{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QULP262MO5FBCV24YOKCJAWAAE","short_pith_number":"pith:QULP262M","schema_version":"1.0","canonical_sha256":"8516fd7b4c774a11575cc3942482c0013c50878cb1a24de9e407eff16e5514a8","source":{"kind":"arxiv","id":"1411.0210","version":1},"attestation_state":"computed","paper":{"title":"Monotonicity properties of certain Laplacian eigenvectors associated with trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ravindra B. Bapat","submitted_at":"2014-11-02T06:41:07Z","abstract_excerpt":"Nath and Paul (Linear Algebra Appl.,460(2014),97-110) have shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has properties similar to the Fiedler vector. We given an alternative proof, establishing a more general result in the process. It is conjectured that a similar phenomenon holds for any tree."},"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":"1411.0210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-02T06:41:07Z","cross_cats_sorted":[],"title_canon_sha256":"f916005e61cf7bbe0541627c10fa6553a9ec0b81c83598528a70fc006ac37537","abstract_canon_sha256":"c4a0ea87d5c4b460e28e3036fa1e4b729b36fde4b46b754ed6118056c9c7992a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.267040Z","signature_b64":"Q1z7Mp2chr+bZETkieWNnW7xz8tNfB7ScDJ3hQR2S5XLTPh2E1JjJ0wExsjNyTuv5hbb6NMe+blLGL2qUn9uDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8516fd7b4c774a11575cc3942482c0013c50878cb1a24de9e407eff16e5514a8","last_reissued_at":"2026-05-18T02:38:52.266456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.266456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monotonicity properties of certain Laplacian eigenvectors associated with trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ravindra B. Bapat","submitted_at":"2014-11-02T06:41:07Z","abstract_excerpt":"Nath and Paul (Linear Algebra Appl.,460(2014),97-110) have shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has properties similar to the Fiedler vector. We given an alternative proof, establishing a more general result in the process. It is conjectured that a similar phenomenon holds for any tree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0210","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":"1411.0210","created_at":"2026-05-18T02:38:52.266533+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.0210v1","created_at":"2026-05-18T02:38:52.266533+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0210","created_at":"2026-05-18T02:38:52.266533+00:00"},{"alias_kind":"pith_short_12","alias_value":"QULP262MO5FB","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QULP262MO5FBCV24","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QULP262M","created_at":"2026-05-18T12:28:46.137349+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/QULP262MO5FBCV24YOKCJAWAAE","json":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE.json","graph_json":"https://pith.science/api/pith-number/QULP262MO5FBCV24YOKCJAWAAE/graph.json","events_json":"https://pith.science/api/pith-number/QULP262MO5FBCV24YOKCJAWAAE/events.json","paper":"https://pith.science/paper/QULP262M"},"agent_actions":{"view_html":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE","download_json":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE.json","view_paper":"https://pith.science/paper/QULP262M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.0210&json=true","fetch_graph":"https://pith.science/api/pith-number/QULP262MO5FBCV24YOKCJAWAAE/graph.json","fetch_events":"https://pith.science/api/pith-number/QULP262MO5FBCV24YOKCJAWAAE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE/action/storage_attestation","attest_author":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE/action/author_attestation","sign_citation":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE/action/citation_signature","submit_replication":"https://pith.science/pith/QULP262MO5FBCV24YOKCJAWAAE/action/replication_record"}},"created_at":"2026-05-18T02:38:52.266533+00:00","updated_at":"2026-05-18T02:38:52.266533+00:00"}