{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Z2IPUFBF2N5V22ACVQCF3YD6JT","short_pith_number":"pith:Z2IPUFBF","schema_version":"1.0","canonical_sha256":"ce90fa1425d37b5d6802ac045de07e4cd504f7c5a8830cb51be7190aa1685761","source":{"kind":"arxiv","id":"1501.01505","version":1},"attestation_state":"computed","paper":{"title":"Inertia of Loewner Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Rajendra Bhatia, Shmuel Friedland, Tanvi Jain","submitted_at":"2015-01-07T14:37:00Z","abstract_excerpt":"Given positive numbers p_1 < p_2 < ... < p_n, and a real number r let L_r be the n by n matrix with its (i,j) entry equal to (p_i^r-p_j^r)/(p_i-p_j). A well-known theorem of C. Loewner says that L_r is positive definite when 0 < r < 1. In contrast, R. Bhatia and J. Holbrook, (Indiana Univ. Math. J, 49 (2000) 1153-1173) showed that when 1 < r < 2, the matrix L_r has only one positive eigenvalue, and made a conjecture about the signatures of eigenvalues of L_r for other r. That conjecture is proved in this paper."},"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":"1501.01505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-01-07T14:37:00Z","cross_cats_sorted":[],"title_canon_sha256":"eda1a1b85dcaeb5b0126dec10128df339d3a7cca76fc51fb6d545dd585b91afb","abstract_canon_sha256":"0b3c841f9bdc6d7d0db3fe20604e785ec3e732480b3f075e9021579f16356dcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:53.948883Z","signature_b64":"OOjG3eKmOrt2PU8FnR7hcwiWK8va4S7016yglSocueH0OE1sL6oNp7NzfgtY0/LvPN29tRFdizT9F9StI8eHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce90fa1425d37b5d6802ac045de07e4cd504f7c5a8830cb51be7190aa1685761","last_reissued_at":"2026-05-18T02:29:53.948348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:53.948348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inertia of Loewner Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Rajendra Bhatia, Shmuel Friedland, Tanvi Jain","submitted_at":"2015-01-07T14:37:00Z","abstract_excerpt":"Given positive numbers p_1 < p_2 < ... < p_n, and a real number r let L_r be the n by n matrix with its (i,j) entry equal to (p_i^r-p_j^r)/(p_i-p_j). A well-known theorem of C. Loewner says that L_r is positive definite when 0 < r < 1. In contrast, R. Bhatia and J. Holbrook, (Indiana Univ. Math. J, 49 (2000) 1153-1173) showed that when 1 < r < 2, the matrix L_r has only one positive eigenvalue, and made a conjecture about the signatures of eigenvalues of L_r for other r. That conjecture is proved in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01505","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.01505","created_at":"2026-05-18T02:29:53.948430+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.01505v1","created_at":"2026-05-18T02:29:53.948430+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01505","created_at":"2026-05-18T02:29:53.948430+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2IPUFBF2N5V","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2IPUFBF2N5V22AC","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2IPUFBF","created_at":"2026-05-18T12:29:52.810259+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/Z2IPUFBF2N5V22ACVQCF3YD6JT","json":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT.json","graph_json":"https://pith.science/api/pith-number/Z2IPUFBF2N5V22ACVQCF3YD6JT/graph.json","events_json":"https://pith.science/api/pith-number/Z2IPUFBF2N5V22ACVQCF3YD6JT/events.json","paper":"https://pith.science/paper/Z2IPUFBF"},"agent_actions":{"view_html":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT","download_json":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT.json","view_paper":"https://pith.science/paper/Z2IPUFBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.01505&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2IPUFBF2N5V22ACVQCF3YD6JT/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2IPUFBF2N5V22ACVQCF3YD6JT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT/action/storage_attestation","attest_author":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT/action/author_attestation","sign_citation":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT/action/citation_signature","submit_replication":"https://pith.science/pith/Z2IPUFBF2N5V22ACVQCF3YD6JT/action/replication_record"}},"created_at":"2026-05-18T02:29:53.948430+00:00","updated_at":"2026-05-18T02:29:53.948430+00:00"}