{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5OOOPJH7QVNZWI3CSR3VU2YTCV","short_pith_number":"pith:5OOOPJH7","canonical_record":{"source":{"id":"1603.08675","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2016-03-29T08:25:22Z","cross_cats_sorted":["cs.DS","cs.IR"],"title_canon_sha256":"0cb40030fd74a0cc985846400128dfff19814b3ebfd2209340a215c61e255a21","abstract_canon_sha256":"8a428cf7b0cb521505dcbd683ca55b70a6edd427be463a52e57fe8ff695d4b3c"},"schema_version":"1.0"},"canonical_sha256":"eb9ce7a4ff855b9b236294775a6b13156072ba0347a0e54a740982c04f67faf4","source":{"kind":"arxiv","id":"1603.08675","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08675","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08675v3","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08675","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"5OOOPJH7QVNZ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5OOOPJH7QVNZWI3C","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5OOOPJH7","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5OOOPJH7QVNZWI3CSR3VU2YTCV","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08675","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2016-03-29T08:25:22Z","cross_cats_sorted":["cs.DS","cs.IR"],"title_canon_sha256":"0cb40030fd74a0cc985846400128dfff19814b3ebfd2209340a215c61e255a21","abstract_canon_sha256":"8a428cf7b0cb521505dcbd683ca55b70a6edd427be463a52e57fe8ff695d4b3c"},"schema_version":"1.0"},"canonical_sha256":"eb9ce7a4ff855b9b236294775a6b13156072ba0347a0e54a740982c04f67faf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:05.642942Z","signature_b64":"U5A08Cjhley1Pmk3qHmgY1NP2g63UlfB67M7Hp98EJrPlUZ3ayMTUz/0Kf4ABij85J+tvJVX2UL+6EuzQvjVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb9ce7a4ff855b9b236294775a6b13156072ba0347a0e54a740982c04f67faf4","last_reissued_at":"2026-05-18T01:04:05.642465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:05.642465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08675","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":"2026-05-18T01:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/6C6CstVcz8QvcjaK/0L1MPzBbulSJgbZuZgZqmM8CCFhepm7yMv0vPVvnW93i3VyIO2V/BFfYUzcnD61Q2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:56:51.589220Z"},"content_sha256":"ff5543177e7c22c500932ea2c3f84d772138660afec9d40270a9540019363bf4","schema_version":"1.0","event_id":"sha256:ff5543177e7c22c500932ea2c3f84d772138660afec9d40270a9540019363bf4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5OOOPJH7QVNZWI3CSR3VU2YTCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Recommendation Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.IR"],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, Iordanis Kerenidis","submitted_at":"2016-03-29T08:25:22Z","abstract_excerpt":"A recommendation system uses the past purchases or ratings of $n$ products by a group of $m$ users, in order to provide personalized recommendations to individual users. The information is modeled as an $m \\times n$ preference matrix which is assumed to have a good rank-$k$ approximation, for a small constant $k$.\n  In this work, we present a quantum algorithm for recommendation systems that has running time $O(\\text{poly}(k)\\text{polylog}(mn))$. All known classical algorithms for recommendation systems that work through reconstructing an approximation of the preference matrix run in time poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08675","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":"2026-05-18T01:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/iNUPRy0UbkfUyK+ErOPCO1kQK8GDiQeGVDNkL5zbK5KdKtcoGJ+8D/iXR8prOTgAze+moFHmZts2zHkThcwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:56:51.589997Z"},"content_sha256":"e9ecefef99dc453dfcbd5507ad66bf9dd29158009efbdaff2f88b216938008fd","schema_version":"1.0","event_id":"sha256:e9ecefef99dc453dfcbd5507ad66bf9dd29158009efbdaff2f88b216938008fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5OOOPJH7QVNZWI3CSR3VU2YTCV/bundle.json","state_url":"https://pith.science/pith/5OOOPJH7QVNZWI3CSR3VU2YTCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5OOOPJH7QVNZWI3CSR3VU2YTCV/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":"2026-06-01T00:56:51Z","links":{"resolver":"https://pith.science/pith/5OOOPJH7QVNZWI3CSR3VU2YTCV","bundle":"https://pith.science/pith/5OOOPJH7QVNZWI3CSR3VU2YTCV/bundle.json","state":"https://pith.science/pith/5OOOPJH7QVNZWI3CSR3VU2YTCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5OOOPJH7QVNZWI3CSR3VU2YTCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5OOOPJH7QVNZWI3CSR3VU2YTCV","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":"8a428cf7b0cb521505dcbd683ca55b70a6edd427be463a52e57fe8ff695d4b3c","cross_cats_sorted":["cs.DS","cs.IR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2016-03-29T08:25:22Z","title_canon_sha256":"0cb40030fd74a0cc985846400128dfff19814b3ebfd2209340a215c61e255a21"},"schema_version":"1.0","source":{"id":"1603.08675","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08675","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08675v3","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08675","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"5OOOPJH7QVNZ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5OOOPJH7QVNZWI3C","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5OOOPJH7","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:e9ecefef99dc453dfcbd5507ad66bf9dd29158009efbdaff2f88b216938008fd","target":"graph","created_at":"2026-05-18T01:04:05Z","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 recommendation system uses the past purchases or ratings of $n$ products by a group of $m$ users, in order to provide personalized recommendations to individual users. The information is modeled as an $m \\times n$ preference matrix which is assumed to have a good rank-$k$ approximation, for a small constant $k$.\n  In this work, we present a quantum algorithm for recommendation systems that has running time $O(\\text{poly}(k)\\text{polylog}(mn))$. All known classical algorithms for recommendation systems that work through reconstructing an approximation of the preference matrix run in time poly","authors_text":"Anupam Prakash, Iordanis Kerenidis","cross_cats":["cs.DS","cs.IR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2016-03-29T08:25:22Z","title":"Quantum Recommendation Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08675","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:ff5543177e7c22c500932ea2c3f84d772138660afec9d40270a9540019363bf4","target":"record","created_at":"2026-05-18T01:04:05Z","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":"8a428cf7b0cb521505dcbd683ca55b70a6edd427be463a52e57fe8ff695d4b3c","cross_cats_sorted":["cs.DS","cs.IR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2016-03-29T08:25:22Z","title_canon_sha256":"0cb40030fd74a0cc985846400128dfff19814b3ebfd2209340a215c61e255a21"},"schema_version":"1.0","source":{"id":"1603.08675","kind":"arxiv","version":3}},"canonical_sha256":"eb9ce7a4ff855b9b236294775a6b13156072ba0347a0e54a740982c04f67faf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb9ce7a4ff855b9b236294775a6b13156072ba0347a0e54a740982c04f67faf4","first_computed_at":"2026-05-18T01:04:05.642465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:05.642465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U5A08Cjhley1Pmk3qHmgY1NP2g63UlfB67M7Hp98EJrPlUZ3ayMTUz/0Kf4ABij85J+tvJVX2UL+6EuzQvjVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:05.642942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08675","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff5543177e7c22c500932ea2c3f84d772138660afec9d40270a9540019363bf4","sha256:e9ecefef99dc453dfcbd5507ad66bf9dd29158009efbdaff2f88b216938008fd"],"state_sha256":"9bf6d12b8bce895f70c6d26e4794d5043af14627b8b74a8bac5ad8136fa0f3a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pphf5SpjrFrRi2w92tnS0fIvovvm7rnAP0tpO17bjBgaN3tjwOud9UZbyfl0et2xY1lLdDmcE26vzHQWICJ1BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:56:51.594911Z","bundle_sha256":"3182eb7493c1ca0270b1085edc1d9374084c0117d2048136bc9c96970781e442"}}