{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NBOZO32355LCLBQBVUMKRDTYHG","short_pith_number":"pith:NBOZO323","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"},"canonical_sha256":"685d976f5bef56258601ad18a88e783997c0a71f878eb4e8d5bdaf94ae58b096","source":{"kind":"arxiv","id":"1106.2988","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2988","created_at":"2026-05-18T04:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2988v1","created_at":"2026-05-18T04:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2988","created_at":"2026-05-18T04:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"NBOZO32355LC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NBOZO32355LCLBQB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NBOZO323","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NBOZO32355LCLBQBVUMKRDTYHG","target":"record","payload":{"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"},"canonical_sha256":"685d976f5bef56258601ad18a88e783997c0a71f878eb4e8d5bdaf94ae58b096","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"},"source_kind":"arxiv","source_id":"1106.2988","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWUH2kdV8W6gKrhUA+ek0uKimbd9NP8rTBWfmDLBWMKN85hQe3X+9hSp4fa5MZFBn9vxrr6eCxZMYNjk/6kcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:31.218598Z"},"content_sha256":"15ec30da1df2f4fbae913f46d618a0310e2d58e6a7e5320a59bfd6445e36d88c","schema_version":"1.0","event_id":"sha256:15ec30da1df2f4fbae913f46d618a0310e2d58e6a7e5320a59bfd6445e36d88c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NBOZO32355LCLBQBVUMKRDTYHG","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOkaQsFt5wN7faDYVbonNo53DwkkleBzNBLIAI+OuRHBgLChwv8ZWwGDYz+D7U1qSHlzPiKw6UXC+EtkuNA/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:31.219265Z"},"content_sha256":"050dc8be9cdbfeed1e28f47b3b5eaab40f31f6f9182708dfd58e500021fa7455","schema_version":"1.0","event_id":"sha256:050dc8be9cdbfeed1e28f47b3b5eaab40f31f6f9182708dfd58e500021fa7455"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/bundle.json","state_url":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBOZO32355LCLBQBVUMKRDTYHG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T22:10:31Z","links":{"resolver":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG","bundle":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/bundle.json","state":"https://pith.science/pith/NBOZO32355LCLBQBVUMKRDTYHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBOZO32355LCLBQBVUMKRDTYHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NBOZO32355LCLBQBVUMKRDTYHG","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":"4006b04b87f4f508c68356cb0bacd42aa85d6ce6418f2e49170635ce6bd13d0b","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-15T14:50:43Z","title_canon_sha256":"c99fc1f09bf24f3f2b73ce733777b944267511221237df23e60c8356a2f4c830"},"schema_version":"1.0","source":{"id":"1106.2988","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2988","created_at":"2026-05-18T04:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2988v1","created_at":"2026-05-18T04:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2988","created_at":"2026-05-18T04:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"NBOZO32355LC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NBOZO32355LCLBQB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NBOZO323","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:050dc8be9cdbfeed1e28f47b3b5eaab40f31f6f9182708dfd58e500021fa7455","target":"graph","created_at":"2026-05-18T04:19:55Z","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":"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.","authors_text":"Murray R. Bremner","cross_cats":["hep-th","math-ph","math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-15T14:50:43Z","title":"A hyperdeterminant for 2 x 2 x 3 arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2988","kind":"arxiv","version":1},"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":"sha256:15ec30da1df2f4fbae913f46d618a0310e2d58e6a7e5320a59bfd6445e36d88c","target":"record","created_at":"2026-05-18T04:19:55Z","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":"4006b04b87f4f508c68356cb0bacd42aa85d6ce6418f2e49170635ce6bd13d0b","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-15T14:50:43Z","title_canon_sha256":"c99fc1f09bf24f3f2b73ce733777b944267511221237df23e60c8356a2f4c830"},"schema_version":"1.0","source":{"id":"1106.2988","kind":"arxiv","version":1}},"canonical_sha256":"685d976f5bef56258601ad18a88e783997c0a71f878eb4e8d5bdaf94ae58b096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"685d976f5bef56258601ad18a88e783997c0a71f878eb4e8d5bdaf94ae58b096","first_computed_at":"2026-05-18T04:19:55.204032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:55.204032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"okjLmJCCU5WDD3iVjQFKcYdRVdVM1/21PUPlgtbPF5IjAEsu8/qeN6DwQb01hA9Zi79XpuZ2UY2IrcAxgFOKCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:55.204617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2988","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15ec30da1df2f4fbae913f46d618a0310e2d58e6a7e5320a59bfd6445e36d88c","sha256:050dc8be9cdbfeed1e28f47b3b5eaab40f31f6f9182708dfd58e500021fa7455"],"state_sha256":"0a3de95479e0760a04888842beaa111229d5cc07300d7781a25eee083506c980"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"byTJNSh6L21r8as4oXIimAydeSfyQLSBow/THYMhW3VR4FcVfPLYUwENz9TXgB/Kcd+MnDqybVR+VEbnsFPLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:10:31.222551Z","bundle_sha256":"6825167f01f2c37f1f217ac4bef2052d13db2ee02971362163419b69408db0b2"}}