{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LOIAW7DHONKYF3LIBVJSQ7EWLT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1e1a55168792163f7e062cbb1a7fa48a3ef78003aa62bc7df09312c82eca56d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-30T10:53:23Z","title_canon_sha256":"2d9e74f98cd0b4335ce4c841a41ebd9f902cca316f981f8d0836d18db357d52a"},"schema_version":"1.0","source":{"id":"2307.06313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.06313","created_at":"2026-07-05T06:30:21Z"},{"alias_kind":"arxiv_version","alias_value":"2307.06313v1","created_at":"2026-07-05T06:30:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.06313","created_at":"2026-07-05T06:30:21Z"},{"alias_kind":"pith_short_12","alias_value":"LOIAW7DHONKY","created_at":"2026-07-05T06:30:21Z"},{"alias_kind":"pith_short_16","alias_value":"LOIAW7DHONKYF3LI","created_at":"2026-07-05T06:30:21Z"},{"alias_kind":"pith_short_8","alias_value":"LOIAW7DH","created_at":"2026-07-05T06:30:21Z"}],"graph_snapshots":[{"event_id":"sha256:defd44f6ba9d4207ffebb744eeab9c83446899cfaf7ade941575421ce3ef71a4","target":"graph","created_at":"2026-07-05T06:30:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2307.06313/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main purpose of this article is using the analytic mathods and the quadratic residual transformation technique, and properties of Dedekind sums to study the calculating problem of two kinds hybrid power mean involving the two-term exponential sums and Dedekind sums, and give two asymptotic formulas for it. This work is a generalization for existing conclusions.","authors_text":"Jinmin Yu, Tingting Wang, Xue Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-30T10:53:23Z","title":"Two Kinds Hybrid Power Mean Involving Two-Term Exponential Sums and Dedekind Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.06313","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cf5d4b792d0d77bda8b7881282e266e05bd4726f87a644ab5c7f409aa4351545","target":"record","created_at":"2026-07-05T06:30:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1e1a55168792163f7e062cbb1a7fa48a3ef78003aa62bc7df09312c82eca56d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-30T10:53:23Z","title_canon_sha256":"2d9e74f98cd0b4335ce4c841a41ebd9f902cca316f981f8d0836d18db357d52a"},"schema_version":"1.0","source":{"id":"2307.06313","kind":"arxiv","version":1}},"canonical_sha256":"5b900b7c67735582ed680d53287c965ccac29358839e13e728cccd53d9e200e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b900b7c67735582ed680d53287c965ccac29358839e13e728cccd53d9e200e8","first_computed_at":"2026-07-05T06:30:21.909782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:30:21.909782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lZlEyT7fEF6ftk9GtVwO2pBOY273Qrr/KnOGwyIOfAca/VnzitzERQ7Lxb5M8rfwGPHRmEudDqXFkHfgRGrxCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:30:21.910231Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.06313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf5d4b792d0d77bda8b7881282e266e05bd4726f87a644ab5c7f409aa4351545","sha256:defd44f6ba9d4207ffebb744eeab9c83446899cfaf7ade941575421ce3ef71a4"],"state_sha256":"33dc20f5cb351410535d6b9f32b0351351a55ebee2bd8daab212972ec05c8c68"}