{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NZ2HHVHTBIXFQQLLMSAUAVKUZR","short_pith_number":"pith:NZ2HHVHT","canonical_record":{"source":{"id":"1704.03124","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-11T03:11:59Z","cross_cats_sorted":[],"title_canon_sha256":"796c2897f1dd86cbc917754af558c4df4d926a58a75a97ddd315e0287f7d47f7","abstract_canon_sha256":"e9baf68916ebb5dcb38770622caa1699fd0d132152e7d985ce509ae08025f2b4"},"schema_version":"1.0"},"canonical_sha256":"6e7473d4f30a2e58416b6481405554cc53277c840b7c28cb1bfe6da329c146ca","source":{"kind":"arxiv","id":"1704.03124","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03124","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03124v2","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03124","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"NZ2HHVHTBIXF","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NZ2HHVHTBIXFQQLL","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NZ2HHVHT","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NZ2HHVHTBIXFQQLLMSAUAVKUZR","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03124","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-11T03:11:59Z","cross_cats_sorted":[],"title_canon_sha256":"796c2897f1dd86cbc917754af558c4df4d926a58a75a97ddd315e0287f7d47f7","abstract_canon_sha256":"e9baf68916ebb5dcb38770622caa1699fd0d132152e7d985ce509ae08025f2b4"},"schema_version":"1.0"},"canonical_sha256":"6e7473d4f30a2e58416b6481405554cc53277c840b7c28cb1bfe6da329c146ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:18.317350Z","signature_b64":"3Dp85rPSoMhZjxTTAXj4z94XF09IR7f3LuAAJUwv9VfTNYaSGUt0FNDn+bjiYaLUpdNwTNjqyqzv1UMMRaTiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e7473d4f30a2e58416b6481405554cc53277c840b7c28cb1bfe6da329c146ca","last_reissued_at":"2026-05-18T00:46:18.316968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:18.316968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03124","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":"2026-05-18T00:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"71sbqWu9ZPT8UNw6lGz+EO3KLCPXaH9pv8E4WsipPGp6U913XjBopchkUEQRnj2iSuh5YsNH8kSuHqMt5BijBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:39:03.793302Z"},"content_sha256":"432b02174734edbd246b3cf0593010ff911b4fb5ae8f18a2194cb9bc453dc5b4","schema_version":"1.0","event_id":"sha256:432b02174734edbd246b3cf0593010ff911b4fb5ae8f18a2194cb9bc453dc5b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NZ2HHVHTBIXFQQLLMSAUAVKUZR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting $G$-Extensions by Discriminant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Evan P. Dummit","submitted_at":"2017-04-11T03:11:59Z","abstract_excerpt":"The problem of analyzing the number of number field extensions $L/K$ with bounded (relative) discriminant has been the subject of renewed interest in recent years, with significant advances made by Schmidt, Ellenberg-Venkatesh, Bhargava, Bhargava-Shankar-Wang, and others. In this paper, we use the geometry of numbers and invariant theory of finite groups, in a manner similar to Ellenberg and Venkatesh, to give an upper bound on the number of extensions $L/K$ with fixed degree, bounded relative discriminant, and specified Galois closure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03124","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":"2026-05-18T00:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XGH5zx3aBfqfbiMjinaxDkzu5a4kx4BHuh9Ivv8uZ83tAAlC62WyRz5sMGR9/2PMdRnn4pZk0qyXUoeCI5qTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:39:03.793967Z"},"content_sha256":"5e352b86539883d8165cde7f588ce0c12e5588519372b6805835f3702bb67d44","schema_version":"1.0","event_id":"sha256:5e352b86539883d8165cde7f588ce0c12e5588519372b6805835f3702bb67d44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZ2HHVHTBIXFQQLLMSAUAVKUZR/bundle.json","state_url":"https://pith.science/pith/NZ2HHVHTBIXFQQLLMSAUAVKUZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZ2HHVHTBIXFQQLLMSAUAVKUZR/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":"2026-06-09T03:39:03Z","links":{"resolver":"https://pith.science/pith/NZ2HHVHTBIXFQQLLMSAUAVKUZR","bundle":"https://pith.science/pith/NZ2HHVHTBIXFQQLLMSAUAVKUZR/bundle.json","state":"https://pith.science/pith/NZ2HHVHTBIXFQQLLMSAUAVKUZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZ2HHVHTBIXFQQLLMSAUAVKUZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NZ2HHVHTBIXFQQLLMSAUAVKUZR","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":"e9baf68916ebb5dcb38770622caa1699fd0d132152e7d985ce509ae08025f2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-11T03:11:59Z","title_canon_sha256":"796c2897f1dd86cbc917754af558c4df4d926a58a75a97ddd315e0287f7d47f7"},"schema_version":"1.0","source":{"id":"1704.03124","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03124","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03124v2","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03124","created_at":"2026-05-18T00:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"NZ2HHVHTBIXF","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NZ2HHVHTBIXFQQLL","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NZ2HHVHT","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:5e352b86539883d8165cde7f588ce0c12e5588519372b6805835f3702bb67d44","target":"graph","created_at":"2026-05-18T00:46:18Z","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 problem of analyzing the number of number field extensions $L/K$ with bounded (relative) discriminant has been the subject of renewed interest in recent years, with significant advances made by Schmidt, Ellenberg-Venkatesh, Bhargava, Bhargava-Shankar-Wang, and others. In this paper, we use the geometry of numbers and invariant theory of finite groups, in a manner similar to Ellenberg and Venkatesh, to give an upper bound on the number of extensions $L/K$ with fixed degree, bounded relative discriminant, and specified Galois closure.","authors_text":"Evan P. Dummit","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-11T03:11:59Z","title":"Counting $G$-Extensions by Discriminant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03124","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":"sha256:432b02174734edbd246b3cf0593010ff911b4fb5ae8f18a2194cb9bc453dc5b4","target":"record","created_at":"2026-05-18T00:46:18Z","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":"e9baf68916ebb5dcb38770622caa1699fd0d132152e7d985ce509ae08025f2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-11T03:11:59Z","title_canon_sha256":"796c2897f1dd86cbc917754af558c4df4d926a58a75a97ddd315e0287f7d47f7"},"schema_version":"1.0","source":{"id":"1704.03124","kind":"arxiv","version":2}},"canonical_sha256":"6e7473d4f30a2e58416b6481405554cc53277c840b7c28cb1bfe6da329c146ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e7473d4f30a2e58416b6481405554cc53277c840b7c28cb1bfe6da329c146ca","first_computed_at":"2026-05-18T00:46:18.316968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:18.316968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Dp85rPSoMhZjxTTAXj4z94XF09IR7f3LuAAJUwv9VfTNYaSGUt0FNDn+bjiYaLUpdNwTNjqyqzv1UMMRaTiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:18.317350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03124","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:432b02174734edbd246b3cf0593010ff911b4fb5ae8f18a2194cb9bc453dc5b4","sha256:5e352b86539883d8165cde7f588ce0c12e5588519372b6805835f3702bb67d44"],"state_sha256":"a6f1481c2fa802d34043cbc6691d32ebab0d6038b243bf21d64dde3a579acc66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZlP6/dH3X0P1ogCVQDk5rrlTw2DiLglCRxc6IbIcrZ04CDihoKcutaem+KImoOILDi1UqNmpNPE7bNOfa9FAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:39:03.797472Z","bundle_sha256":"b1b8087a938c44771618b24f8cd13f400575aa96514a2d36e88565f42146cbd8"}}