{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:K5JZEK6336PYO3JAOQYLTGZ3PH","short_pith_number":"pith:K5JZEK63","schema_version":"1.0","canonical_sha256":"5753922bdbdf9f876d207430b99b3b79de7946413541d3a9d7563e954fecc7f5","source":{"kind":"arxiv","id":"1103.4702","version":2},"attestation_state":"computed","paper":{"title":"An indispensable classification of monomial curves in $\\mathbb{A}^4(\\mathbbmss{k}) $","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Anargyros Katsabekis, Ignacio Ojeda","submitted_at":"2011-03-24T09:01:20Z","abstract_excerpt":"In this paper a new classification of monomial curves in $\\mathbb{A}^4(\\mathbbmss{k})$ is given. Our classification relies on the detection of those binomials and monomials that have to appear in every system of binomial generators of the defining ideal of the monomial curve; these special binomials and monomials are called indispensable in the literature. This way to proceed has the advantage of producing a natural necessary and sufficient condition for the definining ideal of a monomial curve in $\\mathbb{A}^4(\\mathbbmss{k})$ to have a unique minimal system of binomial generators. Furthermore"},"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":"1103.4702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-03-24T09:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"ee9822a15dfa36f476feb66b4c14e76ba3dba7709937928b6ca3a93a74aadd41","abstract_canon_sha256":"12881f62aecb162258481faa2a093bea6c0a4e432bf59c8bc596e765d64e2cde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:23.745820Z","signature_b64":"8r0j5iD0Ert3dkNpTVeoOqfmmVHPftZgsq/kGDoieHATA/oXWbt5d+6V7F142OEn55/D+Gvm7RsmSqO11hocDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5753922bdbdf9f876d207430b99b3b79de7946413541d3a9d7563e954fecc7f5","last_reissued_at":"2026-05-18T02:51:23.745121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:23.745121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An indispensable classification of monomial curves in $\\mathbb{A}^4(\\mathbbmss{k}) $","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Anargyros Katsabekis, Ignacio Ojeda","submitted_at":"2011-03-24T09:01:20Z","abstract_excerpt":"In this paper a new classification of monomial curves in $\\mathbb{A}^4(\\mathbbmss{k})$ is given. Our classification relies on the detection of those binomials and monomials that have to appear in every system of binomial generators of the defining ideal of the monomial curve; these special binomials and monomials are called indispensable in the literature. This way to proceed has the advantage of producing a natural necessary and sufficient condition for the definining ideal of a monomial curve in $\\mathbb{A}^4(\\mathbbmss{k})$ to have a unique minimal system of binomial generators. Furthermore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4702","kind":"arxiv","version":2},"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":"1103.4702","created_at":"2026-05-18T02:51:23.745221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.4702v2","created_at":"2026-05-18T02:51:23.745221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4702","created_at":"2026-05-18T02:51:23.745221+00:00"},{"alias_kind":"pith_short_12","alias_value":"K5JZEK6336PY","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"K5JZEK6336PYO3JA","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"K5JZEK63","created_at":"2026-05-18T12:26:32.869790+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/K5JZEK6336PYO3JAOQYLTGZ3PH","json":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH.json","graph_json":"https://pith.science/api/pith-number/K5JZEK6336PYO3JAOQYLTGZ3PH/graph.json","events_json":"https://pith.science/api/pith-number/K5JZEK6336PYO3JAOQYLTGZ3PH/events.json","paper":"https://pith.science/paper/K5JZEK63"},"agent_actions":{"view_html":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH","download_json":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH.json","view_paper":"https://pith.science/paper/K5JZEK63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.4702&json=true","fetch_graph":"https://pith.science/api/pith-number/K5JZEK6336PYO3JAOQYLTGZ3PH/graph.json","fetch_events":"https://pith.science/api/pith-number/K5JZEK6336PYO3JAOQYLTGZ3PH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH/action/storage_attestation","attest_author":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH/action/author_attestation","sign_citation":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH/action/citation_signature","submit_replication":"https://pith.science/pith/K5JZEK6336PYO3JAOQYLTGZ3PH/action/replication_record"}},"created_at":"2026-05-18T02:51:23.745221+00:00","updated_at":"2026-05-18T02:51:23.745221+00:00"}