{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WRVA4FESH5UNPCTVG5O6SWDYHL","short_pith_number":"pith:WRVA4FES","canonical_record":{"source":{"id":"1511.04385","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-13T18:14:37Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"1d91d80904d53dd5a0086159db9e8362a15ce9bc805b59150decaee6b1eba353","abstract_canon_sha256":"c5af9b472c9b7513357552a799af99f23e98a36a37b16587082fc4df1c0a18be"},"schema_version":"1.0"},"canonical_sha256":"b46a0e14923f68d78a75375de958783aca8f983326baee9567ae6617eb660cf4","source":{"kind":"arxiv","id":"1511.04385","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04385","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04385v3","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04385","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"WRVA4FESH5UN","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WRVA4FESH5UNPCTV","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WRVA4FES","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WRVA4FESH5UNPCTVG5O6SWDYHL","target":"record","payload":{"canonical_record":{"source":{"id":"1511.04385","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-13T18:14:37Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"1d91d80904d53dd5a0086159db9e8362a15ce9bc805b59150decaee6b1eba353","abstract_canon_sha256":"c5af9b472c9b7513357552a799af99f23e98a36a37b16587082fc4df1c0a18be"},"schema_version":"1.0"},"canonical_sha256":"b46a0e14923f68d78a75375de958783aca8f983326baee9567ae6617eb660cf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:42.614157Z","signature_b64":"rgOG3i4A21neKjQlsrKEY+Q0j/Juz0iByoBdba9xGWlzkDe2BGLU/+wDY6NuzP9zSGaZp89k1A6lVHcAxN8EDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b46a0e14923f68d78a75375de958783aca8f983326baee9567ae6617eb660cf4","last_reissued_at":"2026-05-18T00:49:42.613573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:42.613573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.04385","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":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fx+QVWUWFuRmB42VnJK3azUKEp0U4e5UBJyHimf7FHl3hUIKo4MLsRTBq9tO96F0kr8bKNvCjSOjkGFLd6taAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:14:40.399525Z"},"content_sha256":"08de21cc6a1c97d5d0563952e81aef6bd61403c092a1c9dde67a1738b768017f","schema_version":"1.0","event_id":"sha256:08de21cc6a1c97d5d0563952e81aef6bd61403c092a1c9dde67a1738b768017f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WRVA4FESH5UNPCTVG5O6SWDYHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factoring Safe Semiprimes with a Single Quantum Query","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Benjamin Smith, Fran\\c{c}ois Morain, Fr\\'ed\\'eric Grosshans, Thomas Lawson","submitted_at":"2015-11-13T18:14:37Z","abstract_excerpt":"Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform efficiently. SFA thus consists of a \\emph{quantum order finding algorithm} (QOFA), bookended by classical routines which, given the order, return the factors. But, with probability up to $1/2$, these classical routines fail, and QOFA must be rerun. We modify these routines using elementary results in number theory, improving the likelihood that they return the factors"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04385","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":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6ZynRrxoaKy7IJ4kQt5WQLftJtdXxKv5LyglScvpzFI1Li2sJDvaRebpsZLDuLd/iylOw7S7tqpCTp2D2FyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:14:40.399869Z"},"content_sha256":"b0938dc7bf59e0219946145500d7ecdb31e04f18e69c6437ad22501955599afd","schema_version":"1.0","event_id":"sha256:b0938dc7bf59e0219946145500d7ecdb31e04f18e69c6437ad22501955599afd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WRVA4FESH5UNPCTVG5O6SWDYHL/bundle.json","state_url":"https://pith.science/pith/WRVA4FESH5UNPCTVG5O6SWDYHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WRVA4FESH5UNPCTVG5O6SWDYHL/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":"2026-05-30T07:14:40Z","links":{"resolver":"https://pith.science/pith/WRVA4FESH5UNPCTVG5O6SWDYHL","bundle":"https://pith.science/pith/WRVA4FESH5UNPCTVG5O6SWDYHL/bundle.json","state":"https://pith.science/pith/WRVA4FESH5UNPCTVG5O6SWDYHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WRVA4FESH5UNPCTVG5O6SWDYHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WRVA4FESH5UNPCTVG5O6SWDYHL","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":"c5af9b472c9b7513357552a799af99f23e98a36a37b16587082fc4df1c0a18be","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-13T18:14:37Z","title_canon_sha256":"1d91d80904d53dd5a0086159db9e8362a15ce9bc805b59150decaee6b1eba353"},"schema_version":"1.0","source":{"id":"1511.04385","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04385","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04385v3","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04385","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"WRVA4FESH5UN","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WRVA4FESH5UNPCTV","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WRVA4FES","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:b0938dc7bf59e0219946145500d7ecdb31e04f18e69c6437ad22501955599afd","target":"graph","created_at":"2026-05-18T00:49:42Z","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":"Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform efficiently. SFA thus consists of a \\emph{quantum order finding algorithm} (QOFA), bookended by classical routines which, given the order, return the factors. But, with probability up to $1/2$, these classical routines fail, and QOFA must be rerun. We modify these routines using elementary results in number theory, improving the likelihood that they return the factors","authors_text":"Benjamin Smith, Fran\\c{c}ois Morain, Fr\\'ed\\'eric Grosshans, Thomas Lawson","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-13T18:14:37Z","title":"Factoring Safe Semiprimes with a Single Quantum Query"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04385","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":"sha256:08de21cc6a1c97d5d0563952e81aef6bd61403c092a1c9dde67a1738b768017f","target":"record","created_at":"2026-05-18T00:49:42Z","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":"c5af9b472c9b7513357552a799af99f23e98a36a37b16587082fc4df1c0a18be","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-13T18:14:37Z","title_canon_sha256":"1d91d80904d53dd5a0086159db9e8362a15ce9bc805b59150decaee6b1eba353"},"schema_version":"1.0","source":{"id":"1511.04385","kind":"arxiv","version":3}},"canonical_sha256":"b46a0e14923f68d78a75375de958783aca8f983326baee9567ae6617eb660cf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b46a0e14923f68d78a75375de958783aca8f983326baee9567ae6617eb660cf4","first_computed_at":"2026-05-18T00:49:42.613573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:42.613573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgOG3i4A21neKjQlsrKEY+Q0j/Juz0iByoBdba9xGWlzkDe2BGLU/+wDY6NuzP9zSGaZp89k1A6lVHcAxN8EDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:42.614157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04385","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08de21cc6a1c97d5d0563952e81aef6bd61403c092a1c9dde67a1738b768017f","sha256:b0938dc7bf59e0219946145500d7ecdb31e04f18e69c6437ad22501955599afd"],"state_sha256":"cd5cb86a1e2d631474f6de24ad50ed4caee8bf36cdd5c80555bedd8815893c39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GyHQh0E79pWmtkk0zn8F+uU7/sDZlZBEzolyA1r11a/3QHCV4oJQJr1zAKLBgIjwHB9+cTt1HnRVC6Ov9/R/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:14:40.402310Z","bundle_sha256":"04299b1d4a5cbba3e4a1a0a568912aaae7d795cb1fa74db005a6647ec490c7d7"}}