{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3VSGN6YLGX4BSSBKIS7CHQ3CVA","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":"6d131d498f9916067e7f87031945ba0ded93cc6adfd03cf2bf0ad899ee7ec0c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-05T19:17:20Z","title_canon_sha256":"586c2f4893df0f6f340302121f752dd17e1dd768d607377dc1159c12e2c66f82"},"schema_version":"1.0","source":{"id":"1309.1447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1447","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1447v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1447","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"3VSGN6YLGX4B","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3VSGN6YLGX4BSSBK","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3VSGN6YL","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:5e8619b179c9c64d49adf8c1f0d37b3818d67c78d7cc96e7a93311f872abe9a4","target":"graph","created_at":"2026-05-18T03:14:07Z","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 investigate one-dimensional families of diagonal forms, considering the evolution of the asymptotic formula and error term. We then discuss properties of the average asymptotic formula obtained. The subsequent second moment analysis precipitates an effective means of computing $p$-adic densities of zeros for large primes $p$.","authors_text":"Sam Chow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-05T19:17:20Z","title":"Averaging on thin sets of diagonal forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1447","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":"sha256:540ad1d8b243acf6225921cf3f696dc5dcdb73fb0789056d915c42b6e4e48e04","target":"record","created_at":"2026-05-18T03:14:07Z","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":"6d131d498f9916067e7f87031945ba0ded93cc6adfd03cf2bf0ad899ee7ec0c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-05T19:17:20Z","title_canon_sha256":"586c2f4893df0f6f340302121f752dd17e1dd768d607377dc1159c12e2c66f82"},"schema_version":"1.0","source":{"id":"1309.1447","kind":"arxiv","version":1}},"canonical_sha256":"dd6466fb0b35f819482a44be23c362a81a5cf8b2b3cfad969166a34af479deaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd6466fb0b35f819482a44be23c362a81a5cf8b2b3cfad969166a34af479deaf","first_computed_at":"2026-05-18T03:14:07.281892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:07.281892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EHG9QmuckIcYIOEdFHAFw54GsBSLXl/vicoK1YFAapM+AAerTqXTU9gpI4020c3otbWkdUckXVHJggnGgn2jCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:07.282344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:540ad1d8b243acf6225921cf3f696dc5dcdb73fb0789056d915c42b6e4e48e04","sha256:5e8619b179c9c64d49adf8c1f0d37b3818d67c78d7cc96e7a93311f872abe9a4"],"state_sha256":"aa7dc437902cb85b432b1d3c0971ed3ce620e7b5b4dc859b0659f302abbcfc71"}