{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IQJ44K2EIE7PBWXZ4DIB7HWRXX","short_pith_number":"pith:IQJ44K2E","schema_version":"1.0","canonical_sha256":"4413ce2b44413ef0daf9e0d01f9ed1bdd6894ea1e09cebd1b2af0a014cabddca","source":{"kind":"arxiv","id":"1503.03053","version":1},"attestation_state":"computed","paper":{"title":"A note on spectral properties of the $p$-adic tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Kaoru Sakai, Slawomir Klimek, Sumedha Rathnayake","submitted_at":"2015-03-10T19:50:29Z","abstract_excerpt":"We study the spectrum of the operator $D^*D$, where the operator $D$, introduced in \\cite{KMR}, is a forward derivative on the $p$-adic tree, a weighted rooted tree associated to $\\mathbb Z_p$ via Michon's correspondence. We show that the spectrum is closely related to the roots of a certain $q-$hypergeometric function and discuss the analytic continuation of the zeta function associated with $D^*D$."},"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":"1503.03053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-03-10T19:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"7b1ddad7810eafdf52d21c969026bf44e91dd9d18b207f06351cb5ac818dc8c0","abstract_canon_sha256":"bb12f4e0cb75e3b5269013aee9a795bbd81ad7d08cb9cc8fa25ac9e1ac6bce5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:47.588987Z","signature_b64":"BxvN2pS2+okFuDCyKr6cVhiOoT/uWKW4OE0ybFe8kBFO4GRSoPFHdnNNQYm9c5dFKjiTwnYrbV5T1D6awDxCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4413ce2b44413ef0daf9e0d01f9ed1bdd6894ea1e09cebd1b2af0a014cabddca","last_reissued_at":"2026-05-18T01:18:47.588121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:47.588121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on spectral properties of the $p$-adic tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Kaoru Sakai, Slawomir Klimek, Sumedha Rathnayake","submitted_at":"2015-03-10T19:50:29Z","abstract_excerpt":"We study the spectrum of the operator $D^*D$, where the operator $D$, introduced in \\cite{KMR}, is a forward derivative on the $p$-adic tree, a weighted rooted tree associated to $\\mathbb Z_p$ via Michon's correspondence. We show that the spectrum is closely related to the roots of a certain $q-$hypergeometric function and discuss the analytic continuation of the zeta function associated with $D^*D$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03053","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":"1503.03053","created_at":"2026-05-18T01:18:47.588264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03053v1","created_at":"2026-05-18T01:18:47.588264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03053","created_at":"2026-05-18T01:18:47.588264+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQJ44K2EIE7P","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQJ44K2EIE7PBWXZ","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQJ44K2E","created_at":"2026-05-18T12:29:25.134429+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/IQJ44K2EIE7PBWXZ4DIB7HWRXX","json":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX.json","graph_json":"https://pith.science/api/pith-number/IQJ44K2EIE7PBWXZ4DIB7HWRXX/graph.json","events_json":"https://pith.science/api/pith-number/IQJ44K2EIE7PBWXZ4DIB7HWRXX/events.json","paper":"https://pith.science/paper/IQJ44K2E"},"agent_actions":{"view_html":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX","download_json":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX.json","view_paper":"https://pith.science/paper/IQJ44K2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03053&json=true","fetch_graph":"https://pith.science/api/pith-number/IQJ44K2EIE7PBWXZ4DIB7HWRXX/graph.json","fetch_events":"https://pith.science/api/pith-number/IQJ44K2EIE7PBWXZ4DIB7HWRXX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX/action/storage_attestation","attest_author":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX/action/author_attestation","sign_citation":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX/action/citation_signature","submit_replication":"https://pith.science/pith/IQJ44K2EIE7PBWXZ4DIB7HWRXX/action/replication_record"}},"created_at":"2026-05-18T01:18:47.588264+00:00","updated_at":"2026-05-18T01:18:47.588264+00:00"}