{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:3EZIT3SABUEH7JWNSIA5JQIBCB","short_pith_number":"pith:3EZIT3SA","canonical_record":{"source":{"id":"2405.11454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-19T05:39:46Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"c60736565be94b771c54a09d31650a4769b74dc2b3f2041d07fb618e00efb4a5","abstract_canon_sha256":"0dbe17318bca8bc46268cf69c017c05f607ad1665785b406b889ab0c2ae1c837"},"schema_version":"1.0"},"canonical_sha256":"d93289ee400d087fa6cd9201d4c101107b01b0abea1dd1e0eb5cfd70a7833952","source":{"kind":"arxiv","id":"2405.11454","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.11454","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"2405.11454v3","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11454","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"3EZIT3SABUEH","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_16","alias_value":"3EZIT3SABUEH7JWN","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_8","alias_value":"3EZIT3SA","created_at":"2026-06-26T01:15:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:3EZIT3SABUEH7JWNSIA5JQIBCB","target":"record","payload":{"canonical_record":{"source":{"id":"2405.11454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-19T05:39:46Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"c60736565be94b771c54a09d31650a4769b74dc2b3f2041d07fb618e00efb4a5","abstract_canon_sha256":"0dbe17318bca8bc46268cf69c017c05f607ad1665785b406b889ab0c2ae1c837"},"schema_version":"1.0"},"canonical_sha256":"d93289ee400d087fa6cd9201d4c101107b01b0abea1dd1e0eb5cfd70a7833952","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:42.232974Z","signature_b64":"pohXx92yY1NXSkpN22VqPmqfPLIUAa06eVmJbsYJ9sDIrlLttmh9UAS5LSQUCZj792X5TRG1DJ1xvZ//gA8LCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d93289ee400d087fa6cd9201d4c101107b01b0abea1dd1e0eb5cfd70a7833952","last_reissued_at":"2026-06-26T01:15:42.232467Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:42.232467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.11454","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-26T01:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4OwuhvvlCrnRiY3XrW6cpSTqJrzenqVTHyTBwnQ2t5/l8hTEANNysibCqFObGvIgDnN0S8XEbXMzuJfwoq2/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:08:53.120722Z"},"content_sha256":"59b98bc1e707d4f23f449f8aa6a9c8321392f412f32b4245778f718beb3c1a1e","schema_version":"1.0","event_id":"sha256:59b98bc1e707d4f23f449f8aa6a9c8321392f412f32b4245778f718beb3c1a1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:3EZIT3SABUEH7JWNSIA5JQIBCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient Testing and Estimation by Comparisons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"cs.LG","authors_text":"Chenyi Zhang, Helin Wang, Tongyang Li, Xiwen Tao, Yexin Zhang","submitted_at":"2024-05-19T05:39:46Z","abstract_excerpt":"We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates which one has the larger function value. For any smooth $f\\colon\\mathbb R^n\\to\\mathbb R$, $\\mathbf{x}\\in\\mathbb R^n$, and $\\varepsilon>0$, we design a gradient testing algorithm that determines whether the normalized gradient $\\nabla f(\\mathbf{x})/\\|\\nabla f(\\mathbf{x})\\|$ is $\\varepsilon$-close or $2\\varepsilon$-far from a given unit vector $\\mathbf{v}$ using $O(1)$ queries, as well as a gradient estimation algorithm that outputs an $\\varepsilon$-estimate of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11454","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.11454/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-26T01:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTrnNGxkkCVYxF9zKWoy9dBEd0gs3TDPl4P0O2R54U75tLA8My8FS/sK05VDVEj/TijwaeHBmoyVO6aOodefDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:08:53.121346Z"},"content_sha256":"848ee90a579e5864ef30dd41258a8a5c7399d0d07fbc90e26b5a3cf14efba78f","schema_version":"1.0","event_id":"sha256:848ee90a579e5864ef30dd41258a8a5c7399d0d07fbc90e26b5a3cf14efba78f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3EZIT3SABUEH7JWNSIA5JQIBCB/bundle.json","state_url":"https://pith.science/pith/3EZIT3SABUEH7JWNSIA5JQIBCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3EZIT3SABUEH7JWNSIA5JQIBCB/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":"2026-07-01T21:08:53Z","links":{"resolver":"https://pith.science/pith/3EZIT3SABUEH7JWNSIA5JQIBCB","bundle":"https://pith.science/pith/3EZIT3SABUEH7JWNSIA5JQIBCB/bundle.json","state":"https://pith.science/pith/3EZIT3SABUEH7JWNSIA5JQIBCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3EZIT3SABUEH7JWNSIA5JQIBCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3EZIT3SABUEH7JWNSIA5JQIBCB","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":"0dbe17318bca8bc46268cf69c017c05f607ad1665785b406b889ab0c2ae1c837","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-19T05:39:46Z","title_canon_sha256":"c60736565be94b771c54a09d31650a4769b74dc2b3f2041d07fb618e00efb4a5"},"schema_version":"1.0","source":{"id":"2405.11454","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.11454","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"2405.11454v3","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11454","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"3EZIT3SABUEH","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_16","alias_value":"3EZIT3SABUEH7JWN","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_8","alias_value":"3EZIT3SA","created_at":"2026-06-26T01:15:42Z"}],"graph_snapshots":[{"event_id":"sha256:848ee90a579e5864ef30dd41258a8a5c7399d0d07fbc90e26b5a3cf14efba78f","target":"graph","created_at":"2026-06-26T01:15:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.11454/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates which one has the larger function value. For any smooth $f\\colon\\mathbb R^n\\to\\mathbb R$, $\\mathbf{x}\\in\\mathbb R^n$, and $\\varepsilon>0$, we design a gradient testing algorithm that determines whether the normalized gradient $\\nabla f(\\mathbf{x})/\\|\\nabla f(\\mathbf{x})\\|$ is $\\varepsilon$-close or $2\\varepsilon$-far from a given unit vector $\\mathbf{v}$ using $O(1)$ queries, as well as a gradient estimation algorithm that outputs an $\\varepsilon$-estimate of $","authors_text":"Chenyi Zhang, Helin Wang, Tongyang Li, Xiwen Tao, Yexin Zhang","cross_cats":["cs.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-19T05:39:46Z","title":"Gradient Testing and Estimation by Comparisons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11454","kind":"arxiv","version":3},"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":"sha256:59b98bc1e707d4f23f449f8aa6a9c8321392f412f32b4245778f718beb3c1a1e","target":"record","created_at":"2026-06-26T01:15:42Z","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":"0dbe17318bca8bc46268cf69c017c05f607ad1665785b406b889ab0c2ae1c837","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-19T05:39:46Z","title_canon_sha256":"c60736565be94b771c54a09d31650a4769b74dc2b3f2041d07fb618e00efb4a5"},"schema_version":"1.0","source":{"id":"2405.11454","kind":"arxiv","version":3}},"canonical_sha256":"d93289ee400d087fa6cd9201d4c101107b01b0abea1dd1e0eb5cfd70a7833952","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d93289ee400d087fa6cd9201d4c101107b01b0abea1dd1e0eb5cfd70a7833952","first_computed_at":"2026-06-26T01:15:42.232467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:42.232467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pohXx92yY1NXSkpN22VqPmqfPLIUAa06eVmJbsYJ9sDIrlLttmh9UAS5LSQUCZj792X5TRG1DJ1xvZ//gA8LCA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:42.232974Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.11454","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59b98bc1e707d4f23f449f8aa6a9c8321392f412f32b4245778f718beb3c1a1e","sha256:848ee90a579e5864ef30dd41258a8a5c7399d0d07fbc90e26b5a3cf14efba78f"],"state_sha256":"9bf1f8a2cbe32eff671e842d012c30cfbf66e70197c897680d3b7d3e3c651ddb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dn8nbUt/oqNcaTPGz6s9lXGCcvQ7SJkJHZw9W9APu9KDMnQJqvKAlxlWacUURhluQ0nvB5gZOCdDepTPhIVbCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:08:53.123453Z","bundle_sha256":"e3684e56919b015a5c2611668bd82931758d7f6d9686e92f56d826bdb4fd6427"}}