{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VFQB37DNUA5XXSDJAGHEZ2JZ7H","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":"6a0ed62328cc38da425de024c72d55ae2773b4393003ae69d4e96326c115973e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T10:20:57Z","title_canon_sha256":"caed179c5556256b937aafdbc22fae10b067f9655c87d13fc2da155edb7534fc"},"schema_version":"1.0","source":{"id":"1706.02114","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02114","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02114v2","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02114","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"VFQB37DNUA5X","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VFQB37DNUA5XXSDJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VFQB37DN","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:ed27341058c78a847d636c4bf1de62688a7cace0c5e8a8c935b9a714b3c08a59","target":"graph","created_at":"2026-05-18T00:39:06Z","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":"In this article, we give the answer to the following question: Given a field $\\mathbb{F}$, finite subsets $A_1,\\dots,A_m$ of $\\mathbb{F}$, and $r$ linearly independent polynomials $f_1,\\dots,f_r \\in \\mathbb{F}[x_1,\\dots,x_m]$ of total degree at most $d$. What is the maximal number of common zeros $f_1,\\dots,f_r$ can have in $A_1 \\times \\cdots \\times A_m$? For $\\mathbb{F}=\\mathbb{F}_q$, the finite field with $q$ elements, answering this question is equivalent to determining the generalized Hamming weights of the so-called affine Cartesian codes. Seen in this light, our work is a generalization ","authors_text":"Mrinmoy Datta, Peter Beelen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T10:20:57Z","title":"Generalized Hamming weights of affine cartesian codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02114","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:e13646e23486d7a2de70bf68ff47fffdd69d2a7e9c5e8405c30105887a5c6609","target":"record","created_at":"2026-05-18T00:39:06Z","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":"6a0ed62328cc38da425de024c72d55ae2773b4393003ae69d4e96326c115973e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T10:20:57Z","title_canon_sha256":"caed179c5556256b937aafdbc22fae10b067f9655c87d13fc2da155edb7534fc"},"schema_version":"1.0","source":{"id":"1706.02114","kind":"arxiv","version":2}},"canonical_sha256":"a9601dfc6da03b7bc869018e4ce939f9c0eb83089e37cb701406bc9a069638a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9601dfc6da03b7bc869018e4ce939f9c0eb83089e37cb701406bc9a069638a8","first_computed_at":"2026-05-18T00:39:06.439412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:06.439412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b5qOGJDJWdEOQrK0ujDk2k8Chwiu37nMlgdlqyh9Eb9nxgoEuWLZAVeUXMAgji8pPcLNg14TV4Ko7UYgwrD8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:06.439932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02114","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e13646e23486d7a2de70bf68ff47fffdd69d2a7e9c5e8405c30105887a5c6609","sha256:ed27341058c78a847d636c4bf1de62688a7cace0c5e8a8c935b9a714b3c08a59"],"state_sha256":"d04a2eb7473cb44e149439f44d8ff49148d59fcb37762039fb2c67f4f1ee6917"}