{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BCBMYNLAPWBTHKSS27ZZQWDLRK","short_pith_number":"pith:BCBMYNLA","schema_version":"1.0","canonical_sha256":"0882cc35607d8333aa52d7f398586b8aafd439d92d8a32cec01fbfec890a479e","source":{"kind":"arxiv","id":"1210.4230","version":3},"attestation_state":"computed","paper":{"title":"s-Hankel hypermatrices and 2 x 2 determinantal ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Alessio Sammartano","submitted_at":"2012-10-16T02:01:33Z","abstract_excerpt":"We introduce the concept of s-Hankel hypermatrix, which generalizes both Hankel matrices and generic hypermatrices. We study two determinantal ideals associated to an s-Hankel hypermatrix: the ideal I<s,t> generated by certain 2 x 2 slice minors, and the ideal \\tilde{I}<s,t> generated by certain 2 x 2 generalized minors. We describe the structure of these two ideals, with particular attention to the primary decomposition of I<s,t>, and provide the explicit list of minimal primes for large values of s. Finally we give some geometrical interpretations and generalise a theorem of Watanabe."},"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":"1210.4230","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-10-16T02:01:33Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"1aee350bc727a4dff5a65c82597ffbf77f98e678e0564b053dde096867bbad57","abstract_canon_sha256":"bb3799e6eb50c824fdee88bb5985f694fb3ca6f8d5e6074aa269bd9a341d7fce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.775421Z","signature_b64":"tiN6y2fluGtwr9ah0usK3Iu8rbqmtdmgD6tTeGJCojY+p2i+qGjPy6SH+QbThHag7mb9sdBWHXVXb+eBRjSPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0882cc35607d8333aa52d7f398586b8aafd439d92d8a32cec01fbfec890a479e","last_reissued_at":"2026-05-18T01:12:36.774890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.774890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"s-Hankel hypermatrices and 2 x 2 determinantal ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Alessio Sammartano","submitted_at":"2012-10-16T02:01:33Z","abstract_excerpt":"We introduce the concept of s-Hankel hypermatrix, which generalizes both Hankel matrices and generic hypermatrices. We study two determinantal ideals associated to an s-Hankel hypermatrix: the ideal I<s,t> generated by certain 2 x 2 slice minors, and the ideal \\tilde{I}<s,t> generated by certain 2 x 2 generalized minors. We describe the structure of these two ideals, with particular attention to the primary decomposition of I<s,t>, and provide the explicit list of minimal primes for large values of s. Finally we give some geometrical interpretations and generalise a theorem of Watanabe."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4230","kind":"arxiv","version":3},"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":"1210.4230","created_at":"2026-05-18T01:12:36.774975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4230v3","created_at":"2026-05-18T01:12:36.774975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4230","created_at":"2026-05-18T01:12:36.774975+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCBMYNLAPWBT","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCBMYNLAPWBTHKSS","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCBMYNLA","created_at":"2026-05-18T12:26:58.693483+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/BCBMYNLAPWBTHKSS27ZZQWDLRK","json":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK.json","graph_json":"https://pith.science/api/pith-number/BCBMYNLAPWBTHKSS27ZZQWDLRK/graph.json","events_json":"https://pith.science/api/pith-number/BCBMYNLAPWBTHKSS27ZZQWDLRK/events.json","paper":"https://pith.science/paper/BCBMYNLA"},"agent_actions":{"view_html":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK","download_json":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK.json","view_paper":"https://pith.science/paper/BCBMYNLA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4230&json=true","fetch_graph":"https://pith.science/api/pith-number/BCBMYNLAPWBTHKSS27ZZQWDLRK/graph.json","fetch_events":"https://pith.science/api/pith-number/BCBMYNLAPWBTHKSS27ZZQWDLRK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK/action/storage_attestation","attest_author":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK/action/author_attestation","sign_citation":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK/action/citation_signature","submit_replication":"https://pith.science/pith/BCBMYNLAPWBTHKSS27ZZQWDLRK/action/replication_record"}},"created_at":"2026-05-18T01:12:36.774975+00:00","updated_at":"2026-05-18T01:12:36.774975+00:00"}