{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TI7TKBK7RJ7XX5GNOM3CHQRACV","short_pith_number":"pith:TI7TKBK7","canonical_record":{"source":{"id":"1607.01557","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-06T11:00:56Z","cross_cats_sorted":[],"title_canon_sha256":"f408c99ef15285848efb1a4200e2e4e1c465c8beba714598d4dc17a7c5e72b94","abstract_canon_sha256":"5363d96d491c8d8d2d2200672228134476cf30ecff380a0f9306a76ad62b9880"},"schema_version":"1.0"},"canonical_sha256":"9a3f35055f8a7f7bf4cd733623c2201558a8c618f86d934653f302d5f549e760","source":{"kind":"arxiv","id":"1607.01557","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01557","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01557v4","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01557","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"TI7TKBK7RJ7X","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TI7TKBK7RJ7XX5GN","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TI7TKBK7","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TI7TKBK7RJ7XX5GNOM3CHQRACV","target":"record","payload":{"canonical_record":{"source":{"id":"1607.01557","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-06T11:00:56Z","cross_cats_sorted":[],"title_canon_sha256":"f408c99ef15285848efb1a4200e2e4e1c465c8beba714598d4dc17a7c5e72b94","abstract_canon_sha256":"5363d96d491c8d8d2d2200672228134476cf30ecff380a0f9306a76ad62b9880"},"schema_version":"1.0"},"canonical_sha256":"9a3f35055f8a7f7bf4cd733623c2201558a8c618f86d934653f302d5f549e760","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:49.300580Z","signature_b64":"mX4PGAW+ewssXEIb7r38CRgCKZiwDPNm5fbCkxl6MWqbu1i/Zt3MRsBuh+4OpYPFJqMeogT3KP040eGL7jmmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a3f35055f8a7f7bf4cd733623c2201558a8c618f86d934653f302d5f549e760","last_reissued_at":"2026-05-18T00:46:49.299905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:49.299905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.01557","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3G+oA65Vucn/jX18R4Yy57HFJrYn2hgK4rFTBQTnxlYm0nxaYjgnoT3B2Qsr1vd8d3NnWB6gGFW+t2qe1TYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:05:45.785435Z"},"content_sha256":"598d30da402931e235be16b402bc65258e17d81668727b9b995d9e7c0e8ef5ec","schema_version":"1.0","event_id":"sha256:598d30da402931e235be16b402bc65258e17d81668727b9b995d9e7c0e8ef5ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TI7TKBK7RJ7XX5GNOM3CHQRACV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Squarefree smooth numbers and Euclidean prime generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew R. Booker, Carl Pomerance","submitted_at":"2016-07-06T11:00:56Z","abstract_excerpt":"We show that for each prime p > 7, every residue mod p can be represented by a squarefree number with largest prime factor at most p. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01557","kind":"arxiv","version":4},"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":"2026-05-18T00:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gRtX5cktq81WjfxdVGx8xwDQhuYgD/eq/o8id78Du21AYLEshX3wbPpfdjhoxdoGv44a99Ubs5rG2CBoTXtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:05:45.785782Z"},"content_sha256":"46bb220eea43e2afb75f50453c7e7720392b5fa6e4bf9bdf2de78d32801cda6f","schema_version":"1.0","event_id":"sha256:46bb220eea43e2afb75f50453c7e7720392b5fa6e4bf9bdf2de78d32801cda6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TI7TKBK7RJ7XX5GNOM3CHQRACV/bundle.json","state_url":"https://pith.science/pith/TI7TKBK7RJ7XX5GNOM3CHQRACV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TI7TKBK7RJ7XX5GNOM3CHQRACV/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":"2026-06-03T19:05:45Z","links":{"resolver":"https://pith.science/pith/TI7TKBK7RJ7XX5GNOM3CHQRACV","bundle":"https://pith.science/pith/TI7TKBK7RJ7XX5GNOM3CHQRACV/bundle.json","state":"https://pith.science/pith/TI7TKBK7RJ7XX5GNOM3CHQRACV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TI7TKBK7RJ7XX5GNOM3CHQRACV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TI7TKBK7RJ7XX5GNOM3CHQRACV","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":"5363d96d491c8d8d2d2200672228134476cf30ecff380a0f9306a76ad62b9880","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-06T11:00:56Z","title_canon_sha256":"f408c99ef15285848efb1a4200e2e4e1c465c8beba714598d4dc17a7c5e72b94"},"schema_version":"1.0","source":{"id":"1607.01557","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01557","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01557v4","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01557","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"TI7TKBK7RJ7X","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TI7TKBK7RJ7XX5GN","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TI7TKBK7","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:46bb220eea43e2afb75f50453c7e7720392b5fa6e4bf9bdf2de78d32801cda6f","target":"graph","created_at":"2026-05-18T00:46:49Z","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 show that for each prime p > 7, every residue mod p can be represented by a squarefree number with largest prime factor at most p. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes.","authors_text":"Andrew R. Booker, Carl Pomerance","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-06T11:00:56Z","title":"Squarefree smooth numbers and Euclidean prime generators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01557","kind":"arxiv","version":4},"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":"sha256:598d30da402931e235be16b402bc65258e17d81668727b9b995d9e7c0e8ef5ec","target":"record","created_at":"2026-05-18T00:46:49Z","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":"5363d96d491c8d8d2d2200672228134476cf30ecff380a0f9306a76ad62b9880","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-06T11:00:56Z","title_canon_sha256":"f408c99ef15285848efb1a4200e2e4e1c465c8beba714598d4dc17a7c5e72b94"},"schema_version":"1.0","source":{"id":"1607.01557","kind":"arxiv","version":4}},"canonical_sha256":"9a3f35055f8a7f7bf4cd733623c2201558a8c618f86d934653f302d5f549e760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a3f35055f8a7f7bf4cd733623c2201558a8c618f86d934653f302d5f549e760","first_computed_at":"2026-05-18T00:46:49.299905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:49.299905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mX4PGAW+ewssXEIb7r38CRgCKZiwDPNm5fbCkxl6MWqbu1i/Zt3MRsBuh+4OpYPFJqMeogT3KP040eGL7jmmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:49.300580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01557","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:598d30da402931e235be16b402bc65258e17d81668727b9b995d9e7c0e8ef5ec","sha256:46bb220eea43e2afb75f50453c7e7720392b5fa6e4bf9bdf2de78d32801cda6f"],"state_sha256":"2f00fb1e640c2581d2c088f1c7a593bd83fa0504ebea0d476ba3a167e99886c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MOH0jQigQAHu6yhtlDcBvHMZMq+R05Nric8lGDyReU4TwOZfHvPTzc1qR0TjI8ZBl2T4cYKiFA+6hhUl00HkCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:05:45.787780Z","bundle_sha256":"48bece11643e931e17c1d802c6ff794af96d82e4a3dd084bbf6ddb99109ab449"}}