{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BWXLANGLY2LCRJE2HD2UFNE4PB","short_pith_number":"pith:BWXLANGL","canonical_record":{"source":{"id":"1111.1832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-08T09:01:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"cd28e972469d473f9c1fef9de2aa6c000b9b4b95badfc8012a4894d39ffca731","abstract_canon_sha256":"a64bb642a62773f49ae81dd8a011c4308ac979486ad6c5b8520363743631a04e"},"schema_version":"1.0"},"canonical_sha256":"0daeb034cbc69628a49a38f542b49c785a914f4f89d41e00428d6cee9dee565f","source":{"kind":"arxiv","id":"1111.1832","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1832","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1832v2","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1832","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"BWXLANGLY2LC","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BWXLANGLY2LCRJE2","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BWXLANGL","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BWXLANGLY2LCRJE2HD2UFNE4PB","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-08T09:01:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"cd28e972469d473f9c1fef9de2aa6c000b9b4b95badfc8012a4894d39ffca731","abstract_canon_sha256":"a64bb642a62773f49ae81dd8a011c4308ac979486ad6c5b8520363743631a04e"},"schema_version":"1.0"},"canonical_sha256":"0daeb034cbc69628a49a38f542b49c785a914f4f89d41e00428d6cee9dee565f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:43.901568Z","signature_b64":"+5cDAa7ih7RhEpnPALWbyUNmz3PuPAarrJ9KQpIA4wkOLyF5MvXXjCTTRIVwiitZCsJUQzKbyCropvrljRtdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0daeb034cbc69628a49a38f542b49c785a914f4f89d41e00428d6cee9dee565f","last_reissued_at":"2026-05-18T01:59:43.900917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:43.900917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1832","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":"2026-05-18T01:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1M9wJxLrIBEc6ZJBfwFdjfDc4fl7vwRhtz2bIl0I2sN/CBJhG59rPWJaX3yhS9i+GJE1nLs/nX2WtxIxpSKYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:29:15.979709Z"},"content_sha256":"2509220e158b108014601d4f07f049a0024bb9a1d45ef7f098d1be70fee0e74c","schema_version":"1.0","event_id":"sha256:2509220e158b108014601d4f07f049a0024bb9a1d45ef7f098d1be70fee0e74c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BWXLANGLY2LCRJE2HD2UFNE4PB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Learning Theory of Quasi-Regular Cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Koshi Yamada, Sumio Watanabe","submitted_at":"2011-11-08T09:01:39Z","abstract_excerpt":"Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical asymptotic theory can not be applied to such learning machines because the likelihood function can not be approximated by any normal distribution. Recently, new statistical theory has been established based on algebraic geometry and it was clarified that the generalization and training errors are determined by two birational invariants, the real log canonical thr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1832","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":""},"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":"2026-05-18T01:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gIj4QA2pGzOhFrf/um4ASH1C6FHJGaOpuSTVT3/pQJEc7tNKla35/Hht76qTE4WRckY5Gg1fXfXORzFgFWz5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:29:15.980049Z"},"content_sha256":"6bca046e04032403dcbb433aa913b1cd64856d9ea2465578e00dd73e927952db","schema_version":"1.0","event_id":"sha256:6bca046e04032403dcbb433aa913b1cd64856d9ea2465578e00dd73e927952db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWXLANGLY2LCRJE2HD2UFNE4PB/bundle.json","state_url":"https://pith.science/pith/BWXLANGLY2LCRJE2HD2UFNE4PB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWXLANGLY2LCRJE2HD2UFNE4PB/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":"2026-06-04T19:29:15Z","links":{"resolver":"https://pith.science/pith/BWXLANGLY2LCRJE2HD2UFNE4PB","bundle":"https://pith.science/pith/BWXLANGLY2LCRJE2HD2UFNE4PB/bundle.json","state":"https://pith.science/pith/BWXLANGLY2LCRJE2HD2UFNE4PB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWXLANGLY2LCRJE2HD2UFNE4PB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BWXLANGLY2LCRJE2HD2UFNE4PB","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":"a64bb642a62773f49ae81dd8a011c4308ac979486ad6c5b8520363743631a04e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-08T09:01:39Z","title_canon_sha256":"cd28e972469d473f9c1fef9de2aa6c000b9b4b95badfc8012a4894d39ffca731"},"schema_version":"1.0","source":{"id":"1111.1832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1832","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1832v2","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1832","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"BWXLANGLY2LC","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BWXLANGLY2LCRJE2","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BWXLANGL","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:6bca046e04032403dcbb433aa913b1cd64856d9ea2465578e00dd73e927952db","target":"graph","created_at":"2026-05-18T01:59:43Z","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":"Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical asymptotic theory can not be applied to such learning machines because the likelihood function can not be approximated by any normal distribution. Recently, new statistical theory has been established based on algebraic geometry and it was clarified that the generalization and training errors are determined by two birational invariants, the real log canonical thr","authors_text":"Koshi Yamada, Sumio Watanabe","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-08T09:01:39Z","title":"Statistical Learning Theory of Quasi-Regular Cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1832","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":"sha256:2509220e158b108014601d4f07f049a0024bb9a1d45ef7f098d1be70fee0e74c","target":"record","created_at":"2026-05-18T01:59:43Z","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":"a64bb642a62773f49ae81dd8a011c4308ac979486ad6c5b8520363743631a04e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-08T09:01:39Z","title_canon_sha256":"cd28e972469d473f9c1fef9de2aa6c000b9b4b95badfc8012a4894d39ffca731"},"schema_version":"1.0","source":{"id":"1111.1832","kind":"arxiv","version":2}},"canonical_sha256":"0daeb034cbc69628a49a38f542b49c785a914f4f89d41e00428d6cee9dee565f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0daeb034cbc69628a49a38f542b49c785a914f4f89d41e00428d6cee9dee565f","first_computed_at":"2026-05-18T01:59:43.900917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:43.900917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+5cDAa7ih7RhEpnPALWbyUNmz3PuPAarrJ9KQpIA4wkOLyF5MvXXjCTTRIVwiitZCsJUQzKbyCropvrljRtdDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:43.901568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2509220e158b108014601d4f07f049a0024bb9a1d45ef7f098d1be70fee0e74c","sha256:6bca046e04032403dcbb433aa913b1cd64856d9ea2465578e00dd73e927952db"],"state_sha256":"dff65932e054a880feac23875a1ef4bd38f110075d16b150d0eaba2670d1b3d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bvnldpSp9fst8AubmY/LyES0ux57veerQA/9aKaBWQWC1wYWauex9movfeLTUWq6M4wjSuvYdBUCtCBcihBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:29:15.981901Z","bundle_sha256":"d679338796d387260b3e9957ee26d59b9a2c2e3542d90f742ffbef7ccf210d4b"}}