{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:XF6APFHAVXJB5SD6TF2OUID2YP","short_pith_number":"pith:XF6APFHA","canonical_record":{"source":{"id":"0911.4724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-24T21:07:02Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8dc33f3c8714cce5e65d81e10212bbbc303d51d5afd7006dfb92cd62534b2c85","abstract_canon_sha256":"9dbd48f3cb1ecbde159fca94d5d0b35c0757812ffff1bfed4f55e6dcc05f27df"},"schema_version":"1.0"},"canonical_sha256":"b97c0794e0add21ec87e9974ea207ac3e83c1500a8fe44862bb319d036ac66a8","source":{"kind":"arxiv","id":"0911.4724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4724","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4724v1","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4724","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"XF6APFHAVXJB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XF6APFHAVXJB5SD6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XF6APFHA","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:XF6APFHAVXJB5SD6TF2OUID2YP","target":"record","payload":{"canonical_record":{"source":{"id":"0911.4724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-24T21:07:02Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8dc33f3c8714cce5e65d81e10212bbbc303d51d5afd7006dfb92cd62534b2c85","abstract_canon_sha256":"9dbd48f3cb1ecbde159fca94d5d0b35c0757812ffff1bfed4f55e6dcc05f27df"},"schema_version":"1.0"},"canonical_sha256":"b97c0794e0add21ec87e9974ea207ac3e83c1500a8fe44862bb319d036ac66a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:36.944982Z","signature_b64":"Ap0Q0WA9vTkE4RL3JHiXati/7sIxJj6h7VK5y29bZLu8kx4rn/iuGmSaEwZE22nWv1BP3anm+/JbYJtisg5vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b97c0794e0add21ec87e9974ea207ac3e83c1500a8fe44862bb319d036ac66a8","last_reissued_at":"2026-05-18T02:10:36.944256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:36.944256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.4724","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":"2026-05-18T02:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LnPmb25Zkqv1ma6q0fFY96G3Ehyf3gW/RSdkggmFY8TGKZhSs5LI5HzqDrB789yMFbZQCrJYt0X0+ktVyGyACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:00:08.425857Z"},"content_sha256":"e444539cdd8570986ddccb45944597b522cbe0b45363cf582fa707c208b8979a","schema_version":"1.0","event_id":"sha256:e444539cdd8570986ddccb45944597b522cbe0b45363cf582fa707c208b8979a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:XF6APFHAVXJB5SD6TF2OUID2YP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum algorithms to solve the hidden shift problem for quadratics and for functions of large Gowers norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Martin Roetteler","submitted_at":"2009-11-24T21:07:02Z","abstract_excerpt":"Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular exponentiation function. In a generalization of this idea, quantum Fourier sampling can be used to discover hidden subgroup structures of some functions much more efficiently than it is possible classically. Another problem for which the Fourier transform has been recruited successfully on a quantum computer is the hidden shift problem. Quantum algorithms for h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4724","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":"2026-05-18T02:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdzHC3EuS9fr4+s22p6nv34uAe32cc/3zOh46zWk+jiOxenh0ATqYZ8kYPmLmnMRPc90A30J04tORE+cRV1zDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:00:08.426212Z"},"content_sha256":"cc67170f9b8e9e756e892c8cecf10566eb4f274bc09bf651d3b16d5304d0ffb6","schema_version":"1.0","event_id":"sha256:cc67170f9b8e9e756e892c8cecf10566eb4f274bc09bf651d3b16d5304d0ffb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XF6APFHAVXJB5SD6TF2OUID2YP/bundle.json","state_url":"https://pith.science/pith/XF6APFHAVXJB5SD6TF2OUID2YP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XF6APFHAVXJB5SD6TF2OUID2YP/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":"2026-06-11T11:00:08Z","links":{"resolver":"https://pith.science/pith/XF6APFHAVXJB5SD6TF2OUID2YP","bundle":"https://pith.science/pith/XF6APFHAVXJB5SD6TF2OUID2YP/bundle.json","state":"https://pith.science/pith/XF6APFHAVXJB5SD6TF2OUID2YP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XF6APFHAVXJB5SD6TF2OUID2YP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XF6APFHAVXJB5SD6TF2OUID2YP","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":"9dbd48f3cb1ecbde159fca94d5d0b35c0757812ffff1bfed4f55e6dcc05f27df","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-24T21:07:02Z","title_canon_sha256":"8dc33f3c8714cce5e65d81e10212bbbc303d51d5afd7006dfb92cd62534b2c85"},"schema_version":"1.0","source":{"id":"0911.4724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4724","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4724v1","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4724","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"XF6APFHAVXJB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XF6APFHAVXJB5SD6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XF6APFHA","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:cc67170f9b8e9e756e892c8cecf10566eb4f274bc09bf651d3b16d5304d0ffb6","target":"graph","created_at":"2026-05-18T02:10:36Z","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":"Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular exponentiation function. In a generalization of this idea, quantum Fourier sampling can be used to discover hidden subgroup structures of some functions much more efficiently than it is possible classically. Another problem for which the Fourier transform has been recruited successfully on a quantum computer is the hidden shift problem. Quantum algorithms for h","authors_text":"Martin Roetteler","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-24T21:07:02Z","title":"Quantum algorithms to solve the hidden shift problem for quadratics and for functions of large Gowers norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4724","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:e444539cdd8570986ddccb45944597b522cbe0b45363cf582fa707c208b8979a","target":"record","created_at":"2026-05-18T02:10:36Z","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":"9dbd48f3cb1ecbde159fca94d5d0b35c0757812ffff1bfed4f55e6dcc05f27df","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-11-24T21:07:02Z","title_canon_sha256":"8dc33f3c8714cce5e65d81e10212bbbc303d51d5afd7006dfb92cd62534b2c85"},"schema_version":"1.0","source":{"id":"0911.4724","kind":"arxiv","version":1}},"canonical_sha256":"b97c0794e0add21ec87e9974ea207ac3e83c1500a8fe44862bb319d036ac66a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b97c0794e0add21ec87e9974ea207ac3e83c1500a8fe44862bb319d036ac66a8","first_computed_at":"2026-05-18T02:10:36.944256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:36.944256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ap0Q0WA9vTkE4RL3JHiXati/7sIxJj6h7VK5y29bZLu8kx4rn/iuGmSaEwZE22nWv1BP3anm+/JbYJtisg5vAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:36.944982Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e444539cdd8570986ddccb45944597b522cbe0b45363cf582fa707c208b8979a","sha256:cc67170f9b8e9e756e892c8cecf10566eb4f274bc09bf651d3b16d5304d0ffb6"],"state_sha256":"3c48f71df8c6a46ad217c1770c692345c49c9dee9cf35a81236e719e36e64b72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/Ou5Fc8JE/BN1iaRZtmQ/Qg6TPC0t6MVIhe4N/Tvsez9FpAIISybA1MIoYX/pjsvvJuvM+WUQv0Vmu3qqC+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:00:08.428492Z","bundle_sha256":"62c21facde5cdcbeb0ef6b6d12d70680efc9b6ba484cad91f946181f6bbcfbb6"}}