{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:BHZ74NPUBBTRHABW2ET5OUAONY","short_pith_number":"pith:BHZ74NPU","schema_version":"1.0","canonical_sha256":"09f3fe35f40867138036d127d7500e6e0fa70f121d8fb63461949e93a77307c4","source":{"kind":"arxiv","id":"0709.0424","version":1},"attestation_state":"computed","paper":{"title":"Asymptotics of eigenvalues of Sturm--Liouville problem with discrete self-similar weight","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"A. A. Vladimirov, I. A. Sheipak","submitted_at":"2007-09-04T19:59:58Z","abstract_excerpt":"The Sturm--Liouville problem $-y''-\\lambda\\rho y=0$, $y(0)=y(1)=0$, where $\\rho$ is a generalized derivative of self-similar function $P\\in L_2[0,1]$ with spectral degree D=0, is studied. Asymptotic formulas for eigenvalues are obtained."},"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":"0709.0424","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2007-09-04T19:59:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"92e586862323d3e14c1d17098f1846f1024e3427ca065b6c712b85723a9f69c3","abstract_canon_sha256":"52ab9f20aaf8606a98bcca13f75f342700b41a2c907071d2018a705d6d70d8e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:04:00.597997Z","signature_b64":"hZGeTtcFlh8R2nHFB0suwVLGB9RVuIPGrm9GZ1V7ighXmrY0cAh2EoeTL/1xBOhCzBybRCz5szixMonxFmVzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09f3fe35f40867138036d127d7500e6e0fa70f121d8fb63461949e93a77307c4","last_reissued_at":"2026-07-04T15:04:00.597610Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:04:00.597610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of eigenvalues of Sturm--Liouville problem with discrete self-similar weight","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"A. A. Vladimirov, I. A. Sheipak","submitted_at":"2007-09-04T19:59:58Z","abstract_excerpt":"The Sturm--Liouville problem $-y''-\\lambda\\rho y=0$, $y(0)=y(1)=0$, where $\\rho$ is a generalized derivative of self-similar function $P\\in L_2[0,1]$ with spectral degree D=0, is studied. Asymptotic formulas for eigenvalues are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0424","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0709.0424/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0709.0424","created_at":"2026-07-04T15:04:00.597671+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.0424v1","created_at":"2026-07-04T15:04:00.597671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0424","created_at":"2026-07-04T15:04:00.597671+00:00"},{"alias_kind":"pith_short_12","alias_value":"BHZ74NPUBBTR","created_at":"2026-07-04T15:04:00.597671+00:00"},{"alias_kind":"pith_short_16","alias_value":"BHZ74NPUBBTRHABW","created_at":"2026-07-04T15:04:00.597671+00:00"},{"alias_kind":"pith_short_8","alias_value":"BHZ74NPU","created_at":"2026-07-04T15:04:00.597671+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/BHZ74NPUBBTRHABW2ET5OUAONY","json":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY.json","graph_json":"https://pith.science/api/pith-number/BHZ74NPUBBTRHABW2ET5OUAONY/graph.json","events_json":"https://pith.science/api/pith-number/BHZ74NPUBBTRHABW2ET5OUAONY/events.json","paper":"https://pith.science/paper/BHZ74NPU"},"agent_actions":{"view_html":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY","download_json":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY.json","view_paper":"https://pith.science/paper/BHZ74NPU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.0424&json=true","fetch_graph":"https://pith.science/api/pith-number/BHZ74NPUBBTRHABW2ET5OUAONY/graph.json","fetch_events":"https://pith.science/api/pith-number/BHZ74NPUBBTRHABW2ET5OUAONY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY/action/storage_attestation","attest_author":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY/action/author_attestation","sign_citation":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY/action/citation_signature","submit_replication":"https://pith.science/pith/BHZ74NPUBBTRHABW2ET5OUAONY/action/replication_record"}},"created_at":"2026-07-04T15:04:00.597671+00:00","updated_at":"2026-07-04T15:04:00.597671+00:00"}