{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:34I4PW7ZSAB7ULOASDDWUZIXCZ","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":"5d3b05e3c15adb00457be8aadefcc6693c0febc8e8e6f06237f1e335ab9b7551","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","title_canon_sha256":"a2334baf2f4ff06a0e287cb9943079da2c6a6d340c19e3fec1d299be57d8ed74"},"schema_version":"1.0","source":{"id":"quant-ph/0109004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0109004","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0109004v1","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0109004","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"34I4PW7ZSAB7","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_16","alias_value":"34I4PW7ZSAB7ULOA","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_8","alias_value":"34I4PW7Z","created_at":"2026-07-04T14:45:41Z"}],"graph_snapshots":[{"event_id":"sha256:2f04e532e118e839b0d47ee7e618bb18db95f32938e2e3908a473ae49ffdf037","target":"graph","created_at":"2026-07-04T14:45:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0109004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm. Factoring integers. NP-complete problems.","authors_text":"Igor V. Volovich","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","title":"Quantum Computing and Shor`s Factoring Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0109004","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:f6f92e334822f625c76208510dc4f6079093f13a7170ca9ca33952fad5c6d701","target":"record","created_at":"2026-07-04T14:45:41Z","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":"5d3b05e3c15adb00457be8aadefcc6693c0febc8e8e6f06237f1e335ab9b7551","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","title_canon_sha256":"a2334baf2f4ff06a0e287cb9943079da2c6a6d340c19e3fec1d299be57d8ed74"},"schema_version":"1.0","source":{"id":"quant-ph/0109004","kind":"arxiv","version":1}},"canonical_sha256":"df11c7dbf99003fa2dc090c76a65171655d49780ed72b72677d4bb6eb1d4068f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df11c7dbf99003fa2dc090c76a65171655d49780ed72b72677d4bb6eb1d4068f","first_computed_at":"2026-07-04T14:45:41.606101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:45:41.606101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"utrfCxjGTjL5WLfoFWvhBZ+Mno8c6J6QPC+f+0+/xA4LMFsJlw8VDC9580pzW/KGzq77ZZYQDvAjpYCn+LQKDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:45:41.606561Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0109004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6f92e334822f625c76208510dc4f6079093f13a7170ca9ca33952fad5c6d701","sha256:2f04e532e118e839b0d47ee7e618bb18db95f32938e2e3908a473ae49ffdf037"],"state_sha256":"8f6c68d25bc3ac67327cd39ec44bf67f120873d7142f9b6e29b8b521d0a9c44c"}