{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:ARIJOJEYDJ7NHQURWJMHHAQKRS","short_pith_number":"pith:ARIJOJEY","canonical_record":{"source":{"id":"0808.1167","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-08-08T08:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"0c0a17d66bcc1dc24fe624e05fab083a8a97f2a1cbcd5179bb08b4300f67e75f","abstract_canon_sha256":"d4d46bdba08428d7dd1ef6bc1beb26435d9e21b403aa08423b0166332c69a156"},"schema_version":"1.0"},"canonical_sha256":"04509724981a7ed3c291b25873820a8cb23bd4d3f064e1a05c2c4ad23715fb49","source":{"kind":"arxiv","id":"0808.1167","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.1167","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"0808.1167v3","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1167","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"ARIJOJEYDJ7N","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ARIJOJEYDJ7NHQUR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ARIJOJEY","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:ARIJOJEYDJ7NHQURWJMHHAQKRS","target":"record","payload":{"canonical_record":{"source":{"id":"0808.1167","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-08-08T08:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"0c0a17d66bcc1dc24fe624e05fab083a8a97f2a1cbcd5179bb08b4300f67e75f","abstract_canon_sha256":"d4d46bdba08428d7dd1ef6bc1beb26435d9e21b403aa08423b0166332c69a156"},"schema_version":"1.0"},"canonical_sha256":"04509724981a7ed3c291b25873820a8cb23bd4d3f064e1a05c2c4ad23715fb49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:45.227116Z","signature_b64":"u9/EMV5My+YtrImt5r0tWtYSBSf12tmSHcrGPSoOLyHd+grpzDnXEgeg8o5bsuQsSg0J70yQM9gO+IultzU8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04509724981a7ed3c291b25873820a8cb23bd4d3f064e1a05c2c4ad23715fb49","last_reissued_at":"2026-05-18T04:14:45.226692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:45.226692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.1167","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSM0XGNycihGi5UTMIMUPaz8qvrHev0XoUULNoyCIXqhoZtobHHIJanuKRasJ5E7uUNE7Vd9xyVTTe/sime4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:47:40.940120Z"},"content_sha256":"d47f8b14f180b297e170fd2a83c3fdb90e27f828d6c978ba7807de898f4da706","schema_version":"1.0","event_id":"sha256:d47f8b14f180b297e170fd2a83c3fdb90e27f828d6c978ba7807de898f4da706"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:ARIJOJEYDJ7NHQURWJMHHAQKRS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank of 3-tensors with 2 slices and Kronecker canonical forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mitsuhiro Miyazaki, Toshio Sakata, Toshio Sumi","submitted_at":"2008-08-08T08:18:45Z","abstract_excerpt":"Tensor type data are becoming important recently in various application fields. We determine a rank of a tensor T so that A+T is diagonalizable for a given 3-tensor A with 2 slices over the complex and real number field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1167","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BDBt/swRJfmyI9QQUBWJPrzfVqLPHy2c15B1YrrmPbSknRj101GUtA6wzaU76u6AepU9QfoNTdojnkHzkXNKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:47:40.940478Z"},"content_sha256":"1ca1378068fe49995fe94e5e7692e37fb9edfbec2acaeed78c73ea44a747e060","schema_version":"1.0","event_id":"sha256:1ca1378068fe49995fe94e5e7692e37fb9edfbec2acaeed78c73ea44a747e060"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARIJOJEYDJ7NHQURWJMHHAQKRS/bundle.json","state_url":"https://pith.science/pith/ARIJOJEYDJ7NHQURWJMHHAQKRS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARIJOJEYDJ7NHQURWJMHHAQKRS/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":"2026-06-24T05:47:40Z","links":{"resolver":"https://pith.science/pith/ARIJOJEYDJ7NHQURWJMHHAQKRS","bundle":"https://pith.science/pith/ARIJOJEYDJ7NHQURWJMHHAQKRS/bundle.json","state":"https://pith.science/pith/ARIJOJEYDJ7NHQURWJMHHAQKRS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARIJOJEYDJ7NHQURWJMHHAQKRS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ARIJOJEYDJ7NHQURWJMHHAQKRS","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":"d4d46bdba08428d7dd1ef6bc1beb26435d9e21b403aa08423b0166332c69a156","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-08-08T08:18:45Z","title_canon_sha256":"0c0a17d66bcc1dc24fe624e05fab083a8a97f2a1cbcd5179bb08b4300f67e75f"},"schema_version":"1.0","source":{"id":"0808.1167","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.1167","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"0808.1167v3","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1167","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"ARIJOJEYDJ7N","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ARIJOJEYDJ7NHQUR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ARIJOJEY","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1ca1378068fe49995fe94e5e7692e37fb9edfbec2acaeed78c73ea44a747e060","target":"graph","created_at":"2026-05-18T04:14:45Z","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":"Tensor type data are becoming important recently in various application fields. We determine a rank of a tensor T so that A+T is diagonalizable for a given 3-tensor A with 2 slices over the complex and real number field.","authors_text":"Mitsuhiro Miyazaki, Toshio Sakata, Toshio Sumi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-08-08T08:18:45Z","title":"Rank of 3-tensors with 2 slices and Kronecker canonical forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1167","kind":"arxiv","version":3},"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:d47f8b14f180b297e170fd2a83c3fdb90e27f828d6c978ba7807de898f4da706","target":"record","created_at":"2026-05-18T04:14:45Z","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":"d4d46bdba08428d7dd1ef6bc1beb26435d9e21b403aa08423b0166332c69a156","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-08-08T08:18:45Z","title_canon_sha256":"0c0a17d66bcc1dc24fe624e05fab083a8a97f2a1cbcd5179bb08b4300f67e75f"},"schema_version":"1.0","source":{"id":"0808.1167","kind":"arxiv","version":3}},"canonical_sha256":"04509724981a7ed3c291b25873820a8cb23bd4d3f064e1a05c2c4ad23715fb49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04509724981a7ed3c291b25873820a8cb23bd4d3f064e1a05c2c4ad23715fb49","first_computed_at":"2026-05-18T04:14:45.226692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:45.226692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u9/EMV5My+YtrImt5r0tWtYSBSf12tmSHcrGPSoOLyHd+grpzDnXEgeg8o5bsuQsSg0J70yQM9gO+IultzU8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:45.227116Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.1167","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d47f8b14f180b297e170fd2a83c3fdb90e27f828d6c978ba7807de898f4da706","sha256:1ca1378068fe49995fe94e5e7692e37fb9edfbec2acaeed78c73ea44a747e060"],"state_sha256":"8aa5c633578e76d98fcad11239f373b50c2591d8ec691f9936f63972326854cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MR8z1oS4wGzCDWjshnuNmXK3mye4Q6lWs33jbn1L0MPjyD+IVYJBwveprmjZGVQM9MqWGeAHHVjn1Z6Vb+AkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:47:40.945196Z","bundle_sha256":"a4eb34d035ecdb95102d1e58c45b361d11f3230c84692f85a428540841771846"}}