{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q3U4BJW63N3TMNW4UPDFJ45EIV","short_pith_number":"pith:Q3U4BJW6","canonical_record":{"source":{"id":"1302.5976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T02:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"bc9374f102312b956b7edf38b1780c673b7ce8921afa7c0e1aa0e675ce21b00c","abstract_canon_sha256":"c2c255bd5ca1f72864c05e24f95224bb98937eca13b0407440483191786f03de"},"schema_version":"1.0"},"canonical_sha256":"86e9c0a6dedb773636dca3c654f3a445744b708123cb6e6fa9c487c92674710b","source":{"kind":"arxiv","id":"1302.5976","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5976","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5976v1","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5976","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"Q3U4BJW63N3T","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q3U4BJW63N3TMNW4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q3U4BJW6","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q3U4BJW63N3TMNW4UPDFJ45EIV","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T02:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"bc9374f102312b956b7edf38b1780c673b7ce8921afa7c0e1aa0e675ce21b00c","abstract_canon_sha256":"c2c255bd5ca1f72864c05e24f95224bb98937eca13b0407440483191786f03de"},"schema_version":"1.0"},"canonical_sha256":"86e9c0a6dedb773636dca3c654f3a445744b708123cb6e6fa9c487c92674710b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:11.791848Z","signature_b64":"TxCUNMUwQftH4MO+NtP5O707uBgw6tiyHgVlmk1HynkcO6qX5NmfrI4GpJQXe4YqPpzIorf0r5lZ38Od17LBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86e9c0a6dedb773636dca3c654f3a445744b708123cb6e6fa9c487c92674710b","last_reissued_at":"2026-05-18T03:12:11.791087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:11.791087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5976","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":"2026-05-18T03:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fo/Euu66uBw0V6EUniqtrSVmxeLhFdMJ2YItXKH7drvmaOLHP8RJkBApNkKs/vlOxVPvQbfqqhabHMDf8dd6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T08:30:02.462635Z"},"content_sha256":"785add170edd7f4ee8cf40601861dbc0c3b6246aa0acc3df54fc6f6a242b5fbd","schema_version":"1.0","event_id":"sha256:785add170edd7f4ee8cf40601861dbc0c3b6246aa0acc3df54fc6f6a242b5fbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q3U4BJW63N3TMNW4UPDFJ45EIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The distribution of r-free numbers in arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jason Gibson","submitted_at":"2013-02-25T02:10:34Z","abstract_excerpt":"A positive integer n is called r-free if n is not divisible by the r-th power of a prime. Generalizing earlier work of Orr, we provide an upper bound of Bombieri-Vinogradov type for the r-free numbers in arithmetic progressions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5976","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":"2026-05-18T03:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8cWiaMniWc4/jkAg7I4XPpyAlyc7yQikTw+EEyiTwOrRP6bIROS3a75iL99lalvY2sVH/zOmLuzHozQvA5xDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T08:30:02.463275Z"},"content_sha256":"b7889ce687e016475cc65b1eb7b25581b8155747acef1883268f0b6408e455ee","schema_version":"1.0","event_id":"sha256:b7889ce687e016475cc65b1eb7b25581b8155747acef1883268f0b6408e455ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3U4BJW63N3TMNW4UPDFJ45EIV/bundle.json","state_url":"https://pith.science/pith/Q3U4BJW63N3TMNW4UPDFJ45EIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3U4BJW63N3TMNW4UPDFJ45EIV/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":"2026-05-22T08:30:02Z","links":{"resolver":"https://pith.science/pith/Q3U4BJW63N3TMNW4UPDFJ45EIV","bundle":"https://pith.science/pith/Q3U4BJW63N3TMNW4UPDFJ45EIV/bundle.json","state":"https://pith.science/pith/Q3U4BJW63N3TMNW4UPDFJ45EIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3U4BJW63N3TMNW4UPDFJ45EIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q3U4BJW63N3TMNW4UPDFJ45EIV","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":"c2c255bd5ca1f72864c05e24f95224bb98937eca13b0407440483191786f03de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T02:10:34Z","title_canon_sha256":"bc9374f102312b956b7edf38b1780c673b7ce8921afa7c0e1aa0e675ce21b00c"},"schema_version":"1.0","source":{"id":"1302.5976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5976","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5976v1","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5976","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"Q3U4BJW63N3T","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q3U4BJW63N3TMNW4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q3U4BJW6","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:b7889ce687e016475cc65b1eb7b25581b8155747acef1883268f0b6408e455ee","target":"graph","created_at":"2026-05-18T03:12:11Z","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":"A positive integer n is called r-free if n is not divisible by the r-th power of a prime. Generalizing earlier work of Orr, we provide an upper bound of Bombieri-Vinogradov type for the r-free numbers in arithmetic progressions.","authors_text":"Jason Gibson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T02:10:34Z","title":"The distribution of r-free numbers in arithmetic progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5976","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":"sha256:785add170edd7f4ee8cf40601861dbc0c3b6246aa0acc3df54fc6f6a242b5fbd","target":"record","created_at":"2026-05-18T03:12:11Z","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":"c2c255bd5ca1f72864c05e24f95224bb98937eca13b0407440483191786f03de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T02:10:34Z","title_canon_sha256":"bc9374f102312b956b7edf38b1780c673b7ce8921afa7c0e1aa0e675ce21b00c"},"schema_version":"1.0","source":{"id":"1302.5976","kind":"arxiv","version":1}},"canonical_sha256":"86e9c0a6dedb773636dca3c654f3a445744b708123cb6e6fa9c487c92674710b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86e9c0a6dedb773636dca3c654f3a445744b708123cb6e6fa9c487c92674710b","first_computed_at":"2026-05-18T03:12:11.791087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:11.791087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TxCUNMUwQftH4MO+NtP5O707uBgw6tiyHgVlmk1HynkcO6qX5NmfrI4GpJQXe4YqPpzIorf0r5lZ38Od17LBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:11.791848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:785add170edd7f4ee8cf40601861dbc0c3b6246aa0acc3df54fc6f6a242b5fbd","sha256:b7889ce687e016475cc65b1eb7b25581b8155747acef1883268f0b6408e455ee"],"state_sha256":"0ae16fd6667d130ba41433d7512661038174c6a10f0fa53891e969c9894c4683"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOkKUi6W6Tvj9v2Oow3U9AyyGprsoFc+8hSI2ACNAYG9lKbPcgdYFMtOGhEfLpb+QoHs7ymdixoLsufLUMaSDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T08:30:02.466763Z","bundle_sha256":"57a449b4bcf52acd06a0bd3a9a4c32a0f5311a0f149c6e0f5116b8b77aa38b8c"}}