{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Z3AQQ47EIBQYDKBV6M27UJKANZ","short_pith_number":"pith:Z3AQQ47E","canonical_record":{"source":{"id":"1712.00942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-04T07:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"0065fcea1cf927c44d7bb7d16195105b7891f9e6394d6b858d33139a237794bd","abstract_canon_sha256":"6563bac2d25712e81b82f527b9f7567d53b6b4c6409156baaf9652534aed61b4"},"schema_version":"1.0"},"canonical_sha256":"cec10873e4406181a835f335fa25406e4a46f38469ba70e952aecd0352c33c4b","source":{"kind":"arxiv","id":"1712.00942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00942","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00942v1","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00942","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z3AQQ47EIBQY","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3AQQ47EIBQYDKBV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3AQQ47E","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Z3AQQ47EIBQYDKBV6M27UJKANZ","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-04T07:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"0065fcea1cf927c44d7bb7d16195105b7891f9e6394d6b858d33139a237794bd","abstract_canon_sha256":"6563bac2d25712e81b82f527b9f7567d53b6b4c6409156baaf9652534aed61b4"},"schema_version":"1.0"},"canonical_sha256":"cec10873e4406181a835f335fa25406e4a46f38469ba70e952aecd0352c33c4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:59.758966Z","signature_b64":"znXsBs4aQaj9YUqP3bOVrpGK5XWrC3/7e5m8Tj+4/SZQsbpBvVk/z1m0GqjURrSHB50RtJWAdhWPM4I5DD9YAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cec10873e4406181a835f335fa25406e4a46f38469ba70e952aecd0352c33c4b","last_reissued_at":"2026-05-17T23:55:59.758121Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:59.758121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00942","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":"2026-05-17T23:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxbJ4XOEJPjH/vUdRfKNAukX+BRxO5WCmflkFgJ3o0Qi2D/aOHNUOuzHLWOxOGLEzEiHMF9KpUbc7WwrRhEZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:43:11.523231Z"},"content_sha256":"f3fc0c428ff302e4ad829a072ed9c8900acc87bd082cd268f1aef90fc79eb8d2","schema_version":"1.0","event_id":"sha256:f3fc0c428ff302e4ad829a072ed9c8900acc87bd082cd268f1aef90fc79eb8d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Z3AQQ47EIBQYDKBV6M27UJKANZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"(Gap/S)ETH Hardness of SVP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Divesh Aggarwal, Noah Stephens-Davidowitz","submitted_at":"2017-12-04T07:50:40Z","abstract_excerpt":"$ \\newcommand{\\problem}[1]{\\ensuremath{\\mathrm{#1}} } \\newcommand{\\SVP}{\\problem{SVP}} \\newcommand{\\ensuremath}[1]{#1} $We prove the following quantitative hardness results for the Shortest Vector Problem in the $\\ell_p$ norm ($\\SVP_p$), where $n$ is the rank of the input lattice.\n  $\\bullet$ For \"almost all\" $p > p_0 \\approx 2.1397$, there no $2^{n/C_p}$-time algorithm for $\\SVP_p$ for some explicit constant $C_p > 0$ unless the (randomized) Strong Exponential Time Hypothesis (SETH) is false.\n  $\\bullet$ For any $p > 2$, there is no $2^{o(n)}$-time algorithm for $\\SVP_p$ unless the (randomize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00942","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":"2026-05-17T23:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BsF2qZ6rATEhcSo7rWgf6KsqiEQVRumPF5nfmNmW4GOky1YAbXs/m6pfYnVGKemhTpUGihd1bI/JOBAmvc1tCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:43:11.523982Z"},"content_sha256":"52e357d1fde7bb572c8a6251e87beda558851048ae8a75bbfd6de817cc2cfd2b","schema_version":"1.0","event_id":"sha256:52e357d1fde7bb572c8a6251e87beda558851048ae8a75bbfd6de817cc2cfd2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3AQQ47EIBQYDKBV6M27UJKANZ/bundle.json","state_url":"https://pith.science/pith/Z3AQQ47EIBQYDKBV6M27UJKANZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3AQQ47EIBQYDKBV6M27UJKANZ/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":"2026-06-10T15:43:11Z","links":{"resolver":"https://pith.science/pith/Z3AQQ47EIBQYDKBV6M27UJKANZ","bundle":"https://pith.science/pith/Z3AQQ47EIBQYDKBV6M27UJKANZ/bundle.json","state":"https://pith.science/pith/Z3AQQ47EIBQYDKBV6M27UJKANZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3AQQ47EIBQYDKBV6M27UJKANZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z3AQQ47EIBQYDKBV6M27UJKANZ","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":"6563bac2d25712e81b82f527b9f7567d53b6b4c6409156baaf9652534aed61b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-04T07:50:40Z","title_canon_sha256":"0065fcea1cf927c44d7bb7d16195105b7891f9e6394d6b858d33139a237794bd"},"schema_version":"1.0","source":{"id":"1712.00942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00942","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00942v1","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00942","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z3AQQ47EIBQY","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3AQQ47EIBQYDKBV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3AQQ47E","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:52e357d1fde7bb572c8a6251e87beda558851048ae8a75bbfd6de817cc2cfd2b","target":"graph","created_at":"2026-05-17T23:55:59Z","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":"$ \\newcommand{\\problem}[1]{\\ensuremath{\\mathrm{#1}} } \\newcommand{\\SVP}{\\problem{SVP}} \\newcommand{\\ensuremath}[1]{#1} $We prove the following quantitative hardness results for the Shortest Vector Problem in the $\\ell_p$ norm ($\\SVP_p$), where $n$ is the rank of the input lattice.\n  $\\bullet$ For \"almost all\" $p > p_0 \\approx 2.1397$, there no $2^{n/C_p}$-time algorithm for $\\SVP_p$ for some explicit constant $C_p > 0$ unless the (randomized) Strong Exponential Time Hypothesis (SETH) is false.\n  $\\bullet$ For any $p > 2$, there is no $2^{o(n)}$-time algorithm for $\\SVP_p$ unless the (randomize","authors_text":"Divesh Aggarwal, Noah Stephens-Davidowitz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-04T07:50:40Z","title":"(Gap/S)ETH Hardness of SVP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00942","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:f3fc0c428ff302e4ad829a072ed9c8900acc87bd082cd268f1aef90fc79eb8d2","target":"record","created_at":"2026-05-17T23:55:59Z","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":"6563bac2d25712e81b82f527b9f7567d53b6b4c6409156baaf9652534aed61b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-04T07:50:40Z","title_canon_sha256":"0065fcea1cf927c44d7bb7d16195105b7891f9e6394d6b858d33139a237794bd"},"schema_version":"1.0","source":{"id":"1712.00942","kind":"arxiv","version":1}},"canonical_sha256":"cec10873e4406181a835f335fa25406e4a46f38469ba70e952aecd0352c33c4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cec10873e4406181a835f335fa25406e4a46f38469ba70e952aecd0352c33c4b","first_computed_at":"2026-05-17T23:55:59.758121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:59.758121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"znXsBs4aQaj9YUqP3bOVrpGK5XWrC3/7e5m8Tj+4/SZQsbpBvVk/z1m0GqjURrSHB50RtJWAdhWPM4I5DD9YAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:59.758966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3fc0c428ff302e4ad829a072ed9c8900acc87bd082cd268f1aef90fc79eb8d2","sha256:52e357d1fde7bb572c8a6251e87beda558851048ae8a75bbfd6de817cc2cfd2b"],"state_sha256":"2e719cb3d0a70704f95f0e3aa083f78cbc90281f5f9eab77361ad88bbf8877d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQJR4Z1OfApfifrEUsLRZRLGw7cFg35tnXWEKnsILo9aOIFs7x6Dfx2qnNVH3O2sMzqDAmarylhpMzmdJyRJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T15:43:11.528684Z","bundle_sha256":"501a9e5f31635332dda6a9452dec4cc5a8f6cc31c55f59191e5883210c1a6193"}}