{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V3K5XM5MIVNXFFRO7SKIHRYVEP","short_pith_number":"pith:V3K5XM5M","canonical_record":{"source":{"id":"1707.01242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","cross_cats_sorted":["cs.CC","cs.DS"],"title_canon_sha256":"8fbfcbc4f9b760d6ded99670fd5065af8189be2e4c96060281775e0ab5ccccc4","abstract_canon_sha256":"2b11d01ff4f97cf3d56efc88d414e76f7630b73a40facfb342809def6aa45001"},"schema_version":"1.0"},"canonical_sha256":"aed5dbb3ac455b72962efc9483c71523eb37cf8f0ea161a0d572a8d3919e68aa","source":{"kind":"arxiv","id":"1707.01242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01242","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01242v1","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01242","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"V3K5XM5MIVNX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V3K5XM5MIVNXFFRO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V3K5XM5M","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V3K5XM5MIVNXFFRO7SKIHRYVEP","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","cross_cats_sorted":["cs.CC","cs.DS"],"title_canon_sha256":"8fbfcbc4f9b760d6ded99670fd5065af8189be2e4c96060281775e0ab5ccccc4","abstract_canon_sha256":"2b11d01ff4f97cf3d56efc88d414e76f7630b73a40facfb342809def6aa45001"},"schema_version":"1.0"},"canonical_sha256":"aed5dbb3ac455b72962efc9483c71523eb37cf8f0ea161a0d572a8d3919e68aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.339768Z","signature_b64":"OjsH0/LTnqHu9SsijiIKMjWOk4gVDo1ChQXMVdtvavmsGmEwgS7+siDVxGft3bXjRcgfhrLPVT0ZsLHBZUKSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aed5dbb3ac455b72962efc9483c71523eb37cf8f0ea161a0d572a8d3919e68aa","last_reissued_at":"2026-05-18T00:40:53.339352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.339352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01242","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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xal0lkJkBhMQWTFNgd1ne5xgMGjVX1HJ33CQ0FvIgiHdlKyFrzvnF5h6eKSsS8VV5pPHntAqVqMGPUtHDMkMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:51:53.200101Z"},"content_sha256":"00b6026e58c8f830e43622a9bf7db9e00164fd226ab41a2cc967d8a937ce00e0","schema_version":"1.0","event_id":"sha256:00b6026e58c8f830e43622a9bf7db9e00164fd226ab41a2cc967d8a937ce00e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V3K5XM5MIVNXFFRO7SKIHRYVEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Geometric Concepts with Nasty Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.LG","authors_text":"Alistair Stewart, Daniel M. Kane, Ilias Diakonikolas","submitted_at":"2017-07-05T07:41:40Z","abstract_excerpt":"We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first polynomial-time PAC learning algorithms for these concept classes with dimension-independent error guarantees in the presence of nasty noise under the Gaussian distribution. In the nasty noise model, an omniscient adversary can arbitrarily corrupt a small fraction of both the unlabeled data points and their labels. This model generalizes well-studied noise mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01242","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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xaMtC8VG4ZqkvkOuthnvn0F5S7obdbjpcOG12xo47R9bm5c/rmDNRjyQOxbkxDk1BTZ5+EqsAW6dMUd8+HXkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:51:53.200472Z"},"content_sha256":"b7d04ba4e8905182d3d061557e6fabf0f5b0e801508862ccacdab5a47de866ec","schema_version":"1.0","event_id":"sha256:b7d04ba4e8905182d3d061557e6fabf0f5b0e801508862ccacdab5a47de866ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3K5XM5MIVNXFFRO7SKIHRYVEP/bundle.json","state_url":"https://pith.science/pith/V3K5XM5MIVNXFFRO7SKIHRYVEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3K5XM5MIVNXFFRO7SKIHRYVEP/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":"2026-06-05T17:51:53Z","links":{"resolver":"https://pith.science/pith/V3K5XM5MIVNXFFRO7SKIHRYVEP","bundle":"https://pith.science/pith/V3K5XM5MIVNXFFRO7SKIHRYVEP/bundle.json","state":"https://pith.science/pith/V3K5XM5MIVNXFFRO7SKIHRYVEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3K5XM5MIVNXFFRO7SKIHRYVEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V3K5XM5MIVNXFFRO7SKIHRYVEP","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":"2b11d01ff4f97cf3d56efc88d414e76f7630b73a40facfb342809def6aa45001","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","title_canon_sha256":"8fbfcbc4f9b760d6ded99670fd5065af8189be2e4c96060281775e0ab5ccccc4"},"schema_version":"1.0","source":{"id":"1707.01242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01242","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01242v1","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01242","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"V3K5XM5MIVNX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V3K5XM5MIVNXFFRO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V3K5XM5M","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:b7d04ba4e8905182d3d061557e6fabf0f5b0e801508862ccacdab5a47de866ec","target":"graph","created_at":"2026-05-18T00:40:53Z","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":"We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first polynomial-time PAC learning algorithms for these concept classes with dimension-independent error guarantees in the presence of nasty noise under the Gaussian distribution. In the nasty noise model, an omniscient adversary can arbitrarily corrupt a small fraction of both the unlabeled data points and their labels. This model generalizes well-studied noise mod","authors_text":"Alistair Stewart, Daniel M. Kane, Ilias Diakonikolas","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","title":"Learning Geometric Concepts with Nasty Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01242","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":"sha256:00b6026e58c8f830e43622a9bf7db9e00164fd226ab41a2cc967d8a937ce00e0","target":"record","created_at":"2026-05-18T00:40:53Z","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":"2b11d01ff4f97cf3d56efc88d414e76f7630b73a40facfb342809def6aa45001","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","title_canon_sha256":"8fbfcbc4f9b760d6ded99670fd5065af8189be2e4c96060281775e0ab5ccccc4"},"schema_version":"1.0","source":{"id":"1707.01242","kind":"arxiv","version":1}},"canonical_sha256":"aed5dbb3ac455b72962efc9483c71523eb37cf8f0ea161a0d572a8d3919e68aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aed5dbb3ac455b72962efc9483c71523eb37cf8f0ea161a0d572a8d3919e68aa","first_computed_at":"2026-05-18T00:40:53.339352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:53.339352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OjsH0/LTnqHu9SsijiIKMjWOk4gVDo1ChQXMVdtvavmsGmEwgS7+siDVxGft3bXjRcgfhrLPVT0ZsLHBZUKSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:53.339768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00b6026e58c8f830e43622a9bf7db9e00164fd226ab41a2cc967d8a937ce00e0","sha256:b7d04ba4e8905182d3d061557e6fabf0f5b0e801508862ccacdab5a47de866ec"],"state_sha256":"2c1e931d3531516c4eb7c32cd4f3f55ed5c62f7cd76a34b2b80ee59659853c9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fcw5BcyFdtph87/AH6V5D2jftVhuQa9a1XQEDNkk4vP+HKxML9MK1vjcXDyIeEVVeuOsFKeCgfFKhs/ryU0OBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T17:51:53.202738Z","bundle_sha256":"8fa44bb84b57d7fc421d76554c2975260190b8c8e3eb7e5e09ef4aac2342b945"}}