{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5XLY3UCY3LXS5ASSKKFUMKAMSP","short_pith_number":"pith:5XLY3UCY","canonical_record":{"source":{"id":"1402.0031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-31T23:37:48Z","cross_cats_sorted":[],"title_canon_sha256":"05892ad1983c0ee4eee7a22b86a7e30ab6a6c9a7ca19d0980f37f048e7700bc8","abstract_canon_sha256":"9fd579dc2bd72698db3cb116979a8ea8d3fd81589d45a76088a0bc688baeb2a1"},"schema_version":"1.0"},"canonical_sha256":"edd78dd058daef2e8252528b46280c93eeabb96928cf1e0e3fd4051b7544c4eb","source":{"kind":"arxiv","id":"1402.0031","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0031","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0031v1","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0031","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"5XLY3UCY3LXS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5XLY3UCY3LXS5ASS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5XLY3UCY","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5XLY3UCY3LXS5ASSKKFUMKAMSP","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-31T23:37:48Z","cross_cats_sorted":[],"title_canon_sha256":"05892ad1983c0ee4eee7a22b86a7e30ab6a6c9a7ca19d0980f37f048e7700bc8","abstract_canon_sha256":"9fd579dc2bd72698db3cb116979a8ea8d3fd81589d45a76088a0bc688baeb2a1"},"schema_version":"1.0"},"canonical_sha256":"edd78dd058daef2e8252528b46280c93eeabb96928cf1e0e3fd4051b7544c4eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:25.059100Z","signature_b64":"wWNpeRkcpRxxaTEZaaJ3OJq1eYEfp2INzP1pMJ/bMD9jO/hWpb/b94KuKeM46TzR6CpGk9Cci3qCpbXdxet/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edd78dd058daef2e8252528b46280c93eeabb96928cf1e0e3fd4051b7544c4eb","last_reissued_at":"2026-05-18T03:00:25.058283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:25.058283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0031","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":"2026-05-18T03:00:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9dxlOTbAUiLFg/fsLoE7M7zh8UV2yGloOjuWzTdQGi7FVmaG/gOEIV+1CI8uHRQ7rxOysLKczXvgA21o8TBJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:14:18.259448Z"},"content_sha256":"82f272179760102b9db80d862e5a9a693fb545d79d17e9a86596b313572cec53","schema_version":"1.0","event_id":"sha256:82f272179760102b9db80d862e5a9a693fb545d79d17e9a86596b313572cec53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5XLY3UCY3LXS5ASSKKFUMKAMSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometric sieve and the density of squarefree values of invariant polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Manjul Bhargava","submitted_at":"2014-01-31T23:37:48Z","abstract_excerpt":"We develop a method for determining the density of squarefree values taken by certain multivariate integer polynomials that are invariants for the action of an algebraic group on a vector space. The method is shown to apply to the discriminant polynomials of various prehomogeneous and coregular representations where generic stabilizers are finite. This has applications to a number of arithmetic distribution questions, e.g., to the density of small degree number fields having squarefree discriminant, and the density of certain unramified nonabelian extensions of quadratic fields. In separate wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0031","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":"2026-05-18T03:00:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c3y8Drwb1rqQ2zo/AtjSyFazo490p9ICrcjLXtIeH48KbPw0iOwHbS2PCiKd6ogrFFysCPo4m5XA/iBb4Oy0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:14:18.260130Z"},"content_sha256":"6375c6632ca507a68c23f4d6d053feab5ad5a028838322877116928b1e9185af","schema_version":"1.0","event_id":"sha256:6375c6632ca507a68c23f4d6d053feab5ad5a028838322877116928b1e9185af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XLY3UCY3LXS5ASSKKFUMKAMSP/bundle.json","state_url":"https://pith.science/pith/5XLY3UCY3LXS5ASSKKFUMKAMSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XLY3UCY3LXS5ASSKKFUMKAMSP/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":"2026-05-28T22:14:18Z","links":{"resolver":"https://pith.science/pith/5XLY3UCY3LXS5ASSKKFUMKAMSP","bundle":"https://pith.science/pith/5XLY3UCY3LXS5ASSKKFUMKAMSP/bundle.json","state":"https://pith.science/pith/5XLY3UCY3LXS5ASSKKFUMKAMSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XLY3UCY3LXS5ASSKKFUMKAMSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5XLY3UCY3LXS5ASSKKFUMKAMSP","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":"9fd579dc2bd72698db3cb116979a8ea8d3fd81589d45a76088a0bc688baeb2a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-31T23:37:48Z","title_canon_sha256":"05892ad1983c0ee4eee7a22b86a7e30ab6a6c9a7ca19d0980f37f048e7700bc8"},"schema_version":"1.0","source":{"id":"1402.0031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0031","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0031v1","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0031","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"5XLY3UCY3LXS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5XLY3UCY3LXS5ASS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5XLY3UCY","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:6375c6632ca507a68c23f4d6d053feab5ad5a028838322877116928b1e9185af","target":"graph","created_at":"2026-05-18T03:00:25Z","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 develop a method for determining the density of squarefree values taken by certain multivariate integer polynomials that are invariants for the action of an algebraic group on a vector space. The method is shown to apply to the discriminant polynomials of various prehomogeneous and coregular representations where generic stabilizers are finite. This has applications to a number of arithmetic distribution questions, e.g., to the density of small degree number fields having squarefree discriminant, and the density of certain unramified nonabelian extensions of quadratic fields. In separate wo","authors_text":"Manjul Bhargava","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-31T23:37:48Z","title":"The geometric sieve and the density of squarefree values of invariant polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0031","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":"sha256:82f272179760102b9db80d862e5a9a693fb545d79d17e9a86596b313572cec53","target":"record","created_at":"2026-05-18T03:00:25Z","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":"9fd579dc2bd72698db3cb116979a8ea8d3fd81589d45a76088a0bc688baeb2a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-31T23:37:48Z","title_canon_sha256":"05892ad1983c0ee4eee7a22b86a7e30ab6a6c9a7ca19d0980f37f048e7700bc8"},"schema_version":"1.0","source":{"id":"1402.0031","kind":"arxiv","version":1}},"canonical_sha256":"edd78dd058daef2e8252528b46280c93eeabb96928cf1e0e3fd4051b7544c4eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edd78dd058daef2e8252528b46280c93eeabb96928cf1e0e3fd4051b7544c4eb","first_computed_at":"2026-05-18T03:00:25.058283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:25.058283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wWNpeRkcpRxxaTEZaaJ3OJq1eYEfp2INzP1pMJ/bMD9jO/hWpb/b94KuKeM46TzR6CpGk9Cci3qCpbXdxet/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:25.059100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82f272179760102b9db80d862e5a9a693fb545d79d17e9a86596b313572cec53","sha256:6375c6632ca507a68c23f4d6d053feab5ad5a028838322877116928b1e9185af"],"state_sha256":"e64b89ccb2d2c044f4e019900a7f0967ae71b977c581ad3b00990779265f5ac6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1KsdFotlUE7XBqXdR+O9fuUDScU4D1kZ8Xgy35d99X1JcSqkOBvpsXgqpo236PcAX0F/f3HUBwHcd/cJL/xCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:14:18.263791Z","bundle_sha256":"3a9d903ac76cfc82b84bfc77ced6e3cfed11fe4db21b2ee9c1772591b6a4adda"}}