{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:AWTNDYHIABYKNZTEI4AN6M46IJ","short_pith_number":"pith:AWTNDYHI","canonical_record":{"source":{"id":"0812.0933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2008-12-04T13:34:26Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"86bf28d1d44194c309bc816625f107f0299ffde48879c65e62fc6f1115bffbe1","abstract_canon_sha256":"0e167cbb2327460a21639a4c4850cf9b34bd6214b57f539acd114e656ae8840f"},"schema_version":"1.0"},"canonical_sha256":"05a6d1e0e80070a6e6644700df339e427bdaba01d59ba96fae7913628b32adf7","source":{"kind":"arxiv","id":"0812.0933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0933","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0933v1","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0933","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"AWTNDYHIABYK","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"pith_short_16","alias_value":"AWTNDYHIABYKNZTE","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"pith_short_8","alias_value":"AWTNDYHI","created_at":"2026-07-04T15:33:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:AWTNDYHIABYKNZTEI4AN6M46IJ","target":"record","payload":{"canonical_record":{"source":{"id":"0812.0933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2008-12-04T13:34:26Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"86bf28d1d44194c309bc816625f107f0299ffde48879c65e62fc6f1115bffbe1","abstract_canon_sha256":"0e167cbb2327460a21639a4c4850cf9b34bd6214b57f539acd114e656ae8840f"},"schema_version":"1.0"},"canonical_sha256":"05a6d1e0e80070a6e6644700df339e427bdaba01d59ba96fae7913628b32adf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:33:23.339166Z","signature_b64":"XsKLvXebOae33ZnLw77q9BwB5si/clPcPzzW4xgH6TMA7TTLgljtww7Zp7RG++z60n4YSo81bFhk9BZym/BpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05a6d1e0e80070a6e6644700df339e427bdaba01d59ba96fae7913628b32adf7","last_reissued_at":"2026-07-04T15:33:23.338761Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:33:23.338761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.0933","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":"2026-07-04T15:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkmshW7k0E7nNrc2uCSmFkzkxbpnOVKfuADli6PmSlvAHZGepikjg8TtJ48hVCz4aRP+WyfzTILT5O2+TB6sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T15:01:21.039934Z"},"content_sha256":"5ab32ff6a9f35c7fa83ae65142c3971eae066227a31cb197036574631206d028","schema_version":"1.0","event_id":"sha256:5ab32ff6a9f35c7fa83ae65142c3971eae066227a31cb197036574631206d028"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:AWTNDYHIABYKNZTEI4AN6M46IJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decision trees are PAC-learnable from most product distributions: a smoothed analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.LG","authors_text":"Adam Tauman Kalai, Shang-Hua Teng","submitted_at":"2008-12-04T13:34:26Z","abstract_excerpt":"We consider the problem of PAC-learning decision trees, i.e., learning a decision tree over the n-dimensional hypercube from independent random labeled examples. Despite significant effort, no polynomial-time algorithm is known for learning polynomial-sized decision trees (even trees of any super-constant size), even when examples are assumed to be drawn from the uniform distribution on {0,1}^n. We give an algorithm that learns arbitrary polynomial-sized decision trees for {\\em most product distributions}. In particular, consider a random product distribution where the bias of each bit is chos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0933","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0812.0933/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":"2026-07-04T15:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGdRTMuB5Vatqx3j+hHLBjncdutPgzAv1lAMIX30NEhR7tSBThMV/TuWO7j9ViW59+ddagJVeNCE9+RtCUMfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T15:01:21.040600Z"},"content_sha256":"afad1f72d4434da61b1b3c81c642b8bc16405f81247ea3e00663f9bb1fcbb53d","schema_version":"1.0","event_id":"sha256:afad1f72d4434da61b1b3c81c642b8bc16405f81247ea3e00663f9bb1fcbb53d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWTNDYHIABYKNZTEI4AN6M46IJ/bundle.json","state_url":"https://pith.science/pith/AWTNDYHIABYKNZTEI4AN6M46IJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWTNDYHIABYKNZTEI4AN6M46IJ/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":"2026-08-15T15:01:21Z","links":{"resolver":"https://pith.science/pith/AWTNDYHIABYKNZTEI4AN6M46IJ","bundle":"https://pith.science/pith/AWTNDYHIABYKNZTEI4AN6M46IJ/bundle.json","state":"https://pith.science/pith/AWTNDYHIABYKNZTEI4AN6M46IJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWTNDYHIABYKNZTEI4AN6M46IJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:AWTNDYHIABYKNZTEI4AN6M46IJ","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":"0e167cbb2327460a21639a4c4850cf9b34bd6214b57f539acd114e656ae8840f","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2008-12-04T13:34:26Z","title_canon_sha256":"86bf28d1d44194c309bc816625f107f0299ffde48879c65e62fc6f1115bffbe1"},"schema_version":"1.0","source":{"id":"0812.0933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0933","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0933v1","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0933","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"AWTNDYHIABYK","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"pith_short_16","alias_value":"AWTNDYHIABYKNZTE","created_at":"2026-07-04T15:33:23Z"},{"alias_kind":"pith_short_8","alias_value":"AWTNDYHI","created_at":"2026-07-04T15:33:23Z"}],"graph_snapshots":[{"event_id":"sha256:afad1f72d4434da61b1b3c81c642b8bc16405f81247ea3e00663f9bb1fcbb53d","target":"graph","created_at":"2026-07-04T15:33:23Z","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/0812.0933/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of PAC-learning decision trees, i.e., learning a decision tree over the n-dimensional hypercube from independent random labeled examples. Despite significant effort, no polynomial-time algorithm is known for learning polynomial-sized decision trees (even trees of any super-constant size), even when examples are assumed to be drawn from the uniform distribution on {0,1}^n. We give an algorithm that learns arbitrary polynomial-sized decision trees for {\\em most product distributions}. In particular, consider a random product distribution where the bias of each bit is chos","authors_text":"Adam Tauman Kalai, Shang-Hua Teng","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2008-12-04T13:34:26Z","title":"Decision trees are PAC-learnable from most product distributions: a smoothed analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0933","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":"sha256:5ab32ff6a9f35c7fa83ae65142c3971eae066227a31cb197036574631206d028","target":"record","created_at":"2026-07-04T15:33:23Z","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":"0e167cbb2327460a21639a4c4850cf9b34bd6214b57f539acd114e656ae8840f","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2008-12-04T13:34:26Z","title_canon_sha256":"86bf28d1d44194c309bc816625f107f0299ffde48879c65e62fc6f1115bffbe1"},"schema_version":"1.0","source":{"id":"0812.0933","kind":"arxiv","version":1}},"canonical_sha256":"05a6d1e0e80070a6e6644700df339e427bdaba01d59ba96fae7913628b32adf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05a6d1e0e80070a6e6644700df339e427bdaba01d59ba96fae7913628b32adf7","first_computed_at":"2026-07-04T15:33:23.338761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:33:23.338761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XsKLvXebOae33ZnLw77q9BwB5si/clPcPzzW4xgH6TMA7TTLgljtww7Zp7RG++z60n4YSo81bFhk9BZym/BpDw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:33:23.339166Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab32ff6a9f35c7fa83ae65142c3971eae066227a31cb197036574631206d028","sha256:afad1f72d4434da61b1b3c81c642b8bc16405f81247ea3e00663f9bb1fcbb53d"],"state_sha256":"a0490c8f641b463d23f9f823cfc21c6980cc1039306f6b63d49363e285f5b3e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h+ItgJAyisXnAqS9aiYRApdYxZ4Wby0JRUWkOb1kSRvW5cQEB2LMy9VvyhkhzZAbG4XGiWZmtknye8R4rob2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T15:01:21.045814Z","bundle_sha256":"61c304946f2460b263508e8789f9239bd6f69bdc07340b0a0aa78862370ca4ab"}}