{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SN5ZB34VRQYYQP6BBP6NDSPB4H","short_pith_number":"pith:SN5ZB34V","schema_version":"1.0","canonical_sha256":"937b90ef958c31883fc10bfcd1c9e1e1decedcd1ec22b051a6a0cf18a835b57b","source":{"kind":"arxiv","id":"1608.04780","version":1},"attestation_state":"computed","paper":{"title":"The modulus of Whittaker functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Hans Volkmer","submitted_at":"2016-08-15T01:55:51Z","abstract_excerpt":"The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an integral representation for products of Whittaker functions due to Erd\\'elyi (1938)."},"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":"1608.04780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-08-15T01:55:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d6333374a9eb8b85bcd28196ebcc46a8837b688522fefbb8f29a107f192b997e","abstract_canon_sha256":"67c473a1abd832d38ab22cac9afdc3cfab098f20d5091d37f417d91a248bb8e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:33.600292Z","signature_b64":"zxsWNYUgB6XmAoc+k0GgE8zIiEwK7zO4FO0/n0ncLWjaPljg82W8QHA4P7+pHV6QW3uIrUWN0mnHNWQeM6nAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"937b90ef958c31883fc10bfcd1c9e1e1decedcd1ec22b051a6a0cf18a835b57b","last_reissued_at":"2026-05-18T01:08:33.599582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:33.599582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The modulus of Whittaker functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Hans Volkmer","submitted_at":"2016-08-15T01:55:51Z","abstract_excerpt":"The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an integral representation for products of Whittaker functions due to Erd\\'elyi (1938)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04780","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":"1608.04780","created_at":"2026-05-18T01:08:33.599709+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.04780v1","created_at":"2026-05-18T01:08:33.599709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04780","created_at":"2026-05-18T01:08:33.599709+00:00"},{"alias_kind":"pith_short_12","alias_value":"SN5ZB34VRQYY","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SN5ZB34VRQYYQP6B","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SN5ZB34V","created_at":"2026-05-18T12:30:44.179134+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/SN5ZB34VRQYYQP6BBP6NDSPB4H","json":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H.json","graph_json":"https://pith.science/api/pith-number/SN5ZB34VRQYYQP6BBP6NDSPB4H/graph.json","events_json":"https://pith.science/api/pith-number/SN5ZB34VRQYYQP6BBP6NDSPB4H/events.json","paper":"https://pith.science/paper/SN5ZB34V"},"agent_actions":{"view_html":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H","download_json":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H.json","view_paper":"https://pith.science/paper/SN5ZB34V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.04780&json=true","fetch_graph":"https://pith.science/api/pith-number/SN5ZB34VRQYYQP6BBP6NDSPB4H/graph.json","fetch_events":"https://pith.science/api/pith-number/SN5ZB34VRQYYQP6BBP6NDSPB4H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H/action/storage_attestation","attest_author":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H/action/author_attestation","sign_citation":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H/action/citation_signature","submit_replication":"https://pith.science/pith/SN5ZB34VRQYYQP6BBP6NDSPB4H/action/replication_record"}},"created_at":"2026-05-18T01:08:33.599709+00:00","updated_at":"2026-05-18T01:08:33.599709+00:00"}