{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LXDY3HMPQICIZVXMHGA6SZUPPE","short_pith_number":"pith:LXDY3HMP","canonical_record":{"source":{"id":"1701.02834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-11T03:13:50Z","cross_cats_sorted":[],"title_canon_sha256":"0b12efd109c1403d62b5bc3cde395e0f1404bc5106b4cd46d5794fc9f25eb602","abstract_canon_sha256":"67ac2bcfa988b791456fdfebace5fc41d80be2e11d3e3051d24e3e7a9dc3330a"},"schema_version":"1.0"},"canonical_sha256":"5dc78d9d8f82048cd6ec3981e9668f790dd457979bb1c6a204ff905117f42be8","source":{"kind":"arxiv","id":"1701.02834","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02834","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02834v2","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02834","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"LXDY3HMPQICI","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LXDY3HMPQICIZVXM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LXDY3HMP","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LXDY3HMPQICIZVXMHGA6SZUPPE","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-11T03:13:50Z","cross_cats_sorted":[],"title_canon_sha256":"0b12efd109c1403d62b5bc3cde395e0f1404bc5106b4cd46d5794fc9f25eb602","abstract_canon_sha256":"67ac2bcfa988b791456fdfebace5fc41d80be2e11d3e3051d24e3e7a9dc3330a"},"schema_version":"1.0"},"canonical_sha256":"5dc78d9d8f82048cd6ec3981e9668f790dd457979bb1c6a204ff905117f42be8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:37.596841Z","signature_b64":"cZx/K4IcLVjAVPnvmPvezG2nE/MZ3QrENsVbBMWI2CZHt8evO+8ZPIA6k05qw2PTljvRawpmAH4AP+WQo55wCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dc78d9d8f82048cd6ec3981e9668f790dd457979bb1c6a204ff905117f42be8","last_reissued_at":"2026-05-18T00:41:37.596025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:37.596025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02834","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+c9tlsR/WJNWqRS8aTE6TdujoYFqgVSZRoHoAJKVu1DEJMQ4F8lZSC/NRsEkKP9hPcB9BEmZcDZvEvGlld6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:17:16.784875Z"},"content_sha256":"3111e4dfc99dd5ddf80e771e6ee23c088efd219c990ca739978795297c68ad92","schema_version":"1.0","event_id":"sha256:3111e4dfc99dd5ddf80e771e6ee23c088efd219c990ca739978795297c68ad92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LXDY3HMPQICIZVXMHGA6SZUPPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Davenport-Heilbronn Theorems for Quotients of Class Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zev Klagsbrun","submitted_at":"2017-01-11T03:13:50Z","abstract_excerpt":"We prove a generalization of the Davenport-Heilbronn theorem to quotients of ideal class groups of quadratic fields by the primes lying above a fixed set of rational primes $S$. Additionally, we obtain average sizes for the relaxed Selmer group $\\mathrm{Sel}_3^S(K)$ and for $\\mathcal{O}_{K,S}^\\times/(\\mathcal{O}_{K,S}^\\times)^3$ as $K$ varies among quadratic fields with a fixed signature ordered by discriminant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02834","kind":"arxiv","version":2},"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":"2026-05-18T00:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ynNkCv/pdXS5DKtOROZ+1y7EItTUJIt1r1p0ioEtKQZSlurRdpXkl/7XDRzxu5yJoEshSy7OODRt9vnOFxtYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:17:16.785556Z"},"content_sha256":"0059cf4f18c9a26dab697ab134eac93f57c1a9babd6d1dd8825b2a8c9659b15f","schema_version":"1.0","event_id":"sha256:0059cf4f18c9a26dab697ab134eac93f57c1a9babd6d1dd8825b2a8c9659b15f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXDY3HMPQICIZVXMHGA6SZUPPE/bundle.json","state_url":"https://pith.science/pith/LXDY3HMPQICIZVXMHGA6SZUPPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXDY3HMPQICIZVXMHGA6SZUPPE/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":"2026-06-08T17:17:16Z","links":{"resolver":"https://pith.science/pith/LXDY3HMPQICIZVXMHGA6SZUPPE","bundle":"https://pith.science/pith/LXDY3HMPQICIZVXMHGA6SZUPPE/bundle.json","state":"https://pith.science/pith/LXDY3HMPQICIZVXMHGA6SZUPPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXDY3HMPQICIZVXMHGA6SZUPPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LXDY3HMPQICIZVXMHGA6SZUPPE","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":"67ac2bcfa988b791456fdfebace5fc41d80be2e11d3e3051d24e3e7a9dc3330a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-11T03:13:50Z","title_canon_sha256":"0b12efd109c1403d62b5bc3cde395e0f1404bc5106b4cd46d5794fc9f25eb602"},"schema_version":"1.0","source":{"id":"1701.02834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02834","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02834v2","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02834","created_at":"2026-05-18T00:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"LXDY3HMPQICI","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LXDY3HMPQICIZVXM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LXDY3HMP","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:0059cf4f18c9a26dab697ab134eac93f57c1a9babd6d1dd8825b2a8c9659b15f","target":"graph","created_at":"2026-05-18T00:41:37Z","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 prove a generalization of the Davenport-Heilbronn theorem to quotients of ideal class groups of quadratic fields by the primes lying above a fixed set of rational primes $S$. Additionally, we obtain average sizes for the relaxed Selmer group $\\mathrm{Sel}_3^S(K)$ and for $\\mathcal{O}_{K,S}^\\times/(\\mathcal{O}_{K,S}^\\times)^3$ as $K$ varies among quadratic fields with a fixed signature ordered by discriminant.","authors_text":"Zev Klagsbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-11T03:13:50Z","title":"Davenport-Heilbronn Theorems for Quotients of Class Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02834","kind":"arxiv","version":2},"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":"sha256:3111e4dfc99dd5ddf80e771e6ee23c088efd219c990ca739978795297c68ad92","target":"record","created_at":"2026-05-18T00:41:37Z","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":"67ac2bcfa988b791456fdfebace5fc41d80be2e11d3e3051d24e3e7a9dc3330a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-11T03:13:50Z","title_canon_sha256":"0b12efd109c1403d62b5bc3cde395e0f1404bc5106b4cd46d5794fc9f25eb602"},"schema_version":"1.0","source":{"id":"1701.02834","kind":"arxiv","version":2}},"canonical_sha256":"5dc78d9d8f82048cd6ec3981e9668f790dd457979bb1c6a204ff905117f42be8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dc78d9d8f82048cd6ec3981e9668f790dd457979bb1c6a204ff905117f42be8","first_computed_at":"2026-05-18T00:41:37.596025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:37.596025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cZx/K4IcLVjAVPnvmPvezG2nE/MZ3QrENsVbBMWI2CZHt8evO+8ZPIA6k05qw2PTljvRawpmAH4AP+WQo55wCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:37.596841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3111e4dfc99dd5ddf80e771e6ee23c088efd219c990ca739978795297c68ad92","sha256:0059cf4f18c9a26dab697ab134eac93f57c1a9babd6d1dd8825b2a8c9659b15f"],"state_sha256":"5a195c7888e50cf5311aa5d41469d6982c604766cb3c95fc8fabc3c7d7d48a81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gei4uwNSKLSD9yfhgQ+twnrK1K98p0FiZ0zorr5TEi209vSkCyNa+BXEUGQ7K2WDRMNlwT59379oCeuEE655CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:17:16.789580Z","bundle_sha256":"7975c4541a47cefba2b53b3e41e7d1c0cfa41a3ce8f1258783aed4699ac5969e"}}