{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NQERMDOMB2IHBKMFXLR4WCH7Q5","short_pith_number":"pith:NQERMDOM","canonical_record":{"source":{"id":"1801.00496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T19:18:05Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"5934ef82c2b4282125155a073120010565297f33309d5aa89c9b142a0aa398e3","abstract_canon_sha256":"f6682920f80f9d63e00aba2eb5d8d375324dfb39dc6f8b1f2a05f61a8f7f2a1e"},"schema_version":"1.0"},"canonical_sha256":"6c09160dcc0e9070a985bae3cb08ff876de52a5bac2077b8965f578254703088","source":{"kind":"arxiv","id":"1801.00496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00496","created_at":"2026-05-18T00:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00496v1","created_at":"2026-05-18T00:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00496","created_at":"2026-05-18T00:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"NQERMDOMB2IH","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NQERMDOMB2IHBKMF","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NQERMDOM","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NQERMDOMB2IHBKMFXLR4WCH7Q5","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T19:18:05Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"5934ef82c2b4282125155a073120010565297f33309d5aa89c9b142a0aa398e3","abstract_canon_sha256":"f6682920f80f9d63e00aba2eb5d8d375324dfb39dc6f8b1f2a05f61a8f7f2a1e"},"schema_version":"1.0"},"canonical_sha256":"6c09160dcc0e9070a985bae3cb08ff876de52a5bac2077b8965f578254703088","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:53.204694Z","signature_b64":"LpI4qEbiwnkzAZBoyvOY4QiVZ12OQmu7suFy7ud7xDf01OEISq+j+V3XbE8+CQWC1cWz4unPq451jgQDd2UqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c09160dcc0e9070a985bae3cb08ff876de52a5bac2077b8965f578254703088","last_reissued_at":"2026-05-18T00:26:53.204023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:53.204023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00496","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":"2026-05-18T00:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y7BpUZtLtnhTjFOm22A8jhWbxfZfEOhquBrFjMxW/f20PdxLwjps3Qb0UKE7gqKId3mvKVutsySxsSloFLvUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:41:13.522953Z"},"content_sha256":"6ac039e982536ae6a8c2898f9b23ec41a5202eb49a3f8cbdc59d2e7b38e3bf01","schema_version":"1.0","event_id":"sha256:6ac039e982536ae6a8c2898f9b23ec41a5202eb49a3f8cbdc59d2e7b38e3bf01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NQERMDOMB2IHBKMFXLR4WCH7Q5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the tensor rank of $3\\times 3$ permanent and determinant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.CO","authors_text":"Siddharth Krishna, Visu Makam","submitted_at":"2018-01-01T19:18:05Z","abstract_excerpt":"The tensor rank and border rank of the $3 \\times 3$ determinant tensor is known to be $5$ if characteristic is not two. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well. We also include an analysis of $5 \\times 5$ and $7 \\times 7$ determinant and permanent tensors, as well as the symmetric $3 \\times 3$ permanent and determinant tensors. We end with some remarks on binary tensors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00496","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":"2026-05-18T00:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tlcRi5WPkf+kBkRMmh+n4h4WDFqx0gEQx+kdWONw2ubeT0GNrJRFoGFLz8sHKW9KnCwJlz1Zcf1K9LC1ZGYZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:41:13.523571Z"},"content_sha256":"1463bf2ac7053ceaf5cc63c5d37c42f1cd832b07cd72125cbcdbdae3527c57c7","schema_version":"1.0","event_id":"sha256:1463bf2ac7053ceaf5cc63c5d37c42f1cd832b07cd72125cbcdbdae3527c57c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQERMDOMB2IHBKMFXLR4WCH7Q5/bundle.json","state_url":"https://pith.science/pith/NQERMDOMB2IHBKMFXLR4WCH7Q5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQERMDOMB2IHBKMFXLR4WCH7Q5/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":"2026-05-25T19:41:13Z","links":{"resolver":"https://pith.science/pith/NQERMDOMB2IHBKMFXLR4WCH7Q5","bundle":"https://pith.science/pith/NQERMDOMB2IHBKMFXLR4WCH7Q5/bundle.json","state":"https://pith.science/pith/NQERMDOMB2IHBKMFXLR4WCH7Q5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQERMDOMB2IHBKMFXLR4WCH7Q5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NQERMDOMB2IHBKMFXLR4WCH7Q5","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":"f6682920f80f9d63e00aba2eb5d8d375324dfb39dc6f8b1f2a05f61a8f7f2a1e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T19:18:05Z","title_canon_sha256":"5934ef82c2b4282125155a073120010565297f33309d5aa89c9b142a0aa398e3"},"schema_version":"1.0","source":{"id":"1801.00496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00496","created_at":"2026-05-18T00:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00496v1","created_at":"2026-05-18T00:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00496","created_at":"2026-05-18T00:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"NQERMDOMB2IH","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NQERMDOMB2IHBKMF","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NQERMDOM","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:1463bf2ac7053ceaf5cc63c5d37c42f1cd832b07cd72125cbcdbdae3527c57c7","target":"graph","created_at":"2026-05-18T00:26:53Z","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":"The tensor rank and border rank of the $3 \\times 3$ determinant tensor is known to be $5$ if characteristic is not two. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well. We also include an analysis of $5 \\times 5$ and $7 \\times 7$ determinant and permanent tensors, as well as the symmetric $3 \\times 3$ permanent and determinant tensors. We end with some remarks on binary tensors.","authors_text":"Siddharth Krishna, Visu Makam","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T19:18:05Z","title":"On the tensor rank of $3\\times 3$ permanent and determinant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00496","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":"sha256:6ac039e982536ae6a8c2898f9b23ec41a5202eb49a3f8cbdc59d2e7b38e3bf01","target":"record","created_at":"2026-05-18T00:26:53Z","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":"f6682920f80f9d63e00aba2eb5d8d375324dfb39dc6f8b1f2a05f61a8f7f2a1e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T19:18:05Z","title_canon_sha256":"5934ef82c2b4282125155a073120010565297f33309d5aa89c9b142a0aa398e3"},"schema_version":"1.0","source":{"id":"1801.00496","kind":"arxiv","version":1}},"canonical_sha256":"6c09160dcc0e9070a985bae3cb08ff876de52a5bac2077b8965f578254703088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c09160dcc0e9070a985bae3cb08ff876de52a5bac2077b8965f578254703088","first_computed_at":"2026-05-18T00:26:53.204023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:53.204023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LpI4qEbiwnkzAZBoyvOY4QiVZ12OQmu7suFy7ud7xDf01OEISq+j+V3XbE8+CQWC1cWz4unPq451jgQDd2UqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:53.204694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ac039e982536ae6a8c2898f9b23ec41a5202eb49a3f8cbdc59d2e7b38e3bf01","sha256:1463bf2ac7053ceaf5cc63c5d37c42f1cd832b07cd72125cbcdbdae3527c57c7"],"state_sha256":"dc3782a97b583b4c165f3524b65e265fe9f2570134ef31434cd4ed64ae29cd00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnAn8sPigi23Oh5PJpxRTZI/OhWI+ahlmuuXSMPEFxWK5eA8c44ukrWeHUg1/4BilZOQQCY/UhX9nNCxNfwwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:41:13.526264Z","bundle_sha256":"a94b18e3deabab93e66c308458d9493cbc21175f43bcd13664fc1eb6ac7c5db6"}}