{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HCC4VJFG5JHIUAIUL6SUS5O5UL","short_pith_number":"pith:HCC4VJFG","canonical_record":{"source":{"id":"2606.17319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-15T22:00:03Z","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"title_canon_sha256":"9c5dd3be63ec5bc3b90c61503aa4ec953e08840fa4cfacac30a826cd51eb46b9","abstract_canon_sha256":"ffb9a999093f050877ca9a77ad1363aba5c759825c094302cdf7a21ceb535201"},"schema_version":"1.0"},"canonical_sha256":"3885caa4a6ea4e8a01145fa54975dda2d8c7684edad54e0b37422997b5457e26","source":{"kind":"arxiv","id":"2606.17319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17319","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17319v1","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17319","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"HCC4VJFG5JHI","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_16","alias_value":"HCC4VJFG5JHIUAIU","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_8","alias_value":"HCC4VJFG","created_at":"2026-06-19T16:10:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HCC4VJFG5JHIUAIUL6SUS5O5UL","target":"record","payload":{"canonical_record":{"source":{"id":"2606.17319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-15T22:00:03Z","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"title_canon_sha256":"9c5dd3be63ec5bc3b90c61503aa4ec953e08840fa4cfacac30a826cd51eb46b9","abstract_canon_sha256":"ffb9a999093f050877ca9a77ad1363aba5c759825c094302cdf7a21ceb535201"},"schema_version":"1.0"},"canonical_sha256":"3885caa4a6ea4e8a01145fa54975dda2d8c7684edad54e0b37422997b5457e26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:08.893650Z","signature_b64":"jSvx01jEmzBIi8PVhPjcIkdmUBBmZ5J8WSR3eqosyht1EHDzT93SzCU5eBjfuzMdohgPFQQ7onE0GdX6o54NBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3885caa4a6ea4e8a01145fa54975dda2d8c7684edad54e0b37422997b5457e26","last_reissued_at":"2026-06-19T16:10:08.893291Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:08.893291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.17319","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":"2026-06-19T16:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7sx/xqNuv5KmgdrxbeA9oSEk2LePdQhMrL3C7RRFmgtcLmfDJPN1NS+Ql09SkkP+uBlg3PZcc5ILPQfnbix+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T05:01:35.613054Z"},"content_sha256":"3d0f19539fb25be59bf30633f13afa2968d45a8a9831b10f018c419ac66d6008","schema_version":"1.0","event_id":"sha256:3d0f19539fb25be59bf30633f13afa2968d45a8a9831b10f018c419ac66d6008"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HCC4VJFG5JHIUAIUL6SUS5O5UL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight $L_\\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.CO","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Jasper van Doornmalen, Jos\\'e Verschae, Mathieu Molina, Victor Verdugo","submitted_at":"2026-06-15T22:00:03Z","abstract_excerpt":"Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying objective, we require uniform $L_\\infty$-error guarantees rather than the usual $L_2$-type guarantees. We characterize the minimax sample complexity of uniform estimation under subgaussian noise for two classes of bounded polynomials. First, for polynomials of degree at most $d$ on $n$ variables, the sample complexity scales as $n^{d+1}$. Second, for $s$-sparse Fou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17319","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/2606.17319/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":"2026-06-19T16:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RdMyslf6NKEqzejKevdYHe9ONltq/oTy8uqZGlOIyvxrTSSocUszEP467VoQDcckyIgHKu4QDtk/aJ85JHDlDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T05:01:35.613463Z"},"content_sha256":"71690b5d6fab0af3e76449b77565ba6fa1a5de2141895bb14e30c91b6fb31c9c","schema_version":"1.0","event_id":"sha256:71690b5d6fab0af3e76449b77565ba6fa1a5de2141895bb14e30c91b6fb31c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCC4VJFG5JHIUAIUL6SUS5O5UL/bundle.json","state_url":"https://pith.science/pith/HCC4VJFG5JHIUAIUL6SUS5O5UL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCC4VJFG5JHIUAIUL6SUS5O5UL/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":"2026-06-21T05:01:35Z","links":{"resolver":"https://pith.science/pith/HCC4VJFG5JHIUAIUL6SUS5O5UL","bundle":"https://pith.science/pith/HCC4VJFG5JHIUAIUL6SUS5O5UL/bundle.json","state":"https://pith.science/pith/HCC4VJFG5JHIUAIUL6SUS5O5UL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCC4VJFG5JHIUAIUL6SUS5O5UL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HCC4VJFG5JHIUAIUL6SUS5O5UL","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":"ffb9a999093f050877ca9a77ad1363aba5c759825c094302cdf7a21ceb535201","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-15T22:00:03Z","title_canon_sha256":"9c5dd3be63ec5bc3b90c61503aa4ec953e08840fa4cfacac30a826cd51eb46b9"},"schema_version":"1.0","source":{"id":"2606.17319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17319","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17319v1","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17319","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"HCC4VJFG5JHI","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_16","alias_value":"HCC4VJFG5JHIUAIU","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_8","alias_value":"HCC4VJFG","created_at":"2026-06-19T16:10:08Z"}],"graph_snapshots":[{"event_id":"sha256:71690b5d6fab0af3e76449b77565ba6fa1a5de2141895bb14e30c91b6fb31c9c","target":"graph","created_at":"2026-06-19T16:10:08Z","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/2606.17319/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying objective, we require uniform $L_\\infty$-error guarantees rather than the usual $L_2$-type guarantees. We characterize the minimax sample complexity of uniform estimation under subgaussian noise for two classes of bounded polynomials. First, for polynomials of degree at most $d$ on $n$ variables, the sample complexity scales as $n^{d+1}$. Second, for $s$-sparse Fou","authors_text":"Jasper van Doornmalen, Jos\\'e Verschae, Mathieu Molina, Victor Verdugo","cross_cats":["cs.LG","math.CO","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-15T22:00:03Z","title":"Tight $L_\\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17319","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":"sha256:3d0f19539fb25be59bf30633f13afa2968d45a8a9831b10f018c419ac66d6008","target":"record","created_at":"2026-06-19T16:10:08Z","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":"ffb9a999093f050877ca9a77ad1363aba5c759825c094302cdf7a21ceb535201","cross_cats_sorted":["cs.LG","math.CO","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-15T22:00:03Z","title_canon_sha256":"9c5dd3be63ec5bc3b90c61503aa4ec953e08840fa4cfacac30a826cd51eb46b9"},"schema_version":"1.0","source":{"id":"2606.17319","kind":"arxiv","version":1}},"canonical_sha256":"3885caa4a6ea4e8a01145fa54975dda2d8c7684edad54e0b37422997b5457e26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3885caa4a6ea4e8a01145fa54975dda2d8c7684edad54e0b37422997b5457e26","first_computed_at":"2026-06-19T16:10:08.893291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:08.893291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jSvx01jEmzBIi8PVhPjcIkdmUBBmZ5J8WSR3eqosyht1EHDzT93SzCU5eBjfuzMdohgPFQQ7onE0GdX6o54NBw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:08.893650Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d0f19539fb25be59bf30633f13afa2968d45a8a9831b10f018c419ac66d6008","sha256:71690b5d6fab0af3e76449b77565ba6fa1a5de2141895bb14e30c91b6fb31c9c"],"state_sha256":"25f40af6fbbaaac832d258e44815cd03bc6c4c8d9b9e2b79edb5950ad1489f88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JlTehU8GjGrvNyMl/JTQTNAcluOZi4/kiPhEsnsSp3ZLSnNLXv9rvHsv4SxL59eqdIMbk4tGn9CoFh+rFjWGCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T05:01:35.615601Z","bundle_sha256":"8b8b49c184e31aebf341356f5fba08d379d64373f3d9fccc230ab58e18cd65d5"}}