{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JRFAKQMNCE6KCSTNHEQG2FZIP2","short_pith_number":"pith:JRFAKQMN","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"},"canonical_sha256":"4c4a05418d113ca14a6d39206d17287eb40c44f4f14c11e845ad276c8fc7adfb","source":{"kind":"arxiv","id":"1408.3193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3193","created_at":"2026-05-18T01:36:35Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3193v2","created_at":"2026-05-18T01:36:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3193","created_at":"2026-05-18T01:36:35Z"},{"alias_kind":"pith_short_12","alias_value":"JRFAKQMNCE6K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JRFAKQMNCE6KCSTN","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JRFAKQMN","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JRFAKQMNCE6KCSTNHEQG2FZIP2","target":"record","payload":{"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"},"canonical_sha256":"4c4a05418d113ca14a6d39206d17287eb40c44f4f14c11e845ad276c8fc7adfb","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"},"source_kind":"arxiv","source_id":"1408.3193","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"728JZ/wKsIs7dIcDH+VsOH4OObjRtFT/htwGRMYNzz7he9xmfPeRboJumc3o4uP/HOM3oY0+AfFYMH0wW234BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:29:09.201034Z"},"content_sha256":"d6bbc70f2fc0bc0c458fec304a13de453c1b4db563f723584ee2eca3b5c079b1","schema_version":"1.0","event_id":"sha256:d6bbc70f2fc0bc0c458fec304a13de453c1b4db563f723584ee2eca3b5c079b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JRFAKQMNCE6KCSTNHEQG2FZIP2","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cpdz/K00j8WcdurPl+R+bNpu3ykYzDDKXvR7+SAwXEV7OyjnMcI++l92Qzxbbv9Z8utTjujyfN8cVXPFqz8qBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:29:09.201441Z"},"content_sha256":"04e99cc6fea421bdb8cef5c79525443359a70a29e0e295841384c791c28a555f","schema_version":"1.0","event_id":"sha256:04e99cc6fea421bdb8cef5c79525443359a70a29e0e295841384c791c28a555f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/bundle.json","state_url":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/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":"2026-06-08T23:29:09Z","links":{"resolver":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2","bundle":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/bundle.json","state":"https://pith.science/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JRFAKQMNCE6KCSTNHEQG2FZIP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JRFAKQMNCE6KCSTNHEQG2FZIP2","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":"0cd5470aaa880c7787a3d0941213bf35ccbcca6e984d281602fd8a608b932433","cross_cats_sorted":["cs.CC","cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-14T04:56:23Z","title_canon_sha256":"7ef8756c9df01f95beba93c841e96228285ac65440eb0db8fd9e7ebffcd624a0"},"schema_version":"1.0","source":{"id":"1408.3193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3193","created_at":"2026-05-18T01:36:35Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3193v2","created_at":"2026-05-18T01:36:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3193","created_at":"2026-05-18T01:36:35Z"},{"alias_kind":"pith_short_12","alias_value":"JRFAKQMNCE6K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JRFAKQMNCE6KCSTN","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JRFAKQMN","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:04e99cc6fea421bdb8cef5c79525443359a70a29e0e295841384c791c28a555f","target":"graph","created_at":"2026-05-18T01:36:35Z","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":"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","authors_text":"Aleksandrs Belovs, Aran Nayebi, Luca Trevisan, Scott Aaronson","cross_cats":["cs.CC","cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-14T04:56:23Z","title":"Quantum lower bound for inverting a permutation with advice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3193","kind":"arxiv","version":2},"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:d6bbc70f2fc0bc0c458fec304a13de453c1b4db563f723584ee2eca3b5c079b1","target":"record","created_at":"2026-05-18T01:36:35Z","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":"0cd5470aaa880c7787a3d0941213bf35ccbcca6e984d281602fd8a608b932433","cross_cats_sorted":["cs.CC","cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-14T04:56:23Z","title_canon_sha256":"7ef8756c9df01f95beba93c841e96228285ac65440eb0db8fd9e7ebffcd624a0"},"schema_version":"1.0","source":{"id":"1408.3193","kind":"arxiv","version":2}},"canonical_sha256":"4c4a05418d113ca14a6d39206d17287eb40c44f4f14c11e845ad276c8fc7adfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c4a05418d113ca14a6d39206d17287eb40c44f4f14c11e845ad276c8fc7adfb","first_computed_at":"2026-05-18T01:36:35.929680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:35.929680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9WZn/fh/Nnx3PjXfFE4PLsLnYsZ6cWC4CTza+1TP6zYzGn1xyoAHmJ4LvG4/ql0ecPjYa/UU0wRAGSZz+Y4jBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:35.930324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6bbc70f2fc0bc0c458fec304a13de453c1b4db563f723584ee2eca3b5c079b1","sha256:04e99cc6fea421bdb8cef5c79525443359a70a29e0e295841384c791c28a555f"],"state_sha256":"3c09759932fdf2486d5e7a5e3622c64fdb168886861f8c53b97b46dd7eebce95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGkZnovKeNVuByVSgbuV7Z1hD/3skSCwm0EJcvVyhWTsjZU/MeS6mLXoScgK43NfvWK/FQlLuxN1uZ1O45JdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:29:09.203362Z","bundle_sha256":"6e4f682e8d050a4a947693a66a63d9337727fe6fc783accee3abaacac088fcac"}}