{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MAUA7IHRBPSBVEAECQAAL3U77X","short_pith_number":"pith:MAUA7IHR","schema_version":"1.0","canonical_sha256":"60280fa0f10be41a9004140005ee9ffdc03e619a1674ca91e0d1315fa8995103","source":{"kind":"arxiv","id":"1208.1695","version":1},"attestation_state":"computed","paper":{"title":"A simplified version of the \"Axis of Evil Theorem\" for distinct points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Michela Ceria","submitted_at":"2012-08-08T15:48:26Z","abstract_excerpt":"Given a finite set $\\mathbf{X}$ of distinct points, Marinari-Mora's 'Axis of Evil Theorem' states that a combinatorial algorithm and interpolation enable to find a 'linear' factorization for a lexicographical minimal Groebner basis $\\mathcal{G}(I(\\mathbf{X}))$ of the zerodimensional radical ideal $I(\\mathbf{X})$. In this work we provide such algorithm, showing that it ends in a finite number of steps and that it actually provides the correct result. The 'Axis of Evil' algorithm takes as input the monomial basis of the initial ideal $T(I(\\mathbf{X}))$ but its starting point is the (finite) Groe"},"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":"1208.1695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-08T15:48:26Z","cross_cats_sorted":[],"title_canon_sha256":"81498ac21ee0537d677016f868405d7c06bce215581a3d85b1a7735c1d6f86f5","abstract_canon_sha256":"582840c30e21e7ad39c80eb76121d461f44093e460bf5a39e904480932e2813c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:10.862203Z","signature_b64":"53tWnNgGRNUpnwIVn1l8upxePSIFQ/BPqrcVCG16S7HqB5aDqukt89fQiURxdZ7GpzAVr/fp2v5kYDTl2JM9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60280fa0f10be41a9004140005ee9ffdc03e619a1674ca91e0d1315fa8995103","last_reissued_at":"2026-05-18T03:49:10.861487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:10.861487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A simplified version of the \"Axis of Evil Theorem\" for distinct points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Michela Ceria","submitted_at":"2012-08-08T15:48:26Z","abstract_excerpt":"Given a finite set $\\mathbf{X}$ of distinct points, Marinari-Mora's 'Axis of Evil Theorem' states that a combinatorial algorithm and interpolation enable to find a 'linear' factorization for a lexicographical minimal Groebner basis $\\mathcal{G}(I(\\mathbf{X}))$ of the zerodimensional radical ideal $I(\\mathbf{X})$. In this work we provide such algorithm, showing that it ends in a finite number of steps and that it actually provides the correct result. The 'Axis of Evil' algorithm takes as input the monomial basis of the initial ideal $T(I(\\mathbf{X}))$ but its starting point is the (finite) Groe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1695","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.1695","created_at":"2026-05-18T03:49:10.861612+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.1695v1","created_at":"2026-05-18T03:49:10.861612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1695","created_at":"2026-05-18T03:49:10.861612+00:00"},{"alias_kind":"pith_short_12","alias_value":"MAUA7IHRBPSB","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MAUA7IHRBPSBVEAE","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MAUA7IHR","created_at":"2026-05-18T12:27:14.488303+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/MAUA7IHRBPSBVEAECQAAL3U77X","json":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X.json","graph_json":"https://pith.science/api/pith-number/MAUA7IHRBPSBVEAECQAAL3U77X/graph.json","events_json":"https://pith.science/api/pith-number/MAUA7IHRBPSBVEAECQAAL3U77X/events.json","paper":"https://pith.science/paper/MAUA7IHR"},"agent_actions":{"view_html":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X","download_json":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X.json","view_paper":"https://pith.science/paper/MAUA7IHR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.1695&json=true","fetch_graph":"https://pith.science/api/pith-number/MAUA7IHRBPSBVEAECQAAL3U77X/graph.json","fetch_events":"https://pith.science/api/pith-number/MAUA7IHRBPSBVEAECQAAL3U77X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X/action/storage_attestation","attest_author":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X/action/author_attestation","sign_citation":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X/action/citation_signature","submit_replication":"https://pith.science/pith/MAUA7IHRBPSBVEAECQAAL3U77X/action/replication_record"}},"created_at":"2026-05-18T03:49:10.861612+00:00","updated_at":"2026-05-18T03:49:10.861612+00:00"}