{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LHY2YOGJXXT2CSI3YKA4ASMWJP","short_pith_number":"pith:LHY2YOGJ","canonical_record":{"source":{"id":"1611.07879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-23T16:51:08Z","cross_cats_sorted":[],"title_canon_sha256":"1ec46c7e625458f322a17173c468ee4c32603a84fabeccb31336cc910f2a034d","abstract_canon_sha256":"3135dbd8bd0bac5eff9ebf7c8efb0e2a17b8a9a014932bc8f84b1e394d21ac6e"},"schema_version":"1.0"},"canonical_sha256":"59f1ac38c9bde7a1491bc281c049964be169369a88c01c981c1aecada7c16f62","source":{"kind":"arxiv","id":"1611.07879","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07879","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07879v1","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07879","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"LHY2YOGJXXT2","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LHY2YOGJXXT2CSI3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LHY2YOGJ","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LHY2YOGJXXT2CSI3YKA4ASMWJP","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-23T16:51:08Z","cross_cats_sorted":[],"title_canon_sha256":"1ec46c7e625458f322a17173c468ee4c32603a84fabeccb31336cc910f2a034d","abstract_canon_sha256":"3135dbd8bd0bac5eff9ebf7c8efb0e2a17b8a9a014932bc8f84b1e394d21ac6e"},"schema_version":"1.0"},"canonical_sha256":"59f1ac38c9bde7a1491bc281c049964be169369a88c01c981c1aecada7c16f62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:59.617394Z","signature_b64":"Fx/6r/iZu+OD46lO0JZMHHHcR7F+zj9cD3Sa9Fs6Ww1IZONaxTjQNOElDtJBGYU2VRjYv05pYSj6KnjFyaVzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59f1ac38c9bde7a1491bc281c049964be169369a88c01c981c1aecada7c16f62","last_reissued_at":"2026-05-18T00:56:59.616950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:59.616950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07879","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":"2026-05-18T00:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PhD3Z4gsKMyI1MQVb5n2D3z3muCqSHz1Y/zRHNS8kKX3Yz2Mv543cStTLMzieBEWV7v2vBPSAeBCTKW1elqZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T18:58:19.184880Z"},"content_sha256":"18c29fb459c35542459a6cd02798b3a76d1c65ff4aed075332a34566f932797c","schema_version":"1.0","event_id":"sha256:18c29fb459c35542459a6cd02798b3a76d1c65ff4aed075332a34566f932797c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LHY2YOGJXXT2CSI3YKA4ASMWJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Testing submodularity and other properties of valuation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Abhinav Bommireddi, Eric Blais","submitted_at":"2016-11-23T16:51:08Z","abstract_excerpt":"We show that for any constant $\\epsilon > 0$ and $p \\ge 1$, it is possible to distinguish functions $f : \\{0,1\\}^n \\to [0,1]$ that are submodular from those that are $\\epsilon$-far from every submodular function in $\\ell_p$ distance with a constant number of queries.\n  More generally, we extend the testing-by-implicit-learning framework of Diakonikolas et al. (2007) to show that every property of real-valued functions that is well-approximated in $\\ell_2$ distance by a class of $k$-juntas for some $k = O(1)$ can be tested in the $\\ell_p$-testing model with a constant number of queries. This re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07879","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":"2026-05-18T00:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhxrXB23bgVGqDPpCFYQrsEGrltBZiEDNq61JTA5PDg6ZNRkM16/FphpKUX7IYUawZuOPDy6TnoPtzIsBMHlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T18:58:19.185224Z"},"content_sha256":"6b6c8191199ce3fd123c52277d62c9733b2092dd025b18436c02fa8489b4e513","schema_version":"1.0","event_id":"sha256:6b6c8191199ce3fd123c52277d62c9733b2092dd025b18436c02fa8489b4e513"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHY2YOGJXXT2CSI3YKA4ASMWJP/bundle.json","state_url":"https://pith.science/pith/LHY2YOGJXXT2CSI3YKA4ASMWJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHY2YOGJXXT2CSI3YKA4ASMWJP/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":"2026-05-19T18:58:19Z","links":{"resolver":"https://pith.science/pith/LHY2YOGJXXT2CSI3YKA4ASMWJP","bundle":"https://pith.science/pith/LHY2YOGJXXT2CSI3YKA4ASMWJP/bundle.json","state":"https://pith.science/pith/LHY2YOGJXXT2CSI3YKA4ASMWJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHY2YOGJXXT2CSI3YKA4ASMWJP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LHY2YOGJXXT2CSI3YKA4ASMWJP","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":"3135dbd8bd0bac5eff9ebf7c8efb0e2a17b8a9a014932bc8f84b1e394d21ac6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-23T16:51:08Z","title_canon_sha256":"1ec46c7e625458f322a17173c468ee4c32603a84fabeccb31336cc910f2a034d"},"schema_version":"1.0","source":{"id":"1611.07879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07879","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07879v1","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07879","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"LHY2YOGJXXT2","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LHY2YOGJXXT2CSI3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LHY2YOGJ","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:6b6c8191199ce3fd123c52277d62c9733b2092dd025b18436c02fa8489b4e513","target":"graph","created_at":"2026-05-18T00:56:59Z","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 show that for any constant $\\epsilon > 0$ and $p \\ge 1$, it is possible to distinguish functions $f : \\{0,1\\}^n \\to [0,1]$ that are submodular from those that are $\\epsilon$-far from every submodular function in $\\ell_p$ distance with a constant number of queries.\n  More generally, we extend the testing-by-implicit-learning framework of Diakonikolas et al. (2007) to show that every property of real-valued functions that is well-approximated in $\\ell_2$ distance by a class of $k$-juntas for some $k = O(1)$ can be tested in the $\\ell_p$-testing model with a constant number of queries. This re","authors_text":"Abhinav Bommireddi, Eric Blais","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-23T16:51:08Z","title":"Testing submodularity and other properties of valuation functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07879","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":"sha256:18c29fb459c35542459a6cd02798b3a76d1c65ff4aed075332a34566f932797c","target":"record","created_at":"2026-05-18T00:56:59Z","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":"3135dbd8bd0bac5eff9ebf7c8efb0e2a17b8a9a014932bc8f84b1e394d21ac6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-23T16:51:08Z","title_canon_sha256":"1ec46c7e625458f322a17173c468ee4c32603a84fabeccb31336cc910f2a034d"},"schema_version":"1.0","source":{"id":"1611.07879","kind":"arxiv","version":1}},"canonical_sha256":"59f1ac38c9bde7a1491bc281c049964be169369a88c01c981c1aecada7c16f62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59f1ac38c9bde7a1491bc281c049964be169369a88c01c981c1aecada7c16f62","first_computed_at":"2026-05-18T00:56:59.616950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:59.616950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fx/6r/iZu+OD46lO0JZMHHHcR7F+zj9cD3Sa9Fs6Ww1IZONaxTjQNOElDtJBGYU2VRjYv05pYSj6KnjFyaVzAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:59.617394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18c29fb459c35542459a6cd02798b3a76d1c65ff4aed075332a34566f932797c","sha256:6b6c8191199ce3fd123c52277d62c9733b2092dd025b18436c02fa8489b4e513"],"state_sha256":"cc736365471a398ce10834207213cb4c1fd13deb397c828765accdc421c7bdfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBizJ9fDhipacBXn2OcEWt+jow0Awni6EGPPSyAAknkO6fytk/LtekXBFbg+lfk95H3w2CzNQrZQBOpLXi+vCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T18:58:19.187180Z","bundle_sha256":"97db372aa2647f1f41d06b47979176e795f618ac2a16a8bf74b1bdeb4e1c2083"}}