{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AIIIFTWM5F7JENPXJXF5IPRLQI","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":"51c84716ec5cd95d6587765828fca5ecd1dd4c901333f8681f50a1d866a553b0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-09-20T07:11:32Z","title_canon_sha256":"998e12e601c639bd99199a5cf47ad779e2718c3b0af05dc9a6b83008f3c27906"},"schema_version":"1.0","source":{"id":"1309.5189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5189","created_at":"2026-05-18T03:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5189v2","created_at":"2026-05-18T03:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5189","created_at":"2026-05-18T03:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"AIIIFTWM5F7J","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AIIIFTWM5F7JENPX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AIIIFTWM","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:7974ef6296354a35defdd9e309ad5e708416485b98f2ae1aaf7211199954f3e4","target":"graph","created_at":"2026-05-18T03:08:24Z","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":"Let $\\mathbb{P}_n$ be the set of all matrices which have the same zero patterns with some permutation matrix of order $n$.\n  In this paper, we prove the following result: Let $\\mathbb{I}$ be the unit tensor of order $m\\ge3$ and dimension $n\\ge2$. Suppose that $P$ and $Q$ are two matrices with $P\\mathbb{I}Q=\\mathbb{I}$, then $P,Q\\in \\mathbb{P}_n$. This gives a characterization for the similarities of tensors with order $m\\ge3$.","authors_text":"Lihua You, Pingzhi Yuan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-09-20T07:11:32Z","title":"On the similarity of Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5189","kind":"arxiv","version":2},"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:ad178cceb7790c9b752ff418ac2e1c213357a5a4ad5dc3548f97ca44ce668e3e","target":"record","created_at":"2026-05-18T03:08:24Z","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":"51c84716ec5cd95d6587765828fca5ecd1dd4c901333f8681f50a1d866a553b0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-09-20T07:11:32Z","title_canon_sha256":"998e12e601c639bd99199a5cf47ad779e2718c3b0af05dc9a6b83008f3c27906"},"schema_version":"1.0","source":{"id":"1309.5189","kind":"arxiv","version":2}},"canonical_sha256":"021082cecce97e9235f74dcbd43e2b821e374654e50bd786693c2984ce969dd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021082cecce97e9235f74dcbd43e2b821e374654e50bd786693c2984ce969dd4","first_computed_at":"2026-05-18T03:08:24.594508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:24.594508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZLJr47Z5iQXjzCyrvupGLLA8vMd0zdtSAWWihEYciniF6gvpO2qYgVFbOWslb8wDUAhybvyIaK/toyTYetLHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:24.595108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad178cceb7790c9b752ff418ac2e1c213357a5a4ad5dc3548f97ca44ce668e3e","sha256:7974ef6296354a35defdd9e309ad5e708416485b98f2ae1aaf7211199954f3e4"],"state_sha256":"0f6350dcd386178c6ccee1bc13195a37335beb3d8936891b6460ae698dbf0d47"}