{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WM4N2H4445F6ICYHR6YZ7LUUU6","short_pith_number":"pith:WM4N2H44","canonical_record":{"source":{"id":"1412.7979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-26T19:50:58Z","cross_cats_sorted":[],"title_canon_sha256":"00f3e6de47842281f9540db6f3f020bf477f090ce1455be7569b07dc9029e590","abstract_canon_sha256":"abfee4e8e58f1a05eb2e3e163ee31e79d609cd995eb5c6d87b15827dc53b101f"},"schema_version":"1.0"},"canonical_sha256":"b338dd1f9ce74be40b078fb19fae94a79b133abe73b90a788e04e01db7c991b6","source":{"kind":"arxiv","id":"1412.7979","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7979","created_at":"2026-05-18T02:30:24Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7979v1","created_at":"2026-05-18T02:30:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7979","created_at":"2026-05-18T02:30:24Z"},{"alias_kind":"pith_short_12","alias_value":"WM4N2H4445F6","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WM4N2H4445F6ICYH","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WM4N2H44","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WM4N2H4445F6ICYHR6YZ7LUUU6","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-26T19:50:58Z","cross_cats_sorted":[],"title_canon_sha256":"00f3e6de47842281f9540db6f3f020bf477f090ce1455be7569b07dc9029e590","abstract_canon_sha256":"abfee4e8e58f1a05eb2e3e163ee31e79d609cd995eb5c6d87b15827dc53b101f"},"schema_version":"1.0"},"canonical_sha256":"b338dd1f9ce74be40b078fb19fae94a79b133abe73b90a788e04e01db7c991b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:24.497749Z","signature_b64":"9maQRUQ1ebkmTPsrPsbO9N6cObk5keu3mvrav4G1XoLpX0Mw7naH2E8jNONXKPMD9JgJiA6vHxzbN6JLq7tqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b338dd1f9ce74be40b078fb19fae94a79b133abe73b90a788e04e01db7c991b6","last_reissued_at":"2026-05-18T02:30:24.497255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:24.497255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7979","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":"2026-05-18T02:30:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mqAD0/gas/j9lY5hl2f35osBegBvk4w7ZXuNJYLDIbbUOcNVUJbiGBeTCm7L2nAd9nEfWs0KRbow8lpq5U/4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:03:37.378476Z"},"content_sha256":"fd6581d633b35760ab1b56f3b6230bff889b9c7a09bf8b24d4b03f6166b55693","schema_version":"1.0","event_id":"sha256:fd6581d633b35760ab1b56f3b6230bff889b9c7a09bf8b24d4b03f6166b55693"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WM4N2H4445F6ICYHR6YZ7LUUU6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Lattice Smoothing Parameter Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chris Peikert, Daniel Dadush, Feng-Hao Liu, Kai-Min Chung","submitted_at":"2014-12-26T19:50:58Z","abstract_excerpt":"The smoothing parameter $\\eta_{\\epsilon}(\\mathcal{L})$ of a Euclidean lattice $\\mathcal{L}$, introduced by Micciancio and Regev (FOCS'04; SICOMP'07), is (informally) the smallest amount of Gaussian noise that \"smooths out\" the discrete structure of $\\mathcal{L}$ (up to error $\\epsilon$). It plays a central role in the best known worst-case/average-case reductions for lattice problems, a wealth of lattice-based cryptographic constructions, and (implicitly) the tightest known transference theorems for fundamental lattice quantities.\n  In this work we initiate a study of the complexity of approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7979","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":"2026-05-18T02:30:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFP9JWImgPw2mHEdXIz8+BuzHa7Eb0ehMSMi3anTtte2kgzVUnLoEM8K9/eIHbLy87mrBD5NiWn4x/xHhdvcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:03:37.378985Z"},"content_sha256":"97bca57c0408ff92f0c05f772547ca9dfb86915ea05aca47ce7d0c719281eba9","schema_version":"1.0","event_id":"sha256:97bca57c0408ff92f0c05f772547ca9dfb86915ea05aca47ce7d0c719281eba9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WM4N2H4445F6ICYHR6YZ7LUUU6/bundle.json","state_url":"https://pith.science/pith/WM4N2H4445F6ICYHR6YZ7LUUU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WM4N2H4445F6ICYHR6YZ7LUUU6/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":"2026-05-26T00:03:37Z","links":{"resolver":"https://pith.science/pith/WM4N2H4445F6ICYHR6YZ7LUUU6","bundle":"https://pith.science/pith/WM4N2H4445F6ICYHR6YZ7LUUU6/bundle.json","state":"https://pith.science/pith/WM4N2H4445F6ICYHR6YZ7LUUU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WM4N2H4445F6ICYHR6YZ7LUUU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WM4N2H4445F6ICYHR6YZ7LUUU6","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":"abfee4e8e58f1a05eb2e3e163ee31e79d609cd995eb5c6d87b15827dc53b101f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-26T19:50:58Z","title_canon_sha256":"00f3e6de47842281f9540db6f3f020bf477f090ce1455be7569b07dc9029e590"},"schema_version":"1.0","source":{"id":"1412.7979","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7979","created_at":"2026-05-18T02:30:24Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7979v1","created_at":"2026-05-18T02:30:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7979","created_at":"2026-05-18T02:30:24Z"},{"alias_kind":"pith_short_12","alias_value":"WM4N2H4445F6","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WM4N2H4445F6ICYH","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WM4N2H44","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:97bca57c0408ff92f0c05f772547ca9dfb86915ea05aca47ce7d0c719281eba9","target":"graph","created_at":"2026-05-18T02:30:24Z","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":"The smoothing parameter $\\eta_{\\epsilon}(\\mathcal{L})$ of a Euclidean lattice $\\mathcal{L}$, introduced by Micciancio and Regev (FOCS'04; SICOMP'07), is (informally) the smallest amount of Gaussian noise that \"smooths out\" the discrete structure of $\\mathcal{L}$ (up to error $\\epsilon$). It plays a central role in the best known worst-case/average-case reductions for lattice problems, a wealth of lattice-based cryptographic constructions, and (implicitly) the tightest known transference theorems for fundamental lattice quantities.\n  In this work we initiate a study of the complexity of approxi","authors_text":"Chris Peikert, Daniel Dadush, Feng-Hao Liu, Kai-Min Chung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-26T19:50:58Z","title":"On the Lattice Smoothing Parameter Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7979","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:fd6581d633b35760ab1b56f3b6230bff889b9c7a09bf8b24d4b03f6166b55693","target":"record","created_at":"2026-05-18T02:30:24Z","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":"abfee4e8e58f1a05eb2e3e163ee31e79d609cd995eb5c6d87b15827dc53b101f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-26T19:50:58Z","title_canon_sha256":"00f3e6de47842281f9540db6f3f020bf477f090ce1455be7569b07dc9029e590"},"schema_version":"1.0","source":{"id":"1412.7979","kind":"arxiv","version":1}},"canonical_sha256":"b338dd1f9ce74be40b078fb19fae94a79b133abe73b90a788e04e01db7c991b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b338dd1f9ce74be40b078fb19fae94a79b133abe73b90a788e04e01db7c991b6","first_computed_at":"2026-05-18T02:30:24.497255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:24.497255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9maQRUQ1ebkmTPsrPsbO9N6cObk5keu3mvrav4G1XoLpX0Mw7naH2E8jNONXKPMD9JgJiA6vHxzbN6JLq7tqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:24.497749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7979","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd6581d633b35760ab1b56f3b6230bff889b9c7a09bf8b24d4b03f6166b55693","sha256:97bca57c0408ff92f0c05f772547ca9dfb86915ea05aca47ce7d0c719281eba9"],"state_sha256":"fc3e5a37ac45027423c6bcc786744aa343c05af6216821cf8fbb21fecfd4e828"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8cS8XBX1YZ5Vo07wFhoytlSK7y9TX3ovNL+USknxnPvbU8jD28uCz73Tu4tpZNgtnPlQQHygL8FpU540fIfZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:03:37.381334Z","bundle_sha256":"d5246b36fb0488f17c06287d23da28edec4d83987affc4a55048b99843c81607"}}