{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GY4TDTEENRHJ6EKJ3DLMT4BSIP","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":"6a7e7b3a42c2844187d5ae2fbfd36e1941cde3a603b48ef7ea1692cfda16fb9c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-10T10:48:21Z","title_canon_sha256":"7793300724b832e1ea42b8b3710b32603d92c8dad0ee0fc7d664797b472e3bcb"},"schema_version":"1.0","source":{"id":"1611.03251","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03251","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03251v3","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03251","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"pith_short_12","alias_value":"GY4TDTEENRHJ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GY4TDTEENRHJ6EKJ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GY4TDTEE","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:7787d09247713dfe0a08adf25ecd1b5d4b85eb912b08a9408571a7be24ebd51a","target":"graph","created_at":"2026-05-18T00:50:56Z","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 prove that if any $\\lfloor3d/2 \\rfloor$ or fewer elements of a finite family of linear operators $\\mathbb K^d\\to \\mathbb K^d$ ($\\mathbb K$ is an arbitrary field) have a common eigenvector then all operators in the family have a common eigenvector. Moreover, $\\lfloor 3d/2\\rfloor$ cannot be replaced by a smaller number. Also, we study the following problem, achieving partial results: prove that if any $l=O(d)$ or fewer elements of a finite family of linear operators $\\mathbb K^d\\to \\mathbb K^d$ have a common non-trivial invariant subspace then all operators in the family have a common non-tri","authors_text":"Alexandr Polyanskii","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-10T10:48:21Z","title":"Helly-type theorem for eigenvectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03251","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:c5d891ce81dda4400f47108f4defdb5216808476b8501e31f7c50c1fd72ef5c7","target":"record","created_at":"2026-05-18T00:50:56Z","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":"6a7e7b3a42c2844187d5ae2fbfd36e1941cde3a603b48ef7ea1692cfda16fb9c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-10T10:48:21Z","title_canon_sha256":"7793300724b832e1ea42b8b3710b32603d92c8dad0ee0fc7d664797b472e3bcb"},"schema_version":"1.0","source":{"id":"1611.03251","kind":"arxiv","version":3}},"canonical_sha256":"363931cc846c4e9f1149d8d6c9f03243ef5d89e232d730f8e4b09f55c7a2ee85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"363931cc846c4e9f1149d8d6c9f03243ef5d89e232d730f8e4b09f55c7a2ee85","first_computed_at":"2026-05-18T00:50:56.399896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:56.399896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fD6CoFsZknEnNxnxXLYov/2ShevRG0+vuH1H6bYgPPc9pVupglLUZJMbmvHTBVahIsmhzTdJ08T0+q8vDsw6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:56.400490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03251","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5d891ce81dda4400f47108f4defdb5216808476b8501e31f7c50c1fd72ef5c7","sha256:7787d09247713dfe0a08adf25ecd1b5d4b85eb912b08a9408571a7be24ebd51a"],"state_sha256":"3f55690259d9e3d88ccc97ffd174aa77609d592381d1847224036f5fc75e5e25"}