{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AETNQEFJNMWGMTEPOPK6FU4L6T","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":"575590c64c11ad0565bb25b80e48d37eab1907bba609c83cde9470454e57bec2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-18T10:09:49Z","title_canon_sha256":"4dde32f106ef4680cd8fe6ee35a12ef5a36e8f424277d398f32ffcd15a686b7e"},"schema_version":"1.0","source":{"id":"1312.5701","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5701","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5701v3","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5701","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"AETNQEFJNMWG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AETNQEFJNMWGMTEP","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AETNQEFJ","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:08c7b91006d0dd3afae507de09b0c35ae4a7a0cf6657ecc3db43bc75d5730720","target":"graph","created_at":"2026-05-17T23:56:30Z","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":"The weighted Selberg integral is a discrete mean-square, that is a generalization of the classical Selberg integral of primes to an arithmetic function $f$, whose values in a short interval are suitably attached to a weight function. We give conditions on $f$ and select a particular class of weights, in order to investigate non-trivial bounds of weighted Selberg integrals of both $f$ and $f\\ast\\mu$. In particular, we discuss the cases of the symmetry integral and the modified Selberg integral, the latter involving the Cesaro weight. We also prove some side results when $f$ is a divisor functio","authors_text":"Giovanni Coppola, Maurizio Laporta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-18T10:09:49Z","title":"Symmetry and short interval mean-squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5701","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":"sha256:9466945950808fd314fd71bede443482d755d26319600fce09ec7d96fd1c5c67","target":"record","created_at":"2026-05-17T23:56:30Z","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":"575590c64c11ad0565bb25b80e48d37eab1907bba609c83cde9470454e57bec2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-18T10:09:49Z","title_canon_sha256":"4dde32f106ef4680cd8fe6ee35a12ef5a36e8f424277d398f32ffcd15a686b7e"},"schema_version":"1.0","source":{"id":"1312.5701","kind":"arxiv","version":3}},"canonical_sha256":"0126d810a96b2c664c8f73d5e2d38bf4ca032e6238567568aa97753ed3292988","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0126d810a96b2c664c8f73d5e2d38bf4ca032e6238567568aa97753ed3292988","first_computed_at":"2026-05-17T23:56:30.581914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:30.581914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BK+m/hsk3YMPG/RRF4ygvmI16LJhlBA5oEoh/smzMGUu/tZpO0puNF7gYzTpnBrw6/9LwG3BEvYWPcsyZ2o6Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:30.582247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5701","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9466945950808fd314fd71bede443482d755d26319600fce09ec7d96fd1c5c67","sha256:08c7b91006d0dd3afae507de09b0c35ae4a7a0cf6657ecc3db43bc75d5730720"],"state_sha256":"075b4c9cf0e29503afa4fd434319ed4ca45b83911ef42adc168fec99f33dcc77"}