{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VKMUCYQWSA4IS3ML6AOT3TKVCY","short_pith_number":"pith:VKMUCYQW","canonical_record":{"source":{"id":"1902.10731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-27T19:06:12Z","cross_cats_sorted":["cs.AI","cs.CG","cs.CR","stat.ML"],"title_canon_sha256":"680b7abd98e77976f0c001d5d0a1488fe055a62bfc0e034d670922e7376dcfcd","abstract_canon_sha256":"e4d1cede82ed90687e70088a391a76d8cd0efac5fcd126dc2a0570d7944b4e12"},"schema_version":"1.0"},"canonical_sha256":"aa994162169038896d8bf01d3dcd551616b7121eb05c1a05c6248289be99a8b8","source":{"kind":"arxiv","id":"1902.10731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10731","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10731v1","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10731","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"VKMUCYQWSA4I","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VKMUCYQWSA4IS3ML","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VKMUCYQW","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VKMUCYQWSA4IS3ML6AOT3TKVCY","target":"record","payload":{"canonical_record":{"source":{"id":"1902.10731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-27T19:06:12Z","cross_cats_sorted":["cs.AI","cs.CG","cs.CR","stat.ML"],"title_canon_sha256":"680b7abd98e77976f0c001d5d0a1488fe055a62bfc0e034d670922e7376dcfcd","abstract_canon_sha256":"e4d1cede82ed90687e70088a391a76d8cd0efac5fcd126dc2a0570d7944b4e12"},"schema_version":"1.0"},"canonical_sha256":"aa994162169038896d8bf01d3dcd551616b7121eb05c1a05c6248289be99a8b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:29.867267Z","signature_b64":"yvbEbc4zahabJDLhaS3kc1hz9HxQSc434fwjUEPEOKj32Vhlm2xXMP7J0WUHcxjrJT/r8wCexZouRpIZ9LgXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa994162169038896d8bf01d3dcd551616b7121eb05c1a05c6248289be99a8b8","last_reissued_at":"2026-05-17T23:52:29.866680Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:29.866680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.10731","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":"2026-05-17T23:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBgRuMWCPaaGfiIQ0yiM+ZCxAZLByuueS7PiGLhg5HyAed82gzQwcCQSvhwbdVsxc25KusF3guvZaKqTgA89Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:33:39.132704Z"},"content_sha256":"b82a08b50584b4d8a5f12f4b80f0a3b51eaead3f8496e7c0256ee2f1cfbe0f1d","schema_version":"1.0","event_id":"sha256:b82a08b50584b4d8a5f12f4b80f0a3b51eaead3f8496e7c0256ee2f1cfbe0f1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VKMUCYQWSA4IS3ML6AOT3TKVCY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Private Center Points and Learning of Halfspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CG","cs.CR","stat.ML"],"primary_cat":"cs.LG","authors_text":"Amos Beimel, Kobbi Nissim, Shay Moran, Uri Stemmer","submitted_at":"2019-02-27T19:06:12Z","abstract_excerpt":"We present a private learner for halfspaces over an arbitrary finite domain $X\\subset \\mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\\log^*|X|})$. The building block for this learner is a differentially private algorithm for locating an approximate center point of $m>\\mathrm{poly}(d,2^{\\log^*|X|})$ points -- a high dimensional generalization of the median function. Our construction establishes a relationship between these two problems that is reminiscent of the relation between the median and learning one-dimensional thresholds [Bun et al.\\ FOCS '15]. This relationship suggests that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10731","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":"2026-05-17T23:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZoVqtPwBLuqazkCDt5k4PGFvCjdshBbLgb9+8l6kO6qN4uSaFnzkMuyc+8sImiTlKGF7YGRneL4WTRL2cHcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:33:39.133094Z"},"content_sha256":"6d6490381c35e35d9bfcdd9300b3204da24bf86eeea1dfbeeb2b6794cf190e86","schema_version":"1.0","event_id":"sha256:6d6490381c35e35d9bfcdd9300b3204da24bf86eeea1dfbeeb2b6794cf190e86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKMUCYQWSA4IS3ML6AOT3TKVCY/bundle.json","state_url":"https://pith.science/pith/VKMUCYQWSA4IS3ML6AOT3TKVCY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKMUCYQWSA4IS3ML6AOT3TKVCY/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":"2026-06-01T23:33:39Z","links":{"resolver":"https://pith.science/pith/VKMUCYQWSA4IS3ML6AOT3TKVCY","bundle":"https://pith.science/pith/VKMUCYQWSA4IS3ML6AOT3TKVCY/bundle.json","state":"https://pith.science/pith/VKMUCYQWSA4IS3ML6AOT3TKVCY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKMUCYQWSA4IS3ML6AOT3TKVCY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VKMUCYQWSA4IS3ML6AOT3TKVCY","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":"e4d1cede82ed90687e70088a391a76d8cd0efac5fcd126dc2a0570d7944b4e12","cross_cats_sorted":["cs.AI","cs.CG","cs.CR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-27T19:06:12Z","title_canon_sha256":"680b7abd98e77976f0c001d5d0a1488fe055a62bfc0e034d670922e7376dcfcd"},"schema_version":"1.0","source":{"id":"1902.10731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10731","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10731v1","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10731","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"VKMUCYQWSA4I","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VKMUCYQWSA4IS3ML","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VKMUCYQW","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:6d6490381c35e35d9bfcdd9300b3204da24bf86eeea1dfbeeb2b6794cf190e86","target":"graph","created_at":"2026-05-17T23:52:29Z","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 present a private learner for halfspaces over an arbitrary finite domain $X\\subset \\mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\\log^*|X|})$. The building block for this learner is a differentially private algorithm for locating an approximate center point of $m>\\mathrm{poly}(d,2^{\\log^*|X|})$ points -- a high dimensional generalization of the median function. Our construction establishes a relationship between these two problems that is reminiscent of the relation between the median and learning one-dimensional thresholds [Bun et al.\\ FOCS '15]. This relationship suggests that t","authors_text":"Amos Beimel, Kobbi Nissim, Shay Moran, Uri Stemmer","cross_cats":["cs.AI","cs.CG","cs.CR","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-27T19:06:12Z","title":"Private Center Points and Learning of Halfspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10731","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:b82a08b50584b4d8a5f12f4b80f0a3b51eaead3f8496e7c0256ee2f1cfbe0f1d","target":"record","created_at":"2026-05-17T23:52:29Z","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":"e4d1cede82ed90687e70088a391a76d8cd0efac5fcd126dc2a0570d7944b4e12","cross_cats_sorted":["cs.AI","cs.CG","cs.CR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-27T19:06:12Z","title_canon_sha256":"680b7abd98e77976f0c001d5d0a1488fe055a62bfc0e034d670922e7376dcfcd"},"schema_version":"1.0","source":{"id":"1902.10731","kind":"arxiv","version":1}},"canonical_sha256":"aa994162169038896d8bf01d3dcd551616b7121eb05c1a05c6248289be99a8b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa994162169038896d8bf01d3dcd551616b7121eb05c1a05c6248289be99a8b8","first_computed_at":"2026-05-17T23:52:29.866680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:29.866680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yvbEbc4zahabJDLhaS3kc1hz9HxQSc434fwjUEPEOKj32Vhlm2xXMP7J0WUHcxjrJT/r8wCexZouRpIZ9LgXCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:29.867267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b82a08b50584b4d8a5f12f4b80f0a3b51eaead3f8496e7c0256ee2f1cfbe0f1d","sha256:6d6490381c35e35d9bfcdd9300b3204da24bf86eeea1dfbeeb2b6794cf190e86"],"state_sha256":"1ac9ef07f411545ecdbcc0cf1b434ef1b5065391a3ff6e5888923f1e62f2450b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkQdSYtwILmSgXa/32nf+TCLkBO28dFmOOSLUADAYJ4TRjgbtfcDAa7Q4S49quI8sNN/iTY5UJ4qyeCyc3XpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:33:39.135010Z","bundle_sha256":"b9dae2005a0314f3db8a376c2a63f06c68d709390f31d9ef129172585b93a380"}}