{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:KQ2DUN4AN3TEY2RPY735KJPQBB","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":"155b48010a37099cf13256daad3f8f8379253dba1abea3b4a1197e619f3a977f","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2006-12-16T00:28:15Z","title_canon_sha256":"650a4c932d8a81cf5435f1eab93932ca53455d1cbf62319e92435d509339214e"},"schema_version":"1.0","source":{"id":"math/0612460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612460","created_at":"2026-07-04T14:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612460v1","created_at":"2026-07-04T14:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612460","created_at":"2026-07-04T14:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"KQ2DUN4AN3TE","created_at":"2026-07-04T14:58:05Z"},{"alias_kind":"pith_short_16","alias_value":"KQ2DUN4AN3TEY2RP","created_at":"2026-07-04T14:58:05Z"},{"alias_kind":"pith_short_8","alias_value":"KQ2DUN4A","created_at":"2026-07-04T14:58:05Z"}],"graph_snapshots":[{"event_id":"sha256:0dd37cc2d6f8a040a2036fee6096d62f7bbd36b5438ec1bd567b72f482956770","target":"graph","created_at":"2026-07-04T14:58:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0612460/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V \\to V$ and $A^*:V \\to V$ that satisfy (i)--(iv) below:\n  (i) Each of $A$, $A^*$ is diagonalizable.\n  (ii) There exists an ordering $V_{0},V_{1},...,V_{d}$ of the eigenspaces of $A$ such that $A^* V_i \\subseteq V_{i-1} + V_{i} + V_{i+1}$ for $0 \\leq i \\leq d$, where $V_{-1}=0$, $V_{d+1}=0$.\n  (iii) There exists an ordering $V^*_{0},V^*_{1},...,V^*_{\\delta}$ of the eigenspaces of $A^*$ such that $A V^*_i \\subseteq V^*_{i-1} + V^*_{i} + V^*_{i+1}$ for","authors_text":"Kazumasa Nomura, Paul Terwilliger","cross_cats":[],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2006-12-16T00:28:15Z","title":"The split decomposition of a tridiagonal pair"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612460","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:aac794b9a8f2cd7e83c0f6d8c419d72d51a144fcf87dc0a4622a0bd85693998b","target":"record","created_at":"2026-07-04T14:58:05Z","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":"155b48010a37099cf13256daad3f8f8379253dba1abea3b4a1197e619f3a977f","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2006-12-16T00:28:15Z","title_canon_sha256":"650a4c932d8a81cf5435f1eab93932ca53455d1cbf62319e92435d509339214e"},"schema_version":"1.0","source":{"id":"math/0612460","kind":"arxiv","version":1}},"canonical_sha256":"54343a37806ee64c6a2fc7f7d525f0086fa2da42e606067f994c59b5a9917863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54343a37806ee64c6a2fc7f7d525f0086fa2da42e606067f994c59b5a9917863","first_computed_at":"2026-07-04T14:58:05.447988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:58:05.447988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hOp952/JRmnXJzzUFR3Qi3hR+7oTRonsRI0rlLDyZoDLj7sT+rNHvC+pa5hnunqibfCEyB3Xpe0NbqkDH3t3CA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:58:05.448354Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aac794b9a8f2cd7e83c0f6d8c419d72d51a144fcf87dc0a4622a0bd85693998b","sha256:0dd37cc2d6f8a040a2036fee6096d62f7bbd36b5438ec1bd567b72f482956770"],"state_sha256":"ff7b75a7a1134c1227dec3a2926d9f3c514ebd2042178a45ffcc1cdd8fd1565f"}