{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4PH7BO4MLDBVDI7CPRE2SXK4US","short_pith_number":"pith:4PH7BO4M","schema_version":"1.0","canonical_sha256":"e3cff0bb8c58c351a3e27c49a95d5ca4bd173a1f54086ad6e30c57c2c2822be4","source":{"kind":"arxiv","id":"2606.25060","version":1},"attestation_state":"computed","paper":{"title":"Weddle schemes","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Brian Harbourne, Giuseppe Favacchio, Juan Migliore, Justyna Szpond, Luca Chiantini, {\\L}ucja Farnik, Tomasz Szemberg","submitted_at":"2026-06-23T18:13:07Z","abstract_excerpt":"The classical Weddle surface is the locus of vertices of quadric cones through six points in $\\mathbb{P}^3$ in linear general position. Equivalently, it is the closure of the locus of centers of projection from which those six points map to six points on a plane conic. Motivated by this 1850 construction of T. Weddle, we introduce $d$-Weddle schemes for finite point sets $Z\\subset \\mathbb{P}^n$, defined by an analogous projection-to-degree-$d$ condition. Our main tool is Macaulay duality, which yields a natural multiplication map in an Artinian algebra defined by powers of linear forms. This v"},"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":"2606.25060","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-23T18:13:07Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"8f7e81c5d100f60639ab36b161b232fe8b763859942d498277b92e2b81c7ffea","abstract_canon_sha256":"39d6860427dac82a925f59808ec8097b57df2074eb7601be3151e62dd2b64e42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T00:18:16.671519Z","signature_b64":"i7Ixmzb/hGbAff+Wwj2IUmqYaWf2Hq3AwG0qCSxEaMme1zt/+RSg4VR/wq0D9CjrMWupjV1tafrcgEoRLSYrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3cff0bb8c58c351a3e27c49a95d5ca4bd173a1f54086ad6e30c57c2c2822be4","last_reissued_at":"2026-06-25T00:18:16.671091Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T00:18:16.671091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weddle schemes","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Brian Harbourne, Giuseppe Favacchio, Juan Migliore, Justyna Szpond, Luca Chiantini, {\\L}ucja Farnik, Tomasz Szemberg","submitted_at":"2026-06-23T18:13:07Z","abstract_excerpt":"The classical Weddle surface is the locus of vertices of quadric cones through six points in $\\mathbb{P}^3$ in linear general position. Equivalently, it is the closure of the locus of centers of projection from which those six points map to six points on a plane conic. Motivated by this 1850 construction of T. Weddle, we introduce $d$-Weddle schemes for finite point sets $Z\\subset \\mathbb{P}^n$, defined by an analogous projection-to-degree-$d$ condition. Our main tool is Macaulay duality, which yields a natural multiplication map in an Artinian algebra defined by powers of linear forms. This v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25060","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/2606.25060/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":"2606.25060","created_at":"2026-06-25T00:18:16.671154+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25060v1","created_at":"2026-06-25T00:18:16.671154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25060","created_at":"2026-06-25T00:18:16.671154+00:00"},{"alias_kind":"pith_short_12","alias_value":"4PH7BO4MLDBV","created_at":"2026-06-25T00:18:16.671154+00:00"},{"alias_kind":"pith_short_16","alias_value":"4PH7BO4MLDBVDI7C","created_at":"2026-06-25T00:18:16.671154+00:00"},{"alias_kind":"pith_short_8","alias_value":"4PH7BO4M","created_at":"2026-06-25T00:18:16.671154+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/4PH7BO4MLDBVDI7CPRE2SXK4US","json":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US.json","graph_json":"https://pith.science/api/pith-number/4PH7BO4MLDBVDI7CPRE2SXK4US/graph.json","events_json":"https://pith.science/api/pith-number/4PH7BO4MLDBVDI7CPRE2SXK4US/events.json","paper":"https://pith.science/paper/4PH7BO4M"},"agent_actions":{"view_html":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US","download_json":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US.json","view_paper":"https://pith.science/paper/4PH7BO4M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25060&json=true","fetch_graph":"https://pith.science/api/pith-number/4PH7BO4MLDBVDI7CPRE2SXK4US/graph.json","fetch_events":"https://pith.science/api/pith-number/4PH7BO4MLDBVDI7CPRE2SXK4US/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US/action/storage_attestation","attest_author":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US/action/author_attestation","sign_citation":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US/action/citation_signature","submit_replication":"https://pith.science/pith/4PH7BO4MLDBVDI7CPRE2SXK4US/action/replication_record"}},"created_at":"2026-06-25T00:18:16.671154+00:00","updated_at":"2026-06-25T00:18:16.671154+00:00"}