{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NBOZO32355LCLBQBVUMKRDTYHG","short_pith_number":"pith:NBOZO323","schema_version":"1.0","canonical_sha256":"685d976f5bef56258601ad18a88e783997c0a71f878eb4e8d5bdaf94ae58b096","source":{"kind":"arxiv","id":"1106.2988","version":1},"attestation_state":"computed","paper":{"title":"A hyperdeterminant for 2 x 2 x 3 arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RA"],"primary_cat":"math.RT","authors_text":"Murray R. Bremner","submitted_at":"2011-06-15T14:50:43Z","abstract_excerpt":"We use the representation theory of Lie algebras and computational linear algebra to determine the simplest nonconstant invariant polynomial in the entries of a general 2 x 2 x 3 array. This polynomial is homogeneous of degree 6 and has 66 terms with coefficients 1, -1, 2, -2 in the 12 indeterminates x_ijk where i,j = 1,2 and k = 1,2,3. This invariant can be regarded as a natural generalization of Cayley's hyperdeterminant for 2 x 2 x 2 arrays."},"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":"1106.2988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-15T14:50:43Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RA"],"title_canon_sha256":"c99fc1f09bf24f3f2b73ce733777b944267511221237df23e60c8356a2f4c830","abstract_canon_sha256":"4006b04b87f4f508c68356cb0bacd42aa85d6ce6418f2e49170635ce6bd13d0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:55.204617Z","signature_b64":"okjLmJCCU5WDD3iVjQFKcYdRVdVM1/21PUPlgtbPF5IjAEsu8/qeN6DwQb01hA9Zi79XpuZ2UY2IrcAxgFOKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"685d976f5bef56258601ad18a88e783997c0a71f878eb4e8d5bdaf94ae58b096","last_reissued_at":"2026-05-18T04:19:55.204032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:55.204032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A hyperdeterminant for 2 x 2 x 3 arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RA"],"primary_cat":"math.RT","authors_text":"Murray R. Bremner","submitted_at":"2011-06-15T14:50:43Z","abstract_excerpt":"We use the representation theory of Lie algebras and computational linear algebra to determine the simplest nonconstant invariant polynomial in the entries of a general 2 x 2 x 3 array. This polynomial is homogeneous of degree 6 and has 66 terms with coefficients 1, -1, 2, -2 in the 12 indeterminates x_ijk where i,j = 1,2 and k = 1,2,3. This invariant can be regarded as a natural generalization of Cayley's hyperdeterminant for 2 x 2 x 2 arrays."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2988","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":""},"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":"1106.2988","created_at":"2026-05-18T04:19:55.204127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.2988v1","created_at":"2026-05-18T04:19:55.204127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2988","created_at":"2026-05-18T04:19:55.204127+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBOZO32355LC","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBOZO32355LCLBQB","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBOZO323","created_at":"2026-05-18T12:26:37.096874+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/NBOZO32355LCLBQBVUMKRDTYHG","json":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG.json","graph_json":"https://pith.science/api/pith-number/NBOZO32355LCLBQBVUMKRDTYHG/graph.json","events_json":"https://pith.science/api/pith-number/NBOZO32355LCLBQBVUMKRDTYHG/events.json","paper":"https://pith.science/paper/NBOZO323"},"agent_actions":{"view_html":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG","download_json":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG.json","view_paper":"https://pith.science/paper/NBOZO323","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.2988&json=true","fetch_graph":"https://pith.science/api/pith-number/NBOZO32355LCLBQBVUMKRDTYHG/graph.json","fetch_events":"https://pith.science/api/pith-number/NBOZO32355LCLBQBVUMKRDTYHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/action/storage_attestation","attest_author":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/action/author_attestation","sign_citation":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/action/citation_signature","submit_replication":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/action/replication_record"}},"created_at":"2026-05-18T04:19:55.204127+00:00","updated_at":"2026-05-18T04:19:55.204127+00:00"}