{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:UC6HNCXELZA6BRM4WEZNN4PCZ2","short_pith_number":"pith:UC6HNCXE","schema_version":"1.0","canonical_sha256":"a0bc768ae45e41e0c59cb132d6f1e2ceaf12f4fbb2955f47221209e798aad196","source":{"kind":"arxiv","id":"2211.14210","version":1},"attestation_state":"computed","paper":{"title":"Hadamard Products and Binomial Ideals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Adrian Cook, B\\\"u\\c{s}ra Atar, Jay Yang, Jenna Rajchgot, Kieran Bhaskara, Megumi Harada, Runyue Wang, Sergio Da Silva","submitted_at":"2022-11-25T16:19:47Z","abstract_excerpt":"We study the Hadamard product of two varieties $V$ and $W$, with particular attention to the situation when one or both of $V$ and $W$ is a binomial variety. The main result of this paper shows that when $V$ and $W$ are both binomial varieties, and the binomials that define $V$ and $W$ have the same binomial exponents, then the defining equations of $V \\star W$ can be computed explicitly and directly from the defining equations of $V$ and $W$. This result recovers known results about Hadamard products of binomial hypersurfaces and toric varieties. Moreover, as an application of our main result"},"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":"2211.14210","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2022-11-25T16:19:47Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f198b4c3a6f9182f7ec861305ebd8c49bd4a12376de781a35e3f0683bc755365","abstract_canon_sha256":"e888655d147d238b2af0e86c8eca00865eca58c5829889a999543dcf161b429a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:19:30.596474Z","signature_b64":"kqGCPAXP8Gsx2NXGfg+nZQrnMLnX4r6WGAH5Cbru7XGEIbDK8ezqhW4iNndZPAyr5k0U55rrLGL99UjuPiZ8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0bc768ae45e41e0c59cb132d6f1e2ceaf12f4fbb2955f47221209e798aad196","last_reissued_at":"2026-07-05T05:19:30.595987Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:19:30.595987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hadamard Products and Binomial Ideals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Adrian Cook, B\\\"u\\c{s}ra Atar, Jay Yang, Jenna Rajchgot, Kieran Bhaskara, Megumi Harada, Runyue Wang, Sergio Da Silva","submitted_at":"2022-11-25T16:19:47Z","abstract_excerpt":"We study the Hadamard product of two varieties $V$ and $W$, with particular attention to the situation when one or both of $V$ and $W$ is a binomial variety. The main result of this paper shows that when $V$ and $W$ are both binomial varieties, and the binomials that define $V$ and $W$ have the same binomial exponents, then the defining equations of $V \\star W$ can be computed explicitly and directly from the defining equations of $V$ and $W$. This result recovers known results about Hadamard products of binomial hypersurfaces and toric varieties. Moreover, as an application of our main result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.14210","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.14210/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2211.14210","created_at":"2026-07-05T05:19:30.596046+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.14210v1","created_at":"2026-07-05T05:19:30.596046+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.14210","created_at":"2026-07-05T05:19:30.596046+00:00"},{"alias_kind":"pith_short_12","alias_value":"UC6HNCXELZA6","created_at":"2026-07-05T05:19:30.596046+00:00"},{"alias_kind":"pith_short_16","alias_value":"UC6HNCXELZA6BRM4","created_at":"2026-07-05T05:19:30.596046+00:00"},{"alias_kind":"pith_short_8","alias_value":"UC6HNCXE","created_at":"2026-07-05T05:19:30.596046+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/UC6HNCXELZA6BRM4WEZNN4PCZ2","json":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2.json","graph_json":"https://pith.science/api/pith-number/UC6HNCXELZA6BRM4WEZNN4PCZ2/graph.json","events_json":"https://pith.science/api/pith-number/UC6HNCXELZA6BRM4WEZNN4PCZ2/events.json","paper":"https://pith.science/paper/UC6HNCXE"},"agent_actions":{"view_html":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2","download_json":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2.json","view_paper":"https://pith.science/paper/UC6HNCXE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.14210&json=true","fetch_graph":"https://pith.science/api/pith-number/UC6HNCXELZA6BRM4WEZNN4PCZ2/graph.json","fetch_events":"https://pith.science/api/pith-number/UC6HNCXELZA6BRM4WEZNN4PCZ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2/action/storage_attestation","attest_author":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2/action/author_attestation","sign_citation":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2/action/citation_signature","submit_replication":"https://pith.science/pith/UC6HNCXELZA6BRM4WEZNN4PCZ2/action/replication_record"}},"created_at":"2026-07-05T05:19:30.596046+00:00","updated_at":"2026-07-05T05:19:30.596046+00:00"}