{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FIZLTTQGSEM2HP6YJIS2XMJL7I","short_pith_number":"pith:FIZLTTQG","canonical_record":{"source":{"id":"1612.04882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-14T23:35:11Z","cross_cats_sorted":[],"title_canon_sha256":"358dec3309d4b8f9c1c55f21466f0e440a3b607570afbdfd44a7ae4bc0c4f1ad","abstract_canon_sha256":"e61d7f60dc737ec33d1fe0106b8746c4916cdcc32f5025b0804d25fa09f8da20"},"schema_version":"1.0"},"canonical_sha256":"2a32b9ce069119a3bfd84a25abb12bfa374f23126fe28ec395073a613ea4ad4a","source":{"kind":"arxiv","id":"1612.04882","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04882","created_at":"2026-05-18T00:42:30Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04882v1","created_at":"2026-05-18T00:42:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04882","created_at":"2026-05-18T00:42:30Z"},{"alias_kind":"pith_short_12","alias_value":"FIZLTTQGSEM2","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FIZLTTQGSEM2HP6Y","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FIZLTTQG","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FIZLTTQGSEM2HP6YJIS2XMJL7I","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-14T23:35:11Z","cross_cats_sorted":[],"title_canon_sha256":"358dec3309d4b8f9c1c55f21466f0e440a3b607570afbdfd44a7ae4bc0c4f1ad","abstract_canon_sha256":"e61d7f60dc737ec33d1fe0106b8746c4916cdcc32f5025b0804d25fa09f8da20"},"schema_version":"1.0"},"canonical_sha256":"2a32b9ce069119a3bfd84a25abb12bfa374f23126fe28ec395073a613ea4ad4a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:30.202220Z","signature_b64":"+J0ERWN3fL+qQqHmd05KZa5YeCUSK1pDuFSlperbBvKIllD4g9SfCtJILdnayO/PKwieIL7d69JDDVLje4v1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a32b9ce069119a3bfd84a25abb12bfa374f23126fe28ec395073a613ea4ad4a","last_reissued_at":"2026-05-18T00:42:30.201612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:30.201612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04882","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":"2026-05-18T00:42:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jmcImj50E1NnAiwH3FZMdJ7lS38p1iGOhwCYazr/96+YjLg5ZCHDD0IRWz7qeWP1hmvzLkmQqG0Z3SBDRwCSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:53:24.627346Z"},"content_sha256":"99c402a85ec442330c95775b5363d48f4ea37aaa6c65083cb7319c053f388aea","schema_version":"1.0","event_id":"sha256:99c402a85ec442330c95775b5363d48f4ea37aaa6c65083cb7319c053f388aea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FIZLTTQGSEM2HP6YJIS2XMJL7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bidiagonal Triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Darren Funk-Neubauer","submitted_at":"2016-12-14T23:35:11Z","abstract_excerpt":"We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the eigenspaces of the other two. The concept of bidiagonal triple is a generalization of the previously studied and similarly defined concept of bidiagonal pair. We show that every bidiagonal pair extends to a bidiagonal triple, and we describe the sense in which this extension is unique. In addition we generalize a number of theorems about bidiagonal pairs to the case "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04882","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":"2026-05-18T00:42:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5KAkhCPSGZAgWHNkhT4VsJMCDZHtMEUzsLOhFGc/LZUMkCV7HN7QyWCckMyhzGnk2eZ2UoVmLQnYLYTitaAOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:53:24.627697Z"},"content_sha256":"3e16df2234b6c867b265e95811470d7926a5ce9139ad03ea0ba1b5761e271890","schema_version":"1.0","event_id":"sha256:3e16df2234b6c867b265e95811470d7926a5ce9139ad03ea0ba1b5761e271890"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FIZLTTQGSEM2HP6YJIS2XMJL7I/bundle.json","state_url":"https://pith.science/pith/FIZLTTQGSEM2HP6YJIS2XMJL7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FIZLTTQGSEM2HP6YJIS2XMJL7I/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":"2026-05-30T20:53:24Z","links":{"resolver":"https://pith.science/pith/FIZLTTQGSEM2HP6YJIS2XMJL7I","bundle":"https://pith.science/pith/FIZLTTQGSEM2HP6YJIS2XMJL7I/bundle.json","state":"https://pith.science/pith/FIZLTTQGSEM2HP6YJIS2XMJL7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FIZLTTQGSEM2HP6YJIS2XMJL7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FIZLTTQGSEM2HP6YJIS2XMJL7I","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":"e61d7f60dc737ec33d1fe0106b8746c4916cdcc32f5025b0804d25fa09f8da20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-14T23:35:11Z","title_canon_sha256":"358dec3309d4b8f9c1c55f21466f0e440a3b607570afbdfd44a7ae4bc0c4f1ad"},"schema_version":"1.0","source":{"id":"1612.04882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04882","created_at":"2026-05-18T00:42:30Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04882v1","created_at":"2026-05-18T00:42:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04882","created_at":"2026-05-18T00:42:30Z"},{"alias_kind":"pith_short_12","alias_value":"FIZLTTQGSEM2","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FIZLTTQGSEM2HP6Y","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FIZLTTQG","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:3e16df2234b6c867b265e95811470d7926a5ce9139ad03ea0ba1b5761e271890","target":"graph","created_at":"2026-05-18T00:42:30Z","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 introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the eigenspaces of the other two. The concept of bidiagonal triple is a generalization of the previously studied and similarly defined concept of bidiagonal pair. We show that every bidiagonal pair extends to a bidiagonal triple, and we describe the sense in which this extension is unique. In addition we generalize a number of theorems about bidiagonal pairs to the case ","authors_text":"Darren Funk-Neubauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-14T23:35:11Z","title":"Bidiagonal Triples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04882","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":"sha256:99c402a85ec442330c95775b5363d48f4ea37aaa6c65083cb7319c053f388aea","target":"record","created_at":"2026-05-18T00:42:30Z","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":"e61d7f60dc737ec33d1fe0106b8746c4916cdcc32f5025b0804d25fa09f8da20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-14T23:35:11Z","title_canon_sha256":"358dec3309d4b8f9c1c55f21466f0e440a3b607570afbdfd44a7ae4bc0c4f1ad"},"schema_version":"1.0","source":{"id":"1612.04882","kind":"arxiv","version":1}},"canonical_sha256":"2a32b9ce069119a3bfd84a25abb12bfa374f23126fe28ec395073a613ea4ad4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a32b9ce069119a3bfd84a25abb12bfa374f23126fe28ec395073a613ea4ad4a","first_computed_at":"2026-05-18T00:42:30.201612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:30.201612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+J0ERWN3fL+qQqHmd05KZa5YeCUSK1pDuFSlperbBvKIllD4g9SfCtJILdnayO/PKwieIL7d69JDDVLje4v1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:30.202220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99c402a85ec442330c95775b5363d48f4ea37aaa6c65083cb7319c053f388aea","sha256:3e16df2234b6c867b265e95811470d7926a5ce9139ad03ea0ba1b5761e271890"],"state_sha256":"6fdff5838067a20e30e10bdc2d3b5172de2247eda00849d363809ca8437825f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h3axnOLc09Jg37Tnt7F9y7EB1Cfp7Hu9iYb5wOkN4v7+TCL+Qj/TDXirA+AHhsH9pkgWJgPMG+ZMh1oESSFfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:53:24.629651Z","bundle_sha256":"3e6ee0521d032834a9d44e6453996605bf5deb1526982243c6ba290cf2124b6a"}}