{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CHHNR4HQXTFGQDOBVKG7IKBI5V","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":"500e50af4298ddf29a1523b2671d9abd61ee9428c639e626dcfbe1af9b1659a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-08-05T16:52:11Z","title_canon_sha256":"436efd564a34ebe314e7a651fc6780d426f48ecb5830d80b3bf9bd8df9271a71"},"schema_version":"1.0","source":{"id":"1208.1036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1036","created_at":"2026-05-18T03:34:48Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1036v2","created_at":"2026-05-18T03:34:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1036","created_at":"2026-05-18T03:34:48Z"},{"alias_kind":"pith_short_12","alias_value":"CHHNR4HQXTFG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CHHNR4HQXTFGQDOB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CHHNR4HQ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:76fe9196a9d190d8f14674f625956d6880567d1310c681bbe93f016f491aa8d7","target":"graph","created_at":"2026-05-18T03:34:48Z","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":"Friedland (1981) showed that for a nonnegative square matrix A, the spectral radius r(e^D A) is a log-convex functional over the real diagonal matrices D. He showed that for fully indecomposable A, log r(e^D A) is strictly convex over D_1, D_2 if and only if D_1-D_2 != c I for any c \\in R. Here the condition of full indecomposability is shown to be replaceable by the weaker condition that A and A'A be irreducible, which is the sharpest possible replacement condition. Irreducibility of both A and A'A is shown to be equivalent to irreducibility of A^2 and A'A, which is the condition for a number","authors_text":"Lee Altenberg","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-08-05T16:52:11Z","title":"A Sharpened Condition for Strict Log-Convexity of the Spectral Radius via the Bipartite Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1036","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":"sha256:033e93f5cf8d295ca69bc4dff61646813162407ff43105a72352017c8beb33be","target":"record","created_at":"2026-05-18T03:34:48Z","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":"500e50af4298ddf29a1523b2671d9abd61ee9428c639e626dcfbe1af9b1659a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-08-05T16:52:11Z","title_canon_sha256":"436efd564a34ebe314e7a651fc6780d426f48ecb5830d80b3bf9bd8df9271a71"},"schema_version":"1.0","source":{"id":"1208.1036","kind":"arxiv","version":2}},"canonical_sha256":"11ced8f0f0bcca680dc1aa8df42828ed4fd9e414678bcbcd0b60fe9c8c946e4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11ced8f0f0bcca680dc1aa8df42828ed4fd9e414678bcbcd0b60fe9c8c946e4b","first_computed_at":"2026-05-18T03:34:48.259830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:48.259830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uPPAs7vm7xEldm6E6O/TkOZOIogOSzNGkxI+0sHsOjoeFqjpIB2F8STT37boFc3/+thxtFsLD5bSeAgFf3veBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:48.260395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:033e93f5cf8d295ca69bc4dff61646813162407ff43105a72352017c8beb33be","sha256:76fe9196a9d190d8f14674f625956d6880567d1310c681bbe93f016f491aa8d7"],"state_sha256":"895b15a6e06c53b5ba7bbf9369f1c91ecf043c61db299a54368ba204191da97b"}