{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OO76UZCHU6YTXX6SXSGVUE6U7R","short_pith_number":"pith:OO76UZCH","schema_version":"1.0","canonical_sha256":"73bfea6447a7b13bdfd2bc8d5a13d4fc79c92b44c35b297712918dc75a95a469","source":{"kind":"arxiv","id":"1602.03864","version":3},"attestation_state":"computed","paper":{"title":"Eigenvalue estimates for the Laplacian on a metric tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Jonathan Rohleder","submitted_at":"2016-02-11T20:15:27Z","abstract_excerpt":"We provide explicit upper bounds for the eigenvalues of the Laplacian on a finite metric tree subject to standard vertex conditions. The results include estimates depending on the average length of the edges or the diameter. In particular, we establish a sharp upper bound for the spectral gap, i.e. the smallest positive eigenvalue, and show that equilateral star graphs are the unique maximizers of the spectral gap among all trees of a given average length."},"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":"1602.03864","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-11T20:15:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"80bb2d99c59476c7503f8135e4e80988182a54b5cc622abe8902c8e2039c0a80","abstract_canon_sha256":"45987c03b97232b8bb1b97e99625ffc9b83ef5ecf649611a8e574debf74a07be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:23.468796Z","signature_b64":"JB+3+V/jkSVjv/FpxBa88QevzPAgKVQrDWAcduV0BYCz7Y4QXMO6X2HTv2oMDpeNEW3JCOgVNmQPt98aBLC2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73bfea6447a7b13bdfd2bc8d5a13d4fc79c92b44c35b297712918dc75a95a469","last_reissued_at":"2026-05-18T01:10:23.468205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:23.468205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalue estimates for the Laplacian on a metric tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Jonathan Rohleder","submitted_at":"2016-02-11T20:15:27Z","abstract_excerpt":"We provide explicit upper bounds for the eigenvalues of the Laplacian on a finite metric tree subject to standard vertex conditions. The results include estimates depending on the average length of the edges or the diameter. In particular, we establish a sharp upper bound for the spectral gap, i.e. the smallest positive eigenvalue, and show that equilateral star graphs are the unique maximizers of the spectral gap among all trees of a given average length."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03864","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":"1602.03864","created_at":"2026-05-18T01:10:23.468313+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.03864v3","created_at":"2026-05-18T01:10:23.468313+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03864","created_at":"2026-05-18T01:10:23.468313+00:00"},{"alias_kind":"pith_short_12","alias_value":"OO76UZCHU6YT","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OO76UZCHU6YTXX6S","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OO76UZCH","created_at":"2026-05-18T12:30:36.002864+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/OO76UZCHU6YTXX6SXSGVUE6U7R","json":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R.json","graph_json":"https://pith.science/api/pith-number/OO76UZCHU6YTXX6SXSGVUE6U7R/graph.json","events_json":"https://pith.science/api/pith-number/OO76UZCHU6YTXX6SXSGVUE6U7R/events.json","paper":"https://pith.science/paper/OO76UZCH"},"agent_actions":{"view_html":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R","download_json":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R.json","view_paper":"https://pith.science/paper/OO76UZCH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.03864&json=true","fetch_graph":"https://pith.science/api/pith-number/OO76UZCHU6YTXX6SXSGVUE6U7R/graph.json","fetch_events":"https://pith.science/api/pith-number/OO76UZCHU6YTXX6SXSGVUE6U7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R/action/storage_attestation","attest_author":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R/action/author_attestation","sign_citation":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R/action/citation_signature","submit_replication":"https://pith.science/pith/OO76UZCHU6YTXX6SXSGVUE6U7R/action/replication_record"}},"created_at":"2026-05-18T01:10:23.468313+00:00","updated_at":"2026-05-18T01:10:23.468313+00:00"}