{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JRFAKQMNCE6KCSTNHEQG2FZIP2","short_pith_number":"pith:JRFAKQMN","schema_version":"1.0","canonical_sha256":"4c4a05418d113ca14a6d39206d17287eb40c44f4f14c11e845ad276c8fc7adfb","source":{"kind":"arxiv","id":"1408.3193","version":2},"attestation_state":"computed","paper":{"title":"Quantum lower bound for inverting a permutation with advice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CR"],"primary_cat":"quant-ph","authors_text":"Aleksandrs Belovs, Aran Nayebi, Luca Trevisan, Scott Aaronson","submitted_at":"2014-08-14T04:56:23Z","abstract_excerpt":"Given a random permutation $f: [N] \\to [N]$ as a black box and $y \\in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but \\emph{not} on the input $y$. Classically, there is a data structure of size $\\tilde{O}(S)$ and an algorithm that with the help of the data structure, given $f(x)$, can invert $f$ in time $\\tilde{O}(T)$, for every choice of parameters $S$, $T$, such that $S\\cdot T \\ge N$. We prove a quantum lower bound of $T^2\\cdot S \\ge \\tilde{\\Omega}(\\e"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.3193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-14T04:56:23Z","cross_cats_sorted":["cs.CC","cs.CR"],"title_canon_sha256":"7ef8756c9df01f95beba93c841e96228285ac65440eb0db8fd9e7ebffcd624a0","abstract_canon_sha256":"0cd5470aaa880c7787a3d0941213bf35ccbcca6e984d281602fd8a608b932433"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:35.930324Z","signature_b64":"9WZn/fh/Nnx3PjXfFE4PLsLnYsZ6cWC4CTza+1TP6zYzGn1xyoAHmJ4LvG4/ql0ecPjYa/UU0wRAGSZz+Y4jBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c4a05418d113ca14a6d39206d17287eb40c44f4f14c11e845ad276c8fc7adfb","last_reissued_at":"2026-05-18T01:36:35.929680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:35.929680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum lower bound for inverting a permutation with advice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CR"],"primary_cat":"quant-ph","authors_text":"Aleksandrs Belovs, Aran Nayebi, Luca Trevisan, Scott Aaronson","submitted_at":"2014-08-14T04:56:23Z","abstract_excerpt":"Given a random permutation $f: [N] \\to [N]$ as a black box and $y \\in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but \\emph{not} on the input $y$. Classically, there is a data structure of size $\\tilde{O}(S)$ and an algorithm that with the help of the data structure, given $f(x)$, can invert $f$ in time $\\tilde{O}(T)$, for every choice of parameters $S$, $T$, such that $S\\cdot T \\ge N$. We prove a quantum lower bound of $T^2\\cdot S \\ge \\tilde{\\Omega}(\\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3193","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.3193","created_at":"2026-05-18T01:36:35.929773+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.3193v2","created_at":"2026-05-18T01:36:35.929773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3193","created_at":"2026-05-18T01:36:35.929773+00:00"},{"alias_kind":"pith_short_12","alias_value":"JRFAKQMNCE6K","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JRFAKQMNCE6KCSTN","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JRFAKQMN","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2","json":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2.json","graph_json":"https://pith.science/api/pith-number/JRFAKQMNCE6KCSTNHEQG2FZIP2/graph.json","events_json":"https://pith.science/api/pith-number/JRFAKQMNCE6KCSTNHEQG2FZIP2/events.json","paper":"https://pith.science/paper/JRFAKQMN"},"agent_actions":{"view_html":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2","download_json":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2.json","view_paper":"https://pith.science/paper/JRFAKQMN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.3193&json=true","fetch_graph":"https://pith.science/api/pith-number/JRFAKQMNCE6KCSTNHEQG2FZIP2/graph.json","fetch_events":"https://pith.science/api/pith-number/JRFAKQMNCE6KCSTNHEQG2FZIP2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/action/storage_attestation","attest_author":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/action/author_attestation","sign_citation":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/action/citation_signature","submit_replication":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/action/replication_record"}},"created_at":"2026-05-18T01:36:35.929773+00:00","updated_at":"2026-05-18T01:36:35.929773+00:00"}