{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:24SHM7SVPJGJJCZNVDNKI6CO53","short_pith_number":"pith:24SHM7SV","canonical_record":{"source":{"id":"0801.1451","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2008-01-09T15:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"be4bcaaaa31fe77010e9d57ce5397950eec9756f1734ded241684e896b99cbad","abstract_canon_sha256":"e2fc29684cc97d8a6370988c57c3fce2b58a3f0d68311647d88faae2ff580706"},"schema_version":"1.0"},"canonical_sha256":"d724767e557a4c948b2da8daa4784eeef72d08c1b4b88f2dc111ad5973238bdd","source":{"kind":"arxiv","id":"0801.1451","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1451","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1451v1","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1451","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"24SHM7SVPJGJ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"24SHM7SVPJGJJCZN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"24SHM7SV","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:24SHM7SVPJGJJCZNVDNKI6CO53","target":"record","payload":{"canonical_record":{"source":{"id":"0801.1451","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2008-01-09T15:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"be4bcaaaa31fe77010e9d57ce5397950eec9756f1734ded241684e896b99cbad","abstract_canon_sha256":"e2fc29684cc97d8a6370988c57c3fce2b58a3f0d68311647d88faae2ff580706"},"schema_version":"1.0"},"canonical_sha256":"d724767e557a4c948b2da8daa4784eeef72d08c1b4b88f2dc111ad5973238bdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:00.203799Z","signature_b64":"nUEZHOOeum31RKXGP0bLRJeaQbras5+t3NfKAnaC4CWi9UUbIQ2M9Wsi2nsx8+roahGgtaZwncMj7yDqy/E5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d724767e557a4c948b2da8daa4784eeef72d08c1b4b88f2dc111ad5973238bdd","last_reissued_at":"2026-05-18T03:50:00.203263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:00.203263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.1451","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":"2026-05-18T03:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7qM73/LuJF32rLIo1brVpT3A1nDQRKl91K7ttXFB4WwDN+ZM8lHbAGgbqoBMoMCBJpuwfEuzVYtUH+/3ZdxUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:20:49.007043Z"},"content_sha256":"3c018fafabd8a00218bb80ac46ba9e55493da88b356d614d6605808b48bfd644","schema_version":"1.0","event_id":"sha256:3c018fafabd8a00218bb80ac46ba9e55493da88b356d614d6605808b48bfd644"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:24SHM7SVPJGJJCZNVDNKI6CO53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting RSA-integers","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas Decker, Pieter Moree","submitted_at":"2008-01-09T15:36:28Z","abstract_excerpt":"In the RSA cryptosystem integers of the form n=p.q with p and q primes of comparable size (`RSA-integers') play an important role. It is a folklore result of cryptographers that C_r(x), the number of integers n<=x that are of the form n=pq with p and q primes such that p<q<rp, is for fixed r>1 asymptotically equal to c_r*x*log^{-2}x for some constant c_r>0. Here we prove this and show that c_r=2log r."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1451","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":"2026-05-18T03:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g00ks+XWlbL5MEKB4BgMblWDMxcW/oh3oiDWOPCdaf5XqPVncC75Dll5YOmja4fZitdulI7e4xFNYoHe9ELLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:20:49.007850Z"},"content_sha256":"919782fbbbca7b4afcee71710c1410ce1c8eafc94beda5f28262d3b86b069909","schema_version":"1.0","event_id":"sha256:919782fbbbca7b4afcee71710c1410ce1c8eafc94beda5f28262d3b86b069909"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24SHM7SVPJGJJCZNVDNKI6CO53/bundle.json","state_url":"https://pith.science/pith/24SHM7SVPJGJJCZNVDNKI6CO53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24SHM7SVPJGJJCZNVDNKI6CO53/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":"2026-05-31T13:20:49Z","links":{"resolver":"https://pith.science/pith/24SHM7SVPJGJJCZNVDNKI6CO53","bundle":"https://pith.science/pith/24SHM7SVPJGJJCZNVDNKI6CO53/bundle.json","state":"https://pith.science/pith/24SHM7SVPJGJJCZNVDNKI6CO53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24SHM7SVPJGJJCZNVDNKI6CO53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:24SHM7SVPJGJJCZNVDNKI6CO53","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":"e2fc29684cc97d8a6370988c57c3fce2b58a3f0d68311647d88faae2ff580706","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2008-01-09T15:36:28Z","title_canon_sha256":"be4bcaaaa31fe77010e9d57ce5397950eec9756f1734ded241684e896b99cbad"},"schema_version":"1.0","source":{"id":"0801.1451","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1451","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1451v1","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1451","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"24SHM7SVPJGJ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"24SHM7SVPJGJJCZN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"24SHM7SV","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:919782fbbbca7b4afcee71710c1410ce1c8eafc94beda5f28262d3b86b069909","target":"graph","created_at":"2026-05-18T03:50:00Z","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":"In the RSA cryptosystem integers of the form n=p.q with p and q primes of comparable size (`RSA-integers') play an important role. It is a folklore result of cryptographers that C_r(x), the number of integers n<=x that are of the form n=pq with p and q primes such that p<q<rp, is for fixed r>1 asymptotically equal to c_r*x*log^{-2}x for some constant c_r>0. Here we prove this and show that c_r=2log r.","authors_text":"Andreas Decker, Pieter Moree","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2008-01-09T15:36:28Z","title":"Counting RSA-integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1451","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":"sha256:3c018fafabd8a00218bb80ac46ba9e55493da88b356d614d6605808b48bfd644","target":"record","created_at":"2026-05-18T03:50:00Z","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":"e2fc29684cc97d8a6370988c57c3fce2b58a3f0d68311647d88faae2ff580706","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2008-01-09T15:36:28Z","title_canon_sha256":"be4bcaaaa31fe77010e9d57ce5397950eec9756f1734ded241684e896b99cbad"},"schema_version":"1.0","source":{"id":"0801.1451","kind":"arxiv","version":1}},"canonical_sha256":"d724767e557a4c948b2da8daa4784eeef72d08c1b4b88f2dc111ad5973238bdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d724767e557a4c948b2da8daa4784eeef72d08c1b4b88f2dc111ad5973238bdd","first_computed_at":"2026-05-18T03:50:00.203263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:00.203263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nUEZHOOeum31RKXGP0bLRJeaQbras5+t3NfKAnaC4CWi9UUbIQ2M9Wsi2nsx8+roahGgtaZwncMj7yDqy/E5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:00.203799Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.1451","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c018fafabd8a00218bb80ac46ba9e55493da88b356d614d6605808b48bfd644","sha256:919782fbbbca7b4afcee71710c1410ce1c8eafc94beda5f28262d3b86b069909"],"state_sha256":"8ce69abe5e3748a0d9eb75c3593f92bf48d8204cddbda5d92dba1f5d1e49b107"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyZXrwOPIsMBKlwWJaOXxVBXpPcx/ZmIS4yFISx1n55SC/BgdYHwoJuoG88Xq3E3UGgMdgXlUhQz48N6kGNrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:20:49.013025Z","bundle_sha256":"9d82e9139c4af13979ec801f6a56fbd9ab59d032c53661339b042614b465af77"}}