{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:QTHCRBJZDUP2FVJ5X6GBBCC4FL","short_pith_number":"pith:QTHCRBJZ","canonical_record":{"source":{"id":"0912.4807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-12-24T08:44:40Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8f05b745d8b7c23a2d3818ab2f4bbc4aa7c46dae01be2dd6e8fe3f2e09899263","abstract_canon_sha256":"75410008b10f370fd91fa50c499e60e9fab334d0cf3e93dc6c1826c229d852bf"},"schema_version":"1.0"},"canonical_sha256":"84ce2885391d1fa2d53dbf8c10885c2af07266f6b9731494efd34cc5231601f0","source":{"kind":"arxiv","id":"0912.4807","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4807","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4807v1","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4807","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"QTHCRBJZDUP2","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"pith_short_16","alias_value":"QTHCRBJZDUP2FVJ5","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"pith_short_8","alias_value":"QTHCRBJZ","created_at":"2026-07-04T17:18:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:QTHCRBJZDUP2FVJ5X6GBBCC4FL","target":"record","payload":{"canonical_record":{"source":{"id":"0912.4807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-12-24T08:44:40Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8f05b745d8b7c23a2d3818ab2f4bbc4aa7c46dae01be2dd6e8fe3f2e09899263","abstract_canon_sha256":"75410008b10f370fd91fa50c499e60e9fab334d0cf3e93dc6c1826c229d852bf"},"schema_version":"1.0"},"canonical_sha256":"84ce2885391d1fa2d53dbf8c10885c2af07266f6b9731494efd34cc5231601f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:18:15.800413Z","signature_b64":"GRly3+gyHWNN+r6O/Y/LF+q3vME4LsTxZME6LEN5KGHj37ORZVzk/fUSrNT4ufVNGj0i1ECA1Yafng6MNXHcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84ce2885391d1fa2d53dbf8c10885c2af07266f6b9731494efd34cc5231601f0","last_reissued_at":"2026-07-04T17:18:15.800029Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:18:15.800029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.4807","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":"2026-07-04T17:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5V/f3JuGQIdn2y4i0kO1WGDH+av8MjWJObLA7ulHJCw/oUEG5ApUCBF2MNjadreyD0DxqGzaLcd0EQmiu2uHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T13:57:31.798346Z"},"content_sha256":"9bb0f4e49eee93c804e661b4dfa76a499254674f28df9a8cf079d3f8038cea42","schema_version":"1.0","event_id":"sha256:9bb0f4e49eee93c804e661b4dfa76a499254674f28df9a8cf079d3f8038cea42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:QTHCRBJZDUP2FVJ5X6GBBCC4FL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Algorithms for many-to-one Functions to Solve the Regulator and the Principal Ideal Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Arthur Schmidt","submitted_at":"2009-12-24T08:44:40Z","abstract_excerpt":"We propose new quantum algorithms to solve the regulator and the principal ideal problem in a real-quadratic number field. We improve the algorithms proposed by Hallgren by using two different techniques. The first improvement is the usage of a period function which is not one-to-one on its period. We show that even in this case Shor's algorithm computes the period with constant probability. The second improvement is the usage of reduced forms (a, b, c) of discriminant D with a>0 instead of reduced ideals of the same discriminant. These improvements reduce the number of required qubits by at l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4807","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0912.4807/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbgahePQCsImMgw1L9zB+fStUUkz8+5mE43zsQhYrZULiCy65lgHfXBagCeGxcc8C9AfJVzNMF7RHNSYYCPFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T13:57:31.798900Z"},"content_sha256":"67874c1831e87037c500b5d7a279e431e350d75ff6ccab17f1ebecf2a08f96b5","schema_version":"1.0","event_id":"sha256:67874c1831e87037c500b5d7a279e431e350d75ff6ccab17f1ebecf2a08f96b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTHCRBJZDUP2FVJ5X6GBBCC4FL/bundle.json","state_url":"https://pith.science/pith/QTHCRBJZDUP2FVJ5X6GBBCC4FL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTHCRBJZDUP2FVJ5X6GBBCC4FL/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":"2026-08-18T13:57:31Z","links":{"resolver":"https://pith.science/pith/QTHCRBJZDUP2FVJ5X6GBBCC4FL","bundle":"https://pith.science/pith/QTHCRBJZDUP2FVJ5X6GBBCC4FL/bundle.json","state":"https://pith.science/pith/QTHCRBJZDUP2FVJ5X6GBBCC4FL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTHCRBJZDUP2FVJ5X6GBBCC4FL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QTHCRBJZDUP2FVJ5X6GBBCC4FL","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":"75410008b10f370fd91fa50c499e60e9fab334d0cf3e93dc6c1826c229d852bf","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-12-24T08:44:40Z","title_canon_sha256":"8f05b745d8b7c23a2d3818ab2f4bbc4aa7c46dae01be2dd6e8fe3f2e09899263"},"schema_version":"1.0","source":{"id":"0912.4807","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4807","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4807v1","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4807","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"QTHCRBJZDUP2","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"pith_short_16","alias_value":"QTHCRBJZDUP2FVJ5","created_at":"2026-07-04T17:18:15Z"},{"alias_kind":"pith_short_8","alias_value":"QTHCRBJZ","created_at":"2026-07-04T17:18:15Z"}],"graph_snapshots":[{"event_id":"sha256:67874c1831e87037c500b5d7a279e431e350d75ff6ccab17f1ebecf2a08f96b5","target":"graph","created_at":"2026-07-04T17:18:15Z","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/0912.4807/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose new quantum algorithms to solve the regulator and the principal ideal problem in a real-quadratic number field. We improve the algorithms proposed by Hallgren by using two different techniques. The first improvement is the usage of a period function which is not one-to-one on its period. We show that even in this case Shor's algorithm computes the period with constant probability. The second improvement is the usage of reduced forms (a, b, c) of discriminant D with a>0 instead of reduced ideals of the same discriminant. These improvements reduce the number of required qubits by at l","authors_text":"Arthur Schmidt","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-12-24T08:44:40Z","title":"Quantum Algorithms for many-to-one Functions to Solve the Regulator and the Principal Ideal Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4807","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":"sha256:9bb0f4e49eee93c804e661b4dfa76a499254674f28df9a8cf079d3f8038cea42","target":"record","created_at":"2026-07-04T17:18:15Z","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":"75410008b10f370fd91fa50c499e60e9fab334d0cf3e93dc6c1826c229d852bf","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-12-24T08:44:40Z","title_canon_sha256":"8f05b745d8b7c23a2d3818ab2f4bbc4aa7c46dae01be2dd6e8fe3f2e09899263"},"schema_version":"1.0","source":{"id":"0912.4807","kind":"arxiv","version":1}},"canonical_sha256":"84ce2885391d1fa2d53dbf8c10885c2af07266f6b9731494efd34cc5231601f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84ce2885391d1fa2d53dbf8c10885c2af07266f6b9731494efd34cc5231601f0","first_computed_at":"2026-07-04T17:18:15.800029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:18:15.800029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GRly3+gyHWNN+r6O/Y/LF+q3vME4LsTxZME6LEN5KGHj37ORZVzk/fUSrNT4ufVNGj0i1ECA1Yafng6MNXHcAw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:18:15.800413Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.4807","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bb0f4e49eee93c804e661b4dfa76a499254674f28df9a8cf079d3f8038cea42","sha256:67874c1831e87037c500b5d7a279e431e350d75ff6ccab17f1ebecf2a08f96b5"],"state_sha256":"d538a679a0eef7665701ce5d35587c3bea23c97fb21afaf05e81b4a6cf98aaec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQQIve+FWYogG0u5kcDIORE3gf/zSG1cuawLwuZIBu44AcJLli9ecWjj1EImpqaercGIqb6Ye1h+vAfCi2HZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T13:57:31.805647Z","bundle_sha256":"4c3a9b007f7828852b2597ce56407bb19012d04b6691d524cdcae01685b31c96"}}