{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4KPZQFZZOV7C4EXHCZUYWG5NDG","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":"e6581f1b2184852faf74fdafa4d5a102b9b6c321dafbde4087b71bcfa173c779","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-13T10:26:45Z","title_canon_sha256":"17d853582e11d6809762943fc98086fdb2c327ce6450fec1e02e3eeaca831d11"},"schema_version":"1.0","source":{"id":"1806.05175","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05175","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05175v3","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05175","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"4KPZQFZZOV7C","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4KPZQFZZOV7C4EXH","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4KPZQFZZ","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:0d2ef48ee81c16d736c3e15b3dd9226b109a1a8714736d78bacfda1914b85d50","target":"graph","created_at":"2026-05-17T23:40:41Z","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"},"paper":{"abstract_excerpt":"We continue our recent work on additive problems with prime summands: we already studied the \\emph{average} number of representations of an integer as a sum of two primes, and also considered individual integers. Furthermore, we dealt with representations of integers as sums of powers of prime numbers. In this paper, we study a Ces\\`aro weighted partial \\emph{explicit} formula for generalised Hardy-Littlewood numbers (integers that can be written as a sum of a prime power and a square) thus extending and improving our earlier results.","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-13T10:26:45Z","title":"A Ces\\`aro Average of generalised Hardy-Littlewood numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05175","kind":"arxiv","version":3},"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":"sha256:36db2992ab1b1739d210ff7bb67ca87dbce2cdef7ae2a1a59b5d926bdee90bac","target":"record","created_at":"2026-05-17T23:40:41Z","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":"e6581f1b2184852faf74fdafa4d5a102b9b6c321dafbde4087b71bcfa173c779","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-13T10:26:45Z","title_canon_sha256":"17d853582e11d6809762943fc98086fdb2c327ce6450fec1e02e3eeaca831d11"},"schema_version":"1.0","source":{"id":"1806.05175","kind":"arxiv","version":3}},"canonical_sha256":"e29f981739757e2e12e716698b1bad19b95dd759f193231c2a433e4dbc8547ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e29f981739757e2e12e716698b1bad19b95dd759f193231c2a433e4dbc8547ba","first_computed_at":"2026-05-17T23:40:41.748890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:41.748890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/J1/5Lb6XP7K7mfLYkIaT/NDC0liadmSVpGlM/Z7EgujYW494psW+WbkVsuvMbdS4BLOegaPczZDvxaKGU7iDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:41.749325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05175","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36db2992ab1b1739d210ff7bb67ca87dbce2cdef7ae2a1a59b5d926bdee90bac","sha256:0d2ef48ee81c16d736c3e15b3dd9226b109a1a8714736d78bacfda1914b85d50"],"state_sha256":"412fba3d920da47cb5bd2365fe5dca17e6c18dda63184564aa0ceb7bc266b953"}