{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NNLXBFNIVSVOCR4K4I5YUS3JSK","short_pith_number":"pith:NNLXBFNI","canonical_record":{"source":{"id":"1012.2394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-10T21:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"e41268d34344f1497fa4a5e6a203e41e7d241197a5604c6b32cfe38de3d98c03","abstract_canon_sha256":"8dce1b73a1e1333e800f6edbb463e0afe68a4c3986155f25fd1b0f8f72b0e684"},"schema_version":"1.0"},"canonical_sha256":"6b577095a8acaae1478ae23b8a4b6992bb7f658944bde1afd94e98115b019327","source":{"kind":"arxiv","id":"1012.2394","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2394","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2394v1","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2394","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"pith_short_12","alias_value":"NNLXBFNIVSVO","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NNLXBFNIVSVOCR4K","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NNLXBFNI","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NNLXBFNIVSVOCR4K4I5YUS3JSK","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-10T21:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"e41268d34344f1497fa4a5e6a203e41e7d241197a5604c6b32cfe38de3d98c03","abstract_canon_sha256":"8dce1b73a1e1333e800f6edbb463e0afe68a4c3986155f25fd1b0f8f72b0e684"},"schema_version":"1.0"},"canonical_sha256":"6b577095a8acaae1478ae23b8a4b6992bb7f658944bde1afd94e98115b019327","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:28.671783Z","signature_b64":"Lqef35uG3cWZwdv7eVpn2PkT1xYgj68FxRBBHwW1rLSivA8W1zZX+IAExvI8T4hpv1ocDYD9iOIeGKjm9Hc1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b577095a8acaae1478ae23b8a4b6992bb7f658944bde1afd94e98115b019327","last_reissued_at":"2026-05-18T04:33:28.671338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:28.671338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2394","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":"2026-05-18T04:33:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sMX2l4isT6LBQgfX0Bmva3+4g4D30UGdb3zRel7Jte792Rv8LM+M2pTo1aSJFHJHHfD+CggxALFAvzxs3vWpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:21:22.959037Z"},"content_sha256":"07818fb373af3b788803fc268132aab00ed6dc75f64b13fe5361a590f2ffea8c","schema_version":"1.0","event_id":"sha256:07818fb373af3b788803fc268132aab00ed6dc75f64b13fe5361a590f2ffea8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NNLXBFNIVSVOCR4K4I5YUS3JSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"NE is not NP Turing Reducible to Nonexpoentially Dense NP Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bin Fu","submitted_at":"2010-12-10T21:19:11Z","abstract_excerpt":"A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of $NP_T(NP\\cap P/poly)$. In this paper, we show that $NE\\not\\subseteq NP_(NP \\cap$ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c>0,$|A^{\\le n}|\\le 2^{n^c}$ for infinitely many integers n).\n  Our result implies $NE\\not\\subseteq NP_T({pad(NP, g(n))})$ for every time constructible super-polynomial function g(n) such as $g(n)=n^{\\ceiling{\\log\\ceiling{\\log n}}}$, where Pad(NP, g(n)) is cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2394","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":"2026-05-18T04:33:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mWqXUJGk2jzDi87ZIsVHKicinq3j0tNg87RCyok8vGYFYd6kH6UFllmfKSNBW/EPaxT8RTA1A4DcE9O82pqVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:21:22.959685Z"},"content_sha256":"f86de64f3ac81de8dcc056f01083192e5bdda0376570f25123d9508b83de7525","schema_version":"1.0","event_id":"sha256:f86de64f3ac81de8dcc056f01083192e5bdda0376570f25123d9508b83de7525"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNLXBFNIVSVOCR4K4I5YUS3JSK/bundle.json","state_url":"https://pith.science/pith/NNLXBFNIVSVOCR4K4I5YUS3JSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNLXBFNIVSVOCR4K4I5YUS3JSK/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":"2026-06-08T08:21:22Z","links":{"resolver":"https://pith.science/pith/NNLXBFNIVSVOCR4K4I5YUS3JSK","bundle":"https://pith.science/pith/NNLXBFNIVSVOCR4K4I5YUS3JSK/bundle.json","state":"https://pith.science/pith/NNLXBFNIVSVOCR4K4I5YUS3JSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNLXBFNIVSVOCR4K4I5YUS3JSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NNLXBFNIVSVOCR4K4I5YUS3JSK","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":"8dce1b73a1e1333e800f6edbb463e0afe68a4c3986155f25fd1b0f8f72b0e684","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-10T21:19:11Z","title_canon_sha256":"e41268d34344f1497fa4a5e6a203e41e7d241197a5604c6b32cfe38de3d98c03"},"schema_version":"1.0","source":{"id":"1012.2394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2394","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2394v1","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2394","created_at":"2026-05-18T04:33:28Z"},{"alias_kind":"pith_short_12","alias_value":"NNLXBFNIVSVO","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NNLXBFNIVSVOCR4K","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NNLXBFNI","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:f86de64f3ac81de8dcc056f01083192e5bdda0376570f25123d9508b83de7525","target":"graph","created_at":"2026-05-18T04:33:28Z","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 long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of $NP_T(NP\\cap P/poly)$. In this paper, we show that $NE\\not\\subseteq NP_(NP \\cap$ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c>0,$|A^{\\le n}|\\le 2^{n^c}$ for infinitely many integers n).\n  Our result implies $NE\\not\\subseteq NP_T({pad(NP, g(n))})$ for every time constructible super-polynomial function g(n) such as $g(n)=n^{\\ceiling{\\log\\ceiling{\\log n}}}$, where Pad(NP, g(n)) is cl","authors_text":"Bin Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-10T21:19:11Z","title":"NE is not NP Turing Reducible to Nonexpoentially Dense NP Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2394","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":"sha256:07818fb373af3b788803fc268132aab00ed6dc75f64b13fe5361a590f2ffea8c","target":"record","created_at":"2026-05-18T04:33:28Z","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":"8dce1b73a1e1333e800f6edbb463e0afe68a4c3986155f25fd1b0f8f72b0e684","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-10T21:19:11Z","title_canon_sha256":"e41268d34344f1497fa4a5e6a203e41e7d241197a5604c6b32cfe38de3d98c03"},"schema_version":"1.0","source":{"id":"1012.2394","kind":"arxiv","version":1}},"canonical_sha256":"6b577095a8acaae1478ae23b8a4b6992bb7f658944bde1afd94e98115b019327","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b577095a8acaae1478ae23b8a4b6992bb7f658944bde1afd94e98115b019327","first_computed_at":"2026-05-18T04:33:28.671338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:28.671338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lqef35uG3cWZwdv7eVpn2PkT1xYgj68FxRBBHwW1rLSivA8W1zZX+IAExvI8T4hpv1ocDYD9iOIeGKjm9Hc1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:28.671783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07818fb373af3b788803fc268132aab00ed6dc75f64b13fe5361a590f2ffea8c","sha256:f86de64f3ac81de8dcc056f01083192e5bdda0376570f25123d9508b83de7525"],"state_sha256":"00bea020160cbb5fb5bc83c5f11ad9c84656353dc85c3371c5607c6f67461a5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DGMD/yd5qyPSemAHZELK9hxJA/hw1b70BV/uZiRVS/KT72v65kg++x1rNZskeMdIlNCR9JaGDa40++wkfsrDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T08:21:22.963141Z","bundle_sha256":"c89a4c0fc022cda6b94d6e421513f9fcee61db0430f45a698a13d06a134d1380"}}