contextuality is an inherent feature of pure matrix algebra. We apply this to generalize recent no-go results on noncommutative spectrum functors, showing that any contravariant functor from rings to sets (respectively, topologic"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.03618","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-11T19:18:15Z","cross_cats_sorted":["math.AG","math.MP","math.RA","quant-ph"],"title_canon_sha256":"c3f6e9ed154c00070f5e8374054d038a982e4ff9ac75d4f1b9e471da8684e7bf","abstract_canon_sha256":"b96b17796d9839f6d60c5800a67f9d531f64af74ed1f20b952c43a516b130ad3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:12.907431Z","signature_b64":"W9OYQi+XGecmFRRIINrNjqMNh00Ffpl/K/PXtxbm/5HspFMPczALOR3fj0XTQy0ddfDJhfCTFLlWle2itaVqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51bb77cb5f279bd91dc89d2e3454e595a312a93ec4b8c573a64322d735365f9e","last_reissued_at":"2026-05-18T00:38:12.906813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:12.906813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP","math.RA","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander Ma, Manuel Reyes, Michael Ben-Zvi","submitted_at":"2015-09-11T19:18:15Z","abstract_excerpt":"We investigate the possibility of constructing Kochen-Specker uncolorable sets of idempotent matrices whose entries lie in various rings, including the rational numbers, the integers, and finite fields. Most notably, we show that there is no Kochen-Specker coloring of the $n \\times n$ idempotent integer matrices for $n \\geq 3$, thereby illustrating that Kochen-Specker contextuality is an inherent feature of pure matrix algebra. We apply this to generalize recent no-go results on noncommutative spectrum functors, showing that any contravariant functor from rings to sets (respectively, topologic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03618","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.03618","created_at":"2026-05-18T00:38:12.906897+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.03618v3","created_at":"2026-05-18T00:38:12.906897+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03618","created_at":"2026-05-18T00:38:12.906897+00:00"},{"alias_kind":"pith_short_12","alias_value":"KG5XPS27E6N5","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KG5XPS27E6N5SHOI","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KG5XPS27","created_at":"2026-05-18T12:29:27.538025+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW","json":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW.json","graph_json":"https://pith.science/api/pith-number/KG5XPS27E6N5SHOITUXDIVHFSW/graph.json","events_json":"https://pith.science/api/pith-number/KG5XPS27E6N5SHOITUXDIVHFSW/events.json","paper":"https://pith.science/paper/KG5XPS27"},"agent_actions":{"view_html":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW","download_json":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW.json","view_paper":"https://pith.science/paper/KG5XPS27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.03618&json=true","fetch_graph":"https://pith.science/api/pith-number/KG5XPS27E6N5SHOITUXDIVHFSW/graph.json","fetch_events":"https://pith.science/api/pith-number/KG5XPS27E6N5SHOITUXDIVHFSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW/action/storage_attestation","attest_author":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW/action/author_attestation","sign_citation":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW/action/citation_signature","submit_replication":"https://pith.science/pith/KG5XPS27E6N5SHOITUXDIVHFSW/action/replication_record"}},"created_at":"2026-05-18T00:38:12.906897+00:00","updated_at":"2026-05-18T00:38:12.906897+00:00"}