{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5TNMIFPYONPBJM6WFTM2YGI75D","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":"4d483df9bdbf667410d6baf9b3fd5bc84a7eb1335d4ef0b245b9a8ef5000f238","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-26T12:49:07Z","title_canon_sha256":"14bf07281a08810a13f499ee2773c732f26a21e201eeb0346690469f2f81766d"},"schema_version":"1.0","source":{"id":"1609.07953","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07953","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07953v1","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07953","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"5TNMIFPYONPB","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5TNMIFPYONPBJM6W","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5TNMIFPY","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:19fb6d86c06eba06f7539b13ccf95d5ccb28cb6b2a15df491f652d5f0407ea6b","target":"graph","created_at":"2026-05-18T01:03:54Z","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":"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","authors_text":"Yann Guermeur (ABC)","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-26T12:49:07Z","title":"L p -norm Sauer-Shelah Lemma for Margin Multi-category Classifiers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07953","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:d79ba9fe2180f880739fe4eb12642e7005b919455bf0a00dfaf4b605b53280fc","target":"record","created_at":"2026-05-18T01:03:54Z","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":"4d483df9bdbf667410d6baf9b3fd5bc84a7eb1335d4ef0b245b9a8ef5000f238","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-26T12:49:07Z","title_canon_sha256":"14bf07281a08810a13f499ee2773c732f26a21e201eeb0346690469f2f81766d"},"schema_version":"1.0","source":{"id":"1609.07953","kind":"arxiv","version":1}},"canonical_sha256":"ecdac415f8735e14b3d62cd9ac191fe8c159cee5096384767744bfa21311b506","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecdac415f8735e14b3d62cd9ac191fe8c159cee5096384767744bfa21311b506","first_computed_at":"2026-05-18T01:03:54.857993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:54.857993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"odldYUcwvfUZzCL+qqKK6IGs9uhNhM646A31Zzby98kgN7aw3suvbt02FGnPHzQQmlNd1DabnhXs40upDhRcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:54.858935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07953","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d79ba9fe2180f880739fe4eb12642e7005b919455bf0a00dfaf4b605b53280fc","sha256:19fb6d86c06eba06f7539b13ccf95d5ccb28cb6b2a15df491f652d5f0407ea6b"],"state_sha256":"3afeba377d2f14c25c3f974d8f4e94b375daf757078c5836812604786fe056d1"}