{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AQGRGKEKWUG3E4KKB534SBWL3G","short_pith_number":"pith:AQGRGKEK","canonical_record":{"source":{"id":"2506.01075","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-01T16:24:44Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"d45a9c545702b061f485048e2cb3cc6376936f16fef446392264c8eb6d148299","abstract_canon_sha256":"28a98b108ef7eb59cf30b65bc1f5b93a40148d911e99538a39de1f011c40a49e"},"schema_version":"1.0"},"canonical_sha256":"040d13288ab50db2714a0f77c906cbd9849c8d58815e029fe53bbfe0792edc1c","source":{"kind":"arxiv","id":"2506.01075","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01075","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01075v2","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01075","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"AQGRGKEKWUG3","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"pith_short_16","alias_value":"AQGRGKEKWUG3E4KK","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"pith_short_8","alias_value":"AQGRGKEK","created_at":"2026-06-03T02:05:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AQGRGKEKWUG3E4KKB534SBWL3G","target":"record","payload":{"canonical_record":{"source":{"id":"2506.01075","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-01T16:24:44Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"d45a9c545702b061f485048e2cb3cc6376936f16fef446392264c8eb6d148299","abstract_canon_sha256":"28a98b108ef7eb59cf30b65bc1f5b93a40148d911e99538a39de1f011c40a49e"},"schema_version":"1.0"},"canonical_sha256":"040d13288ab50db2714a0f77c906cbd9849c8d58815e029fe53bbfe0792edc1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:05:41.196775Z","signature_b64":"0UMzN57WO05Rfzp/ZohZDJ7vbGAL7Mj6GwKqM3/80ykr8Z4GU91gPAOpIHfjY/lse3Lumy5HaBL7hHk1KI1rBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"040d13288ab50db2714a0f77c906cbd9849c8d58815e029fe53bbfe0792edc1c","last_reissued_at":"2026-06-03T02:05:41.196270Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:05:41.196270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.01075","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T02:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZVxYiczGEMEflWBg7voNCR2/HxtM1BPSU1z+es/5PeZy1+z0/mXgwfsD2p1v0BtiTO+mJLFw59j9o2g5xKscCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:56:19.273293Z"},"content_sha256":"b598e020aa36892b2c5acedcf86468de9780566edaa09b2c901d3eca4df83685","schema_version":"1.0","event_id":"sha256:b598e020aa36892b2c5acedcf86468de9780566edaa09b2c901d3eca4df83685"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AQGRGKEKWUG3E4KKB534SBWL3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning DNF through Generalized Fourier Representations","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"cs.DS","authors_text":"Mohsen Heidari, Roni Khardon","submitted_at":"2025-06-01T16:24:44Z","abstract_excerpt":"The Boolean Fourier representation has been widely used in learning theory, particularly for learning Disjunctive Normal Form (DNF) under uniform and product distributions. Extending these results to non-product distributions has remained a longstanding open problem.\n  We address this challenge by introducing a generalized Fourier representation that enables learning under a broad class of non-product distributions. Our approach represents any distribution $D$ as a Bayesian network (BN) and derives a corresponding Fourier expansion. We show that standard Fourier-based learning techniques using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01075","kind":"arxiv","version":2},"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/2506.01075/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":"2026-06-03T02:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zaXJSvyHEjq75RrIuvsK2ixy9og5n4doBrQmG83JTlEg+dF/gn+t4h9XyjYbs7SJI3vYiQ0xmYhEfx9cDqHCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:56:19.274096Z"},"content_sha256":"a335799e1ec3a774fda67cafeb2170b2032096f05734a9850182d99eb42a6093","schema_version":"1.0","event_id":"sha256:a335799e1ec3a774fda67cafeb2170b2032096f05734a9850182d99eb42a6093"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQGRGKEKWUG3E4KKB534SBWL3G/bundle.json","state_url":"https://pith.science/pith/AQGRGKEKWUG3E4KKB534SBWL3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQGRGKEKWUG3E4KKB534SBWL3G/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":"2026-06-09T03:56:19Z","links":{"resolver":"https://pith.science/pith/AQGRGKEKWUG3E4KKB534SBWL3G","bundle":"https://pith.science/pith/AQGRGKEKWUG3E4KKB534SBWL3G/bundle.json","state":"https://pith.science/pith/AQGRGKEKWUG3E4KKB534SBWL3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQGRGKEKWUG3E4KKB534SBWL3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AQGRGKEKWUG3E4KKB534SBWL3G","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":"28a98b108ef7eb59cf30b65bc1f5b93a40148d911e99538a39de1f011c40a49e","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-01T16:24:44Z","title_canon_sha256":"d45a9c545702b061f485048e2cb3cc6376936f16fef446392264c8eb6d148299"},"schema_version":"1.0","source":{"id":"2506.01075","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01075","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01075v2","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01075","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"AQGRGKEKWUG3","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"pith_short_16","alias_value":"AQGRGKEKWUG3E4KK","created_at":"2026-06-03T02:05:41Z"},{"alias_kind":"pith_short_8","alias_value":"AQGRGKEK","created_at":"2026-06-03T02:05:41Z"}],"graph_snapshots":[{"event_id":"sha256:a335799e1ec3a774fda67cafeb2170b2032096f05734a9850182d99eb42a6093","target":"graph","created_at":"2026-06-03T02:05:41Z","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/2506.01075/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Boolean Fourier representation has been widely used in learning theory, particularly for learning Disjunctive Normal Form (DNF) under uniform and product distributions. Extending these results to non-product distributions has remained a longstanding open problem.\n  We address this challenge by introducing a generalized Fourier representation that enables learning under a broad class of non-product distributions. Our approach represents any distribution $D$ as a Bayesian network (BN) and derives a corresponding Fourier expansion. We show that standard Fourier-based learning techniques using","authors_text":"Mohsen Heidari, Roni Khardon","cross_cats":["cs.IT","cs.LG","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-01T16:24:44Z","title":"Learning DNF through Generalized Fourier Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01075","kind":"arxiv","version":2},"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:b598e020aa36892b2c5acedcf86468de9780566edaa09b2c901d3eca4df83685","target":"record","created_at":"2026-06-03T02:05:41Z","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":"28a98b108ef7eb59cf30b65bc1f5b93a40148d911e99538a39de1f011c40a49e","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-01T16:24:44Z","title_canon_sha256":"d45a9c545702b061f485048e2cb3cc6376936f16fef446392264c8eb6d148299"},"schema_version":"1.0","source":{"id":"2506.01075","kind":"arxiv","version":2}},"canonical_sha256":"040d13288ab50db2714a0f77c906cbd9849c8d58815e029fe53bbfe0792edc1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"040d13288ab50db2714a0f77c906cbd9849c8d58815e029fe53bbfe0792edc1c","first_computed_at":"2026-06-03T02:05:41.196270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T02:05:41.196270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0UMzN57WO05Rfzp/ZohZDJ7vbGAL7Mj6GwKqM3/80ykr8Z4GU91gPAOpIHfjY/lse3Lumy5HaBL7hHk1KI1rBw==","signature_status":"signed_v1","signed_at":"2026-06-03T02:05:41.196775Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01075","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b598e020aa36892b2c5acedcf86468de9780566edaa09b2c901d3eca4df83685","sha256:a335799e1ec3a774fda67cafeb2170b2032096f05734a9850182d99eb42a6093"],"state_sha256":"999503092423fd26c16d564e11c77722b79c7cb662b972645a86187083175509"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMGqfpBJEzogJC55Vw756B6/Zvpm46v7p4LCf+dvcjN/+14Z4DgaP9z7RQ1NV7m+uq4KxeGrBlLmsbkCr3qxBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:56:19.277334Z","bundle_sha256":"a02269ed85e9baa677a920f002302a37d567bcc8bed074d49f8ac9ac047a2413"}}