{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2MEP3TNU763FZ3RAAP5RNB7HON","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":"0b61587b176188157d9c56b472f79be0df2133d736e0ac0b1255f1e561e1820d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","title_canon_sha256":"09cc625d0f7bd6016ed119c6f1f83edce6db42d3514d75abaddde5bb7b4b5860"},"schema_version":"1.0","source":{"id":"1109.4648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4648","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4648v1","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4648","created_at":"2026-05-18T04:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"2MEP3TNU763F","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2MEP3TNU763FZ3RA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2MEP3TNU","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:326f534d08e569578c01c8dd47669690950287ef3f618ff91e72a624ad5723aa","target":"graph","created_at":"2026-05-18T04:12:33Z","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":"The joint spectral radius of a bounded set of d times d real or complex matrices is defined to be the maximum exponential rate of growth of products of matrices drawn from that set. A set of matrices is said to satisfy the finiteness property if this maximum rate of growth occurs along a periodic infinite sequence. In this note we give some sufficient conditions for a finite set of matrices to satisfy the finiteness property in terms of its rank one elements. We show in particular that if a finite set of matrices does not satisfy the finiteness property, then the subset consisting of all matri","authors_text":"Ian D. Morris","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","title":"Rank one matrices do not contribute to the failure of the finiteness property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4648","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":"sha256:44ab3e6118c65ead7494b275b91bcd843a6721556913046d2d0a5c9fe1ac5174","target":"record","created_at":"2026-05-18T04:12:33Z","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":"0b61587b176188157d9c56b472f79be0df2133d736e0ac0b1255f1e561e1820d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-21T20:20:04Z","title_canon_sha256":"09cc625d0f7bd6016ed119c6f1f83edce6db42d3514d75abaddde5bb7b4b5860"},"schema_version":"1.0","source":{"id":"1109.4648","kind":"arxiv","version":1}},"canonical_sha256":"d308fdcdb4ffb65cee2003fb1687e7734db2ceddac201e5a77cf2e0ea29374d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d308fdcdb4ffb65cee2003fb1687e7734db2ceddac201e5a77cf2e0ea29374d3","first_computed_at":"2026-05-18T04:12:33.277663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:33.277663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S2smz5CqfgFieMGxTWSBvj6dTmfQMyPKEpH9DaNMS3Thkqho2uXPR8azgR96oB2ibroHfYnREIr0C4nyLt0LDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:33.278287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44ab3e6118c65ead7494b275b91bcd843a6721556913046d2d0a5c9fe1ac5174","sha256:326f534d08e569578c01c8dd47669690950287ef3f618ff91e72a624ad5723aa"],"state_sha256":"5b0370d7fef2622ddf11925f752530e2383ddde744669255491b7085da3493be"}