{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KC5WH3UPVMGOEPXWU7XV7DQC6H","short_pith_number":"pith:KC5WH3UP","schema_version":"1.0","canonical_sha256":"50bb63ee8fab0ce23ef6a7ef5f8e02f1e62bb3f639329b7cbe3758e60429ece2","source":{"kind":"arxiv","id":"1407.7059","version":3},"attestation_state":"computed","paper":{"title":"The critical exponent for generalized doubly nonnegative matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Charles Johnson, Pietro Paparella, Xuchen Han","submitted_at":"2014-07-25T21:09:47Z","abstract_excerpt":"It is known that the critical exponent (CE) for conventional, continuous powers of $n$-by-$n$ doubly nonnegative (DN) matrices is $n-2$. Here, we consider the larger class of diagonalizable, entry-wise nonnegative $n$-by-$n$ matrices with nonnegative eigenvalues (GDN). We show that, again, a CE exists and are able to bound it with a low-coefficient quadratic. However, the CE is larger than in the DN case; in particular, 2 for $n=3$. There seems to be a connection with the index of primitivity, and a number of other observations are made and questions raised. It is shown that there is no CE for"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.7059","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-25T21:09:47Z","cross_cats_sorted":[],"title_canon_sha256":"d5eb24abdbd3a091d1b3c64a973b3057c7e191735f3e0507c21cded9922fd81d","abstract_canon_sha256":"d061f2fcbd8f4533739cefa9fe1078e4bb42f41bed00b04d88cb82734ad139f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:05.007585Z","signature_b64":"7Y5ON/4FuEvJG/J1yfZ9EXDJX41ztFZYon5HRAb7XevUnGzmGwIZy7O8zuCTW2PUHKdGdM1QOqHX6gIQ9PNvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50bb63ee8fab0ce23ef6a7ef5f8e02f1e62bb3f639329b7cbe3758e60429ece2","last_reissued_at":"2026-05-18T00:39:05.007187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:05.007187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The critical exponent for generalized doubly nonnegative matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Charles Johnson, Pietro Paparella, Xuchen Han","submitted_at":"2014-07-25T21:09:47Z","abstract_excerpt":"It is known that the critical exponent (CE) for conventional, continuous powers of $n$-by-$n$ doubly nonnegative (DN) matrices is $n-2$. Here, we consider the larger class of diagonalizable, entry-wise nonnegative $n$-by-$n$ matrices with nonnegative eigenvalues (GDN). We show that, again, a CE exists and are able to bound it with a low-coefficient quadratic. However, the CE is larger than in the DN case; in particular, 2 for $n=3$. There seems to be a connection with the index of primitivity, and a number of other observations are made and questions raised. It is shown that there is no CE for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7059","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.7059","created_at":"2026-05-18T00:39:05.007247+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.7059v3","created_at":"2026-05-18T00:39:05.007247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7059","created_at":"2026-05-18T00:39:05.007247+00:00"},{"alias_kind":"pith_short_12","alias_value":"KC5WH3UPVMGO","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KC5WH3UPVMGOEPXW","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KC5WH3UP","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H","json":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H.json","graph_json":"https://pith.science/api/pith-number/KC5WH3UPVMGOEPXWU7XV7DQC6H/graph.json","events_json":"https://pith.science/api/pith-number/KC5WH3UPVMGOEPXWU7XV7DQC6H/events.json","paper":"https://pith.science/paper/KC5WH3UP"},"agent_actions":{"view_html":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H","download_json":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H.json","view_paper":"https://pith.science/paper/KC5WH3UP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.7059&json=true","fetch_graph":"https://pith.science/api/pith-number/KC5WH3UPVMGOEPXWU7XV7DQC6H/graph.json","fetch_events":"https://pith.science/api/pith-number/KC5WH3UPVMGOEPXWU7XV7DQC6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H/action/storage_attestation","attest_author":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H/action/author_attestation","sign_citation":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H/action/citation_signature","submit_replication":"https://pith.science/pith/KC5WH3UPVMGOEPXWU7XV7DQC6H/action/replication_record"}},"created_at":"2026-05-18T00:39:05.007247+00:00","updated_at":"2026-05-18T00:39:05.007247+00:00"}