{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PC64XNRO2KMXCJNGM7JP5QBSAI","short_pith_number":"pith:PC64XNRO","canonical_record":{"source":{"id":"1804.00690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-02T18:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"f574c802d6efdf2d13901d291f0dfd652d7d743cb2554da28614bc04ff8eb58a","abstract_canon_sha256":"5e1bf69db5f784acd94bbb7b31ceb75d05c978febc1249a30e34aa32ba131577"},"schema_version":"1.0"},"canonical_sha256":"78bdcbb62ed2997125a667d2fec032022413d6ad9c0a2bc7ac461ee3b8148dcd","source":{"kind":"arxiv","id":"1804.00690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00690","created_at":"2026-05-18T00:19:32Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00690v1","created_at":"2026-05-18T00:19:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00690","created_at":"2026-05-18T00:19:32Z"},{"alias_kind":"pith_short_12","alias_value":"PC64XNRO2KMX","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PC64XNRO2KMXCJNG","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PC64XNRO","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PC64XNRO2KMXCJNGM7JP5QBSAI","target":"record","payload":{"canonical_record":{"source":{"id":"1804.00690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-02T18:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"f574c802d6efdf2d13901d291f0dfd652d7d743cb2554da28614bc04ff8eb58a","abstract_canon_sha256":"5e1bf69db5f784acd94bbb7b31ceb75d05c978febc1249a30e34aa32ba131577"},"schema_version":"1.0"},"canonical_sha256":"78bdcbb62ed2997125a667d2fec032022413d6ad9c0a2bc7ac461ee3b8148dcd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:32.482536Z","signature_b64":"uGN8U83Tr0ksztiLmWEInDVF1Iyx/GfDdMiYAc8cZmen4NxquD57Nud9Bl2wluaZz3tUPlSirphV5+yVX6pdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78bdcbb62ed2997125a667d2fec032022413d6ad9c0a2bc7ac461ee3b8148dcd","last_reissued_at":"2026-05-18T00:19:32.482021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:32.482021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.00690","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FtSpPOVkjlGSNrTPTRwzbZa882h2iowmbzhexpAFQnozP9LflaVzSdHzGM2k08CmLgDXBd91yD6kJu/m/9jADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:16:40.962085Z"},"content_sha256":"5334d9fe3ac2a298a790e064f4e103b22b19ed5131f09158c7864c4a9c47367a","schema_version":"1.0","event_id":"sha256:5334d9fe3ac2a298a790e064f4e103b22b19ed5131f09158c7864c4a9c47367a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PC64XNRO2KMXCJNGM7JP5QBSAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the third moment of $L(\\tfrac{1}{2}, \\chi_d)$ II: the number field case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian Diaconu, Ian Whitehead","submitted_at":"2018-04-02T18:41:31Z","abstract_excerpt":"We establish a smoothed asymptotic formula for the third moment of quadratic {D}irichlet $L$-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size $x^{\\frac{3}{4}}$. The error term in the asymptotic formula is on the order of $O(x^{\\frac{2}{3}+\\delta})$ for every $\\delta > 0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00690","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ie3hcfv0wCxfeAnB5ltJBLsxhUHyfs5js7KUBRAIL+Ih73pVwtEShE56u5tL7PnyGsGg0FmvzoioF+5IvkTCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:16:40.962783Z"},"content_sha256":"ef8fe888d734c3d7cc6017eb612dcfaf0d9f73ad527eee87de6ba0dedc586921","schema_version":"1.0","event_id":"sha256:ef8fe888d734c3d7cc6017eb612dcfaf0d9f73ad527eee87de6ba0dedc586921"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PC64XNRO2KMXCJNGM7JP5QBSAI/bundle.json","state_url":"https://pith.science/pith/PC64XNRO2KMXCJNGM7JP5QBSAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PC64XNRO2KMXCJNGM7JP5QBSAI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T17:16:40Z","links":{"resolver":"https://pith.science/pith/PC64XNRO2KMXCJNGM7JP5QBSAI","bundle":"https://pith.science/pith/PC64XNRO2KMXCJNGM7JP5QBSAI/bundle.json","state":"https://pith.science/pith/PC64XNRO2KMXCJNGM7JP5QBSAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PC64XNRO2KMXCJNGM7JP5QBSAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PC64XNRO2KMXCJNGM7JP5QBSAI","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":"5e1bf69db5f784acd94bbb7b31ceb75d05c978febc1249a30e34aa32ba131577","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-02T18:41:31Z","title_canon_sha256":"f574c802d6efdf2d13901d291f0dfd652d7d743cb2554da28614bc04ff8eb58a"},"schema_version":"1.0","source":{"id":"1804.00690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00690","created_at":"2026-05-18T00:19:32Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00690v1","created_at":"2026-05-18T00:19:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00690","created_at":"2026-05-18T00:19:32Z"},{"alias_kind":"pith_short_12","alias_value":"PC64XNRO2KMX","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PC64XNRO2KMXCJNG","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PC64XNRO","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:ef8fe888d734c3d7cc6017eb612dcfaf0d9f73ad527eee87de6ba0dedc586921","target":"graph","created_at":"2026-05-18T00:19:32Z","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 establish a smoothed asymptotic formula for the third moment of quadratic {D}irichlet $L$-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size $x^{\\frac{3}{4}}$. The error term in the asymptotic formula is on the order of $O(x^{\\frac{2}{3}+\\delta})$ for every $\\delta > 0.$","authors_text":"Adrian Diaconu, Ian Whitehead","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-02T18:41:31Z","title":"On the third moment of $L(\\tfrac{1}{2}, \\chi_d)$ II: the number field case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00690","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":"sha256:5334d9fe3ac2a298a790e064f4e103b22b19ed5131f09158c7864c4a9c47367a","target":"record","created_at":"2026-05-18T00:19:32Z","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":"5e1bf69db5f784acd94bbb7b31ceb75d05c978febc1249a30e34aa32ba131577","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-02T18:41:31Z","title_canon_sha256":"f574c802d6efdf2d13901d291f0dfd652d7d743cb2554da28614bc04ff8eb58a"},"schema_version":"1.0","source":{"id":"1804.00690","kind":"arxiv","version":1}},"canonical_sha256":"78bdcbb62ed2997125a667d2fec032022413d6ad9c0a2bc7ac461ee3b8148dcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78bdcbb62ed2997125a667d2fec032022413d6ad9c0a2bc7ac461ee3b8148dcd","first_computed_at":"2026-05-18T00:19:32.482021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:32.482021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uGN8U83Tr0ksztiLmWEInDVF1Iyx/GfDdMiYAc8cZmen4NxquD57Nud9Bl2wluaZz3tUPlSirphV5+yVX6pdBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:32.482536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5334d9fe3ac2a298a790e064f4e103b22b19ed5131f09158c7864c4a9c47367a","sha256:ef8fe888d734c3d7cc6017eb612dcfaf0d9f73ad527eee87de6ba0dedc586921"],"state_sha256":"4536133769f224474a26b3dc4c60ff376352892136a328b1bb73ea0716d47b4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2YDjYCb1kiIvvdCNPXlIDfJMnxV3z4UisNLgAxkq+nhtfClzVRnGeXpSJrCDZ33nO3k+bjV8JMW1AJ4wlyuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:16:40.966905Z","bundle_sha256":"1ef46c8284d2ee2ae66a72b71712f53352300bf60479af93677391550596dc2a"}}