{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KOBYFY7DGWSNQ355JRYUTSSH3T","short_pith_number":"pith:KOBYFY7D","canonical_record":{"source":{"id":"1312.7567","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-12-29T18:13:41Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"851652a0df8290c11c6fa7a994c5af4f86fa7bdc9d08ceaec7480a053c1ccc14","abstract_canon_sha256":"6f07a769fec4e411d288f58aa8622bcb74b13e4f2da7e4d80fe5e563c5c7e2bf"},"schema_version":"1.0"},"canonical_sha256":"538382e3e335a4d86fbd4c7149ca47dce244ebcbac9952c1008121eb91322a4f","source":{"kind":"arxiv","id":"1312.7567","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7567","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7567v1","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7567","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"KOBYFY7DGWSN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KOBYFY7DGWSNQ355","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KOBYFY7D","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KOBYFY7DGWSNQ355JRYUTSSH3T","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7567","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-12-29T18:13:41Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"851652a0df8290c11c6fa7a994c5af4f86fa7bdc9d08ceaec7480a053c1ccc14","abstract_canon_sha256":"6f07a769fec4e411d288f58aa8622bcb74b13e4f2da7e4d80fe5e563c5c7e2bf"},"schema_version":"1.0"},"canonical_sha256":"538382e3e335a4d86fbd4c7149ca47dce244ebcbac9952c1008121eb91322a4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:43.019468Z","signature_b64":"evj+6XQdO5A9u0ePz1a36P6nBnQ0oqJBH8o788L1aYosRGVsBVv8uaRafZCJx6sN+ER7OHdm5qlcPU1D+8QeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"538382e3e335a4d86fbd4c7149ca47dce244ebcbac9952c1008121eb91322a4f","last_reissued_at":"2026-05-18T03:03:43.018702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:43.018702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7567","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":"2026-05-18T03:03:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6sYUh51oi9wB8D9u5XocswdOd+m2d7R7zp4gD9+LEzqyL4PWM9d5ICiZgxDlynYQpRDQsNv4GSwSTN7b85naCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T10:50:22.579014Z"},"content_sha256":"b92edd145fc6c32e5b803c42c81c7a4b2e031a13e7eaf0db0127851117e3f649","schema_version":"1.0","event_id":"sha256:b92edd145fc6c32e5b803c42c81c7a4b2e031a13e7eaf0db0127851117e3f649"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KOBYFY7DGWSNQ355JRYUTSSH3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonparametric Inference For Density Modes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ME","authors_text":"Christopher Genovese, Isabella Verdinelli, Larry Wasserman, Marco Perone-Pacifico","submitted_at":"2013-12-29T18:13:41Z","abstract_excerpt":"We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a data-splitting approach in which potential modes are identified using the first half of the data and inference is done with the second half of the data. To get valid confidence sets for the eigenvalues, we use a bootstrap based on an elementary-symmetric-polynomial (ESP) transformation. This leads to valid bootstrap confidence sets regardless of any multiplicities in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7567","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":"2026-05-18T03:03:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OdoUXXnvC9GNDay9ZinVBtlS6b7QNzVfBQuUvUFbymL1q79re+REEQQnaKcK9+nKs0nZWPrY/vURgLq2iNRuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T10:50:22.579375Z"},"content_sha256":"819bf78875df34c9fb5bad7984e673c02b3338a546d1a80f274abd82ec10698f","schema_version":"1.0","event_id":"sha256:819bf78875df34c9fb5bad7984e673c02b3338a546d1a80f274abd82ec10698f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOBYFY7DGWSNQ355JRYUTSSH3T/bundle.json","state_url":"https://pith.science/pith/KOBYFY7DGWSNQ355JRYUTSSH3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOBYFY7DGWSNQ355JRYUTSSH3T/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":"2026-05-20T10:50:22Z","links":{"resolver":"https://pith.science/pith/KOBYFY7DGWSNQ355JRYUTSSH3T","bundle":"https://pith.science/pith/KOBYFY7DGWSNQ355JRYUTSSH3T/bundle.json","state":"https://pith.science/pith/KOBYFY7DGWSNQ355JRYUTSSH3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOBYFY7DGWSNQ355JRYUTSSH3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KOBYFY7DGWSNQ355JRYUTSSH3T","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":"6f07a769fec4e411d288f58aa8622bcb74b13e4f2da7e4d80fe5e563c5c7e2bf","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-12-29T18:13:41Z","title_canon_sha256":"851652a0df8290c11c6fa7a994c5af4f86fa7bdc9d08ceaec7480a053c1ccc14"},"schema_version":"1.0","source":{"id":"1312.7567","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7567","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7567v1","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7567","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"KOBYFY7DGWSN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KOBYFY7DGWSNQ355","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KOBYFY7D","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:819bf78875df34c9fb5bad7984e673c02b3338a546d1a80f274abd82ec10698f","target":"graph","created_at":"2026-05-18T03:03:43Z","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 derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a data-splitting approach in which potential modes are identified using the first half of the data and inference is done with the second half of the data. To get valid confidence sets for the eigenvalues, we use a bootstrap based on an elementary-symmetric-polynomial (ESP) transformation. This leads to valid bootstrap confidence sets regardless of any multiplicities in ","authors_text":"Christopher Genovese, Isabella Verdinelli, Larry Wasserman, Marco Perone-Pacifico","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-12-29T18:13:41Z","title":"Nonparametric Inference For Density Modes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7567","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:b92edd145fc6c32e5b803c42c81c7a4b2e031a13e7eaf0db0127851117e3f649","target":"record","created_at":"2026-05-18T03:03:43Z","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":"6f07a769fec4e411d288f58aa8622bcb74b13e4f2da7e4d80fe5e563c5c7e2bf","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-12-29T18:13:41Z","title_canon_sha256":"851652a0df8290c11c6fa7a994c5af4f86fa7bdc9d08ceaec7480a053c1ccc14"},"schema_version":"1.0","source":{"id":"1312.7567","kind":"arxiv","version":1}},"canonical_sha256":"538382e3e335a4d86fbd4c7149ca47dce244ebcbac9952c1008121eb91322a4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"538382e3e335a4d86fbd4c7149ca47dce244ebcbac9952c1008121eb91322a4f","first_computed_at":"2026-05-18T03:03:43.018702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:43.018702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"evj+6XQdO5A9u0ePz1a36P6nBnQ0oqJBH8o788L1aYosRGVsBVv8uaRafZCJx6sN+ER7OHdm5qlcPU1D+8QeDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:43.019468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7567","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b92edd145fc6c32e5b803c42c81c7a4b2e031a13e7eaf0db0127851117e3f649","sha256:819bf78875df34c9fb5bad7984e673c02b3338a546d1a80f274abd82ec10698f"],"state_sha256":"71cb0f1cc37b847ec794120a0ccc52f768045c321fb8b86485eac385f6b08bf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5y5L0mu2p3DYlTtCxFossqqs4EiszptAuG3vjT8vRDGTFAkNhT9oYYoq2GbX+M2Y1uwAoLSEOMAMjVbjyvCDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T10:50:22.581243Z","bundle_sha256":"26ae9e010cbb2bbefce4f4c6d8fdf8092f578e3e4374e81d4cec63dd3ce87822"}}