{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5TNMIFPYONPBJM6WFTM2YGI75D","short_pith_number":"pith:5TNMIFPY","schema_version":"1.0","canonical_sha256":"ecdac415f8735e14b3d62cd9ac191fe8c159cee5096384767744bfa21311b506","source":{"kind":"arxiv","id":"1609.07953","version":1},"attestation_state":"computed","paper":{"title":"L p -norm Sauer-Shelah Lemma for Margin Multi-category Classifiers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Yann Guermeur (ABC)","submitted_at":"2016-09-26T12:49:07Z","abstract_excerpt":"In the framework of agnostic learning, one of the main open problems of the theory of multi-category pattern classification is the characterization of the way the complexity varies with the number C of categories. More precisely, if the classifier is characterized only through minimal learnability hypotheses, then the optimal dependency on C that an upper bound on the probability of error should exhibit is unknown. We consider margin classifiers. They are based on classes of vector-valued functions with one component function per category, and the classes of component functions are uniform Gli"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.07953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-26T12:49:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"14bf07281a08810a13f499ee2773c732f26a21e201eeb0346690469f2f81766d","abstract_canon_sha256":"4d483df9bdbf667410d6baf9b3fd5bc84a7eb1335d4ef0b245b9a8ef5000f238"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:54.858935Z","signature_b64":"odldYUcwvfUZzCL+qqKK6IGs9uhNhM646A31Zzby98kgN7aw3suvbt02FGnPHzQQmlNd1DabnhXs40upDhRcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecdac415f8735e14b3d62cd9ac191fe8c159cee5096384767744bfa21311b506","last_reissued_at":"2026-05-18T01:03:54.857993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:54.857993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L p -norm Sauer-Shelah Lemma for Margin Multi-category Classifiers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Yann Guermeur (ABC)","submitted_at":"2016-09-26T12:49:07Z","abstract_excerpt":"In the framework of agnostic learning, one of the main open problems of the theory of multi-category pattern classification is the characterization of the way the complexity varies with the number C of categories. More precisely, if the classifier is characterized only through minimal learnability hypotheses, then the optimal dependency on C that an upper bound on the probability of error should exhibit is unknown. We consider margin classifiers. They are based on classes of vector-valued functions with one component function per category, and the classes of component functions are uniform Gli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07953","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.07953","created_at":"2026-05-18T01:03:54.858207+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07953v1","created_at":"2026-05-18T01:03:54.858207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07953","created_at":"2026-05-18T01:03:54.858207+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TNMIFPYONPB","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TNMIFPYONPBJM6W","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TNMIFPY","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D","json":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D.json","graph_json":"https://pith.science/api/pith-number/5TNMIFPYONPBJM6WFTM2YGI75D/graph.json","events_json":"https://pith.science/api/pith-number/5TNMIFPYONPBJM6WFTM2YGI75D/events.json","paper":"https://pith.science/paper/5TNMIFPY"},"agent_actions":{"view_html":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D","download_json":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D.json","view_paper":"https://pith.science/paper/5TNMIFPY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07953&json=true","fetch_graph":"https://pith.science/api/pith-number/5TNMIFPYONPBJM6WFTM2YGI75D/graph.json","fetch_events":"https://pith.science/api/pith-number/5TNMIFPYONPBJM6WFTM2YGI75D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D/action/storage_attestation","attest_author":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D/action/author_attestation","sign_citation":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D/action/citation_signature","submit_replication":"https://pith.science/pith/5TNMIFPYONPBJM6WFTM2YGI75D/action/replication_record"}},"created_at":"2026-05-18T01:03:54.858207+00:00","updated_at":"2026-05-18T01:03:54.858207+00:00"}