{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2X7Y3U247NWDICR7UEDAWSEIEL","short_pith_number":"pith:2X7Y3U24","canonical_record":{"source":{"id":"1411.6299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-23T21:19:14Z","cross_cats_sorted":[],"title_canon_sha256":"0382e14d53fe33be7b252ff7787f6122c253d9159bbae3a7979b7773948c3261","abstract_canon_sha256":"c47ce9177a128bb32aece150817465d7a863fc433a9a752037b8bc716fea58a3"},"schema_version":"1.0"},"canonical_sha256":"d5ff8dd35cfb6c340a3fa1060b488822c7b5edb621918de3e0718975ee578340","source":{"kind":"arxiv","id":"1411.6299","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6299","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6299v2","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6299","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"2X7Y3U247NWD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2X7Y3U247NWDICR7","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2X7Y3U24","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2X7Y3U247NWDICR7UEDAWSEIEL","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-23T21:19:14Z","cross_cats_sorted":[],"title_canon_sha256":"0382e14d53fe33be7b252ff7787f6122c253d9159bbae3a7979b7773948c3261","abstract_canon_sha256":"c47ce9177a128bb32aece150817465d7a863fc433a9a752037b8bc716fea58a3"},"schema_version":"1.0"},"canonical_sha256":"d5ff8dd35cfb6c340a3fa1060b488822c7b5edb621918de3e0718975ee578340","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:12.369790Z","signature_b64":"EeyTdhGsibB6zFlwo8E/Rj842hecSH9GklQBXZEjthB3qLGi3yG4qSM1x3VURf1PEE7pJ0z4La7/BxjcRbc0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5ff8dd35cfb6c340a3fa1060b488822c7b5edb621918de3e0718975ee578340","last_reissued_at":"2026-05-18T02:20:12.369421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:12.369421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6299","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":"2026-05-18T02:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a4KCUL0KcMYplvEXdw5MD2KwuTkqbEMP+0QwaHM3vNLFUzG7c6BXMj4gloK3lV/mm2adsidJNhOwXcKJLj3LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:06:09.945359Z"},"content_sha256":"84f7da2cfe8b4df00fef003083b1f9155706c3f11cc1c9227a99326c44329b81","schema_version":"1.0","event_id":"sha256:84f7da2cfe8b4df00fef003083b1f9155706c3f11cc1c9227a99326c44329b81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2X7Y3U247NWDICR7UEDAWSEIEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost Optimal Pseudorandom Generators for Spherical Caps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Pravesh Kothari, Raghu Meka","submitted_at":"2014-11-23T21:19:14Z","abstract_excerpt":"Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere, aka spherical caps, which besides being interesting and basic geometric objects, also arise frequently in the analysis of various randomized algorithms (e.g., randomized rounding). We give an explicit PRG which fools spherical caps within error $\\epsilon$ and has an almost optimal seed-length of $O(\\log n + \\log(1/\\epsilon) \\cdot \\log\\log(1/\\epsilon))$. For"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6299","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":"2026-05-18T02:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C8EKTjHy8iJjYmfLdUV3gf5Vt+mlZ/eyOoFPIVEQ33Kz4EJ2u6dMS04ffSBoWgCGgpvNs9eaWllcAXFv1kG4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:06:09.945710Z"},"content_sha256":"3a00042b1469f847fb1d5b6b73e88ad745b42e16b54b9fa5e8496f816cdca9ce","schema_version":"1.0","event_id":"sha256:3a00042b1469f847fb1d5b6b73e88ad745b42e16b54b9fa5e8496f816cdca9ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2X7Y3U247NWDICR7UEDAWSEIEL/bundle.json","state_url":"https://pith.science/pith/2X7Y3U247NWDICR7UEDAWSEIEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2X7Y3U247NWDICR7UEDAWSEIEL/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":"2026-05-28T09:06:09Z","links":{"resolver":"https://pith.science/pith/2X7Y3U247NWDICR7UEDAWSEIEL","bundle":"https://pith.science/pith/2X7Y3U247NWDICR7UEDAWSEIEL/bundle.json","state":"https://pith.science/pith/2X7Y3U247NWDICR7UEDAWSEIEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2X7Y3U247NWDICR7UEDAWSEIEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2X7Y3U247NWDICR7UEDAWSEIEL","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":"c47ce9177a128bb32aece150817465d7a863fc433a9a752037b8bc716fea58a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-23T21:19:14Z","title_canon_sha256":"0382e14d53fe33be7b252ff7787f6122c253d9159bbae3a7979b7773948c3261"},"schema_version":"1.0","source":{"id":"1411.6299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6299","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6299v2","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6299","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"2X7Y3U247NWD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2X7Y3U247NWDICR7","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2X7Y3U24","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:3a00042b1469f847fb1d5b6b73e88ad745b42e16b54b9fa5e8496f816cdca9ce","target":"graph","created_at":"2026-05-18T02:20:12Z","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":"Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere, aka spherical caps, which besides being interesting and basic geometric objects, also arise frequently in the analysis of various randomized algorithms (e.g., randomized rounding). We give an explicit PRG which fools spherical caps within error $\\epsilon$ and has an almost optimal seed-length of $O(\\log n + \\log(1/\\epsilon) \\cdot \\log\\log(1/\\epsilon))$. For","authors_text":"Pravesh Kothari, Raghu Meka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-23T21:19:14Z","title":"Almost Optimal Pseudorandom Generators for Spherical Caps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6299","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":"sha256:84f7da2cfe8b4df00fef003083b1f9155706c3f11cc1c9227a99326c44329b81","target":"record","created_at":"2026-05-18T02:20:12Z","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":"c47ce9177a128bb32aece150817465d7a863fc433a9a752037b8bc716fea58a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-23T21:19:14Z","title_canon_sha256":"0382e14d53fe33be7b252ff7787f6122c253d9159bbae3a7979b7773948c3261"},"schema_version":"1.0","source":{"id":"1411.6299","kind":"arxiv","version":2}},"canonical_sha256":"d5ff8dd35cfb6c340a3fa1060b488822c7b5edb621918de3e0718975ee578340","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5ff8dd35cfb6c340a3fa1060b488822c7b5edb621918de3e0718975ee578340","first_computed_at":"2026-05-18T02:20:12.369421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:12.369421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EeyTdhGsibB6zFlwo8E/Rj842hecSH9GklQBXZEjthB3qLGi3yG4qSM1x3VURf1PEE7pJ0z4La7/BxjcRbc0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:12.369790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84f7da2cfe8b4df00fef003083b1f9155706c3f11cc1c9227a99326c44329b81","sha256:3a00042b1469f847fb1d5b6b73e88ad745b42e16b54b9fa5e8496f816cdca9ce"],"state_sha256":"71af574ea4a8e914707ae7f68f051fa0147e8e645839679a7cd69018ac323160"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8tFwU/tkoAf7+vs0PpEgN+9xSnaNZQWpTcqRmJg+djYm6GSSRcgR+HiU83ATswk2+8A67Us2vrj4I+5mSoVDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:06:09.947673Z","bundle_sha256":"e2e8be2eb068c845e3eff58328cff8903b5729502ea7aad5ec838af5813a1185"}}