{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:DLPNFMDF2XEW2XR43AKKOBQVC6","short_pith_number":"pith:DLPNFMDF","schema_version":"1.0","canonical_sha256":"1aded2b065d5c96d5e3cd814a7061517b1b581a2d2e967b61c6d0cb21042bfd9","source":{"kind":"arxiv","id":"math/0506274","version":1},"attestation_state":"computed","paper":{"title":"Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Jiang Zeng, Martin Rubey, Victor J. W. Guo","submitted_at":"2005-06-14T13:41:06Z","abstract_excerpt":"Recently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula involving Salie's coefficients for the alternating sums of powers. In this paper, we show that these are polynomials with symmetric, nonnegative integral coefficients by refining Gessel-Viennot's combinatorial interpretations."},"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":"math/0506274","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2005-06-14T13:41:06Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"61665e423344d245d110cd83022a41795fe90d02e8090f1b686d427595a5a7c3","abstract_canon_sha256":"ec4c7c0fb0090f83c1fd9d2108c8f9bd598cd5e9ddd21dcec81c5eeb0729420c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:23.398075Z","signature_b64":"nxeCsl6P8LXv1JDruLID+dwV32K4We6i+5bYDcqhR7ObzTAh57OuO3VLSp+NRyw1zQqnHW7Zc/IuVI4be9ZqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aded2b065d5c96d5e3cd814a7061517b1b581a2d2e967b61c6d0cb21042bfd9","last_reissued_at":"2026-05-18T01:05:23.397637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:23.397637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Jiang Zeng, Martin Rubey, Victor J. W. Guo","submitted_at":"2005-06-14T13:41:06Z","abstract_excerpt":"Recently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula involving Salie's coefficients for the alternating sums of powers. In this paper, we show that these are polynomials with symmetric, nonnegative integral coefficients by refining Gessel-Viennot's combinatorial interpretations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506274","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":"math/0506274","created_at":"2026-05-18T01:05:23.397705+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0506274v1","created_at":"2026-05-18T01:05:23.397705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506274","created_at":"2026-05-18T01:05:23.397705+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLPNFMDF2XEW","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLPNFMDF2XEW2XR4","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLPNFMDF","created_at":"2026-05-18T12:25:53.335082+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/DLPNFMDF2XEW2XR43AKKOBQVC6","json":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6.json","graph_json":"https://pith.science/api/pith-number/DLPNFMDF2XEW2XR43AKKOBQVC6/graph.json","events_json":"https://pith.science/api/pith-number/DLPNFMDF2XEW2XR43AKKOBQVC6/events.json","paper":"https://pith.science/paper/DLPNFMDF"},"agent_actions":{"view_html":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6","download_json":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6.json","view_paper":"https://pith.science/paper/DLPNFMDF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0506274&json=true","fetch_graph":"https://pith.science/api/pith-number/DLPNFMDF2XEW2XR43AKKOBQVC6/graph.json","fetch_events":"https://pith.science/api/pith-number/DLPNFMDF2XEW2XR43AKKOBQVC6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6/action/storage_attestation","attest_author":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6/action/author_attestation","sign_citation":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6/action/citation_signature","submit_replication":"https://pith.science/pith/DLPNFMDF2XEW2XR43AKKOBQVC6/action/replication_record"}},"created_at":"2026-05-18T01:05:23.397705+00:00","updated_at":"2026-05-18T01:05:23.397705+00:00"}