{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EHVFZJ7EJSFSPD4YRCYOPQ55O5","short_pith_number":"pith:EHVFZJ7E","schema_version":"1.0","canonical_sha256":"21ea5ca7e44c8b278f9888b0e7c3bd7756f94e58d376eb1ff50a7409a83e0a81","source":{"kind":"arxiv","id":"1611.05620","version":2},"attestation_state":"computed","paper":{"title":"Togliatti systems and Galois coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Emilia Mezzetti, Rosa Maria Mir\\'o-Roig","submitted_at":"2016-11-17T10:06:39Z","abstract_excerpt":"We study the homogeneous artinian ideals of the polynomial ring $K[x,y,z]$, generated by the homogenous polynomials of degree $d$ which are invariant under an action of the cyclic group $\\mathbb Z/d\\mathbb Z$, for any $d\\geq 3$. We prove that they are all monomial Togliatti systems, and that they are minimal if the action is defined by a diagonal matrix having on the diagonal $(1, e, e^a)$, where $e$ is a primitive $d$-th root of the unity. We get a complete description when $d$ is prime or a power of a prime. We also establish the relation of these systems with linear Ceva configurations."},"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":"1611.05620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-17T10:06:39Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bbff11fc9c23cee500aa4a5293f36b59bcd1e13f6a7ad780ab50e49fecdacd06","abstract_canon_sha256":"f47f49742bcb5aa49ae23e7511e71e02726499e613c7346a27ce0615f4d742b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:26.690439Z","signature_b64":"hKEkSnrYHawPuAh5bh9QvI9L18narFKLC/fIrsq8ct+KiNkcAqrDu4VymlGO8EaCTjzdUDcvmxwyKBpZ3cS8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21ea5ca7e44c8b278f9888b0e7c3bd7756f94e58d376eb1ff50a7409a83e0a81","last_reissued_at":"2026-05-18T00:06:26.689684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:26.689684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Togliatti systems and Galois coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Emilia Mezzetti, Rosa Maria Mir\\'o-Roig","submitted_at":"2016-11-17T10:06:39Z","abstract_excerpt":"We study the homogeneous artinian ideals of the polynomial ring $K[x,y,z]$, generated by the homogenous polynomials of degree $d$ which are invariant under an action of the cyclic group $\\mathbb Z/d\\mathbb Z$, for any $d\\geq 3$. We prove that they are all monomial Togliatti systems, and that they are minimal if the action is defined by a diagonal matrix having on the diagonal $(1, e, e^a)$, where $e$ is a primitive $d$-th root of the unity. We get a complete description when $d$ is prime or a power of a prime. We also establish the relation of these systems with linear Ceva configurations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05620","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":"1611.05620","created_at":"2026-05-18T00:06:26.689804+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.05620v2","created_at":"2026-05-18T00:06:26.689804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05620","created_at":"2026-05-18T00:06:26.689804+00:00"},{"alias_kind":"pith_short_12","alias_value":"EHVFZJ7EJSFS","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EHVFZJ7EJSFSPD4Y","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EHVFZJ7E","created_at":"2026-05-18T12:30:12.583610+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/EHVFZJ7EJSFSPD4YRCYOPQ55O5","json":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5.json","graph_json":"https://pith.science/api/pith-number/EHVFZJ7EJSFSPD4YRCYOPQ55O5/graph.json","events_json":"https://pith.science/api/pith-number/EHVFZJ7EJSFSPD4YRCYOPQ55O5/events.json","paper":"https://pith.science/paper/EHVFZJ7E"},"agent_actions":{"view_html":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5","download_json":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5.json","view_paper":"https://pith.science/paper/EHVFZJ7E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.05620&json=true","fetch_graph":"https://pith.science/api/pith-number/EHVFZJ7EJSFSPD4YRCYOPQ55O5/graph.json","fetch_events":"https://pith.science/api/pith-number/EHVFZJ7EJSFSPD4YRCYOPQ55O5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5/action/storage_attestation","attest_author":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5/action/author_attestation","sign_citation":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5/action/citation_signature","submit_replication":"https://pith.science/pith/EHVFZJ7EJSFSPD4YRCYOPQ55O5/action/replication_record"}},"created_at":"2026-05-18T00:06:26.689804+00:00","updated_at":"2026-05-18T00:06:26.689804+00:00"}