{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P3GJWG6JY5L6A6LC7RC5J2HCFE","short_pith_number":"pith:P3GJWG6J","canonical_record":{"source":{"id":"1305.0482","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-02T15:37:19Z","cross_cats_sorted":[],"title_canon_sha256":"b9e534b23cd16813ca113e119d4213150a0b9d9d66a892ef29b8601755c63b03","abstract_canon_sha256":"8be8384038496590cacac307189b8c350a6b521bf4f07b68827438ced838a613"},"schema_version":"1.0"},"canonical_sha256":"7ecc9b1bc9c757e07962fc45d4e8e22900b4c5099ccc05be1abda59bfa96175e","source":{"kind":"arxiv","id":"1305.0482","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0482","created_at":"2026-05-18T02:43:02Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0482v3","created_at":"2026-05-18T02:43:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0482","created_at":"2026-05-18T02:43:02Z"},{"alias_kind":"pith_short_12","alias_value":"P3GJWG6JY5L6","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P3GJWG6JY5L6A6LC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P3GJWG6J","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P3GJWG6JY5L6A6LC7RC5J2HCFE","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0482","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-02T15:37:19Z","cross_cats_sorted":[],"title_canon_sha256":"b9e534b23cd16813ca113e119d4213150a0b9d9d66a892ef29b8601755c63b03","abstract_canon_sha256":"8be8384038496590cacac307189b8c350a6b521bf4f07b68827438ced838a613"},"schema_version":"1.0"},"canonical_sha256":"7ecc9b1bc9c757e07962fc45d4e8e22900b4c5099ccc05be1abda59bfa96175e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:02.631718Z","signature_b64":"2H3YxK8jlWRLzCfkKa1edfDMPatyBBdWQrp7sCwr5SA6L7N1g9/1ROdYoclVm6ifwl/98lIPV7t/CYaIAtnzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ecc9b1bc9c757e07962fc45d4e8e22900b4c5099ccc05be1abda59bfa96175e","last_reissued_at":"2026-05-18T02:43:02.631053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:02.631053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0482","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o81fbIUvfe6ZW4kKMK77t/pLUN89hbT0e3wasrrwm9836MEFzvOt2nY33Ku72hWcADSNEzMfuKUeOh4RpD1sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:47:46.731969Z"},"content_sha256":"22ef79f9b361f6cdf7b7a184eae38dd8805c340c915a3e4cca98f7e7d5cdda7c","schema_version":"1.0","event_id":"sha256:22ef79f9b361f6cdf7b7a184eae38dd8805c340c915a3e4cca98f7e7d5cdda7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P3GJWG6JY5L6A6LC7RC5J2HCFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting algebraic integers of fixed degree and bounded height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabrizio Barroero","submitted_at":"2013-05-02T15:37:19Z","abstract_excerpt":"Let $k$ be a number field. For $\\mathcal{H}\\rightarrow \\infty$, we give an asymptotic formula for the number of algebraic integers of absolute Weil height bounded by $\\mathcal{H}$ and fixed degree over $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0482","kind":"arxiv","version":3},"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":"2026-05-18T02:43:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkvekh+ZJmURGLe45wPQnLrBPF8fpXC2zqmqsxUxrMR87SqfuDKYrPDSCmHOOULywnlXcLNwENDBUpvURibvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:47:46.732305Z"},"content_sha256":"7718b5abb79004e4e3b1d1ee1d4f83232926b737dcd00a2d4333139560f0b9d7","schema_version":"1.0","event_id":"sha256:7718b5abb79004e4e3b1d1ee1d4f83232926b737dcd00a2d4333139560f0b9d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3GJWG6JY5L6A6LC7RC5J2HCFE/bundle.json","state_url":"https://pith.science/pith/P3GJWG6JY5L6A6LC7RC5J2HCFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3GJWG6JY5L6A6LC7RC5J2HCFE/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":"2026-06-03T19:47:46Z","links":{"resolver":"https://pith.science/pith/P3GJWG6JY5L6A6LC7RC5J2HCFE","bundle":"https://pith.science/pith/P3GJWG6JY5L6A6LC7RC5J2HCFE/bundle.json","state":"https://pith.science/pith/P3GJWG6JY5L6A6LC7RC5J2HCFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3GJWG6JY5L6A6LC7RC5J2HCFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P3GJWG6JY5L6A6LC7RC5J2HCFE","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":"8be8384038496590cacac307189b8c350a6b521bf4f07b68827438ced838a613","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-02T15:37:19Z","title_canon_sha256":"b9e534b23cd16813ca113e119d4213150a0b9d9d66a892ef29b8601755c63b03"},"schema_version":"1.0","source":{"id":"1305.0482","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0482","created_at":"2026-05-18T02:43:02Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0482v3","created_at":"2026-05-18T02:43:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0482","created_at":"2026-05-18T02:43:02Z"},{"alias_kind":"pith_short_12","alias_value":"P3GJWG6JY5L6","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P3GJWG6JY5L6A6LC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P3GJWG6J","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:7718b5abb79004e4e3b1d1ee1d4f83232926b737dcd00a2d4333139560f0b9d7","target":"graph","created_at":"2026-05-18T02:43:02Z","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":"Let $k$ be a number field. For $\\mathcal{H}\\rightarrow \\infty$, we give an asymptotic formula for the number of algebraic integers of absolute Weil height bounded by $\\mathcal{H}$ and fixed degree over $k$.","authors_text":"Fabrizio Barroero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-02T15:37:19Z","title":"Counting algebraic integers of fixed degree and bounded height"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0482","kind":"arxiv","version":3},"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":"sha256:22ef79f9b361f6cdf7b7a184eae38dd8805c340c915a3e4cca98f7e7d5cdda7c","target":"record","created_at":"2026-05-18T02:43:02Z","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":"8be8384038496590cacac307189b8c350a6b521bf4f07b68827438ced838a613","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-02T15:37:19Z","title_canon_sha256":"b9e534b23cd16813ca113e119d4213150a0b9d9d66a892ef29b8601755c63b03"},"schema_version":"1.0","source":{"id":"1305.0482","kind":"arxiv","version":3}},"canonical_sha256":"7ecc9b1bc9c757e07962fc45d4e8e22900b4c5099ccc05be1abda59bfa96175e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ecc9b1bc9c757e07962fc45d4e8e22900b4c5099ccc05be1abda59bfa96175e","first_computed_at":"2026-05-18T02:43:02.631053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:02.631053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2H3YxK8jlWRLzCfkKa1edfDMPatyBBdWQrp7sCwr5SA6L7N1g9/1ROdYoclVm6ifwl/98lIPV7t/CYaIAtnzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:02.631718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0482","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22ef79f9b361f6cdf7b7a184eae38dd8805c340c915a3e4cca98f7e7d5cdda7c","sha256:7718b5abb79004e4e3b1d1ee1d4f83232926b737dcd00a2d4333139560f0b9d7"],"state_sha256":"bd509ea8897d01d9c77203db4af00574abccf662e56e81e25522d22d9496e408"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cceWhG+wGh+ozyRIzdJIEMpZk/86NB5SCSLXMxe+5SJKYFGwx+IxrVO8biG1hZC31EvBwmMgNF+TLQ/xLzxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:47:46.734385Z","bundle_sha256":"9b986308fc8058fbf84f968442088beacb73bfdbb2e9ea479d19d93f6a8bb56f"}}