{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KQ4AVDVXQZTH2GDZ2XRMKNF7C5","short_pith_number":"pith:KQ4AVDVX","canonical_record":{"source":{"id":"1912.13289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-12-31T12:32:09Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"bd5f66556d2781acbb63e7e1af006a2b059011e5d9f44621be5cbc3bcc1acff0","abstract_canon_sha256":"73d4dc16abf9fc165030a8e82110eddaf90d0129b811fbdb0bf85c3632a04ddc"},"schema_version":"1.0"},"canonical_sha256":"54380a8eb786667d1879d5e2c534bf17411c5f73f9821c73b13df34f1433198a","source":{"kind":"arxiv","id":"1912.13289","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.13289","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"arxiv_version","alias_value":"1912.13289v1","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.13289","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"pith_short_12","alias_value":"KQ4AVDVXQZTH","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"KQ4AVDVXQZTH2GDZ","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"KQ4AVDVX","created_at":"2026-07-05T00:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KQ4AVDVXQZTH2GDZ2XRMKNF7C5","target":"record","payload":{"canonical_record":{"source":{"id":"1912.13289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-12-31T12:32:09Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"bd5f66556d2781acbb63e7e1af006a2b059011e5d9f44621be5cbc3bcc1acff0","abstract_canon_sha256":"73d4dc16abf9fc165030a8e82110eddaf90d0129b811fbdb0bf85c3632a04ddc"},"schema_version":"1.0"},"canonical_sha256":"54380a8eb786667d1879d5e2c534bf17411c5f73f9821c73b13df34f1433198a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:29:07.549293Z","signature_b64":"p/ZRZ2tzhcTwnflJsmHGuwD7A7JOQxHdv3QzM7smAQRElFgzpyZhDjwG+OicVzvYWT6flWbyF1RLAYjzvoRqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54380a8eb786667d1879d5e2c534bf17411c5f73f9821c73b13df34f1433198a","last_reissued_at":"2026-07-05T00:29:07.548907Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:29:07.548907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.13289","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":"2026-07-05T00:29:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJtk5lzB1MXzqhbTzk+0BLkjlaOjkzjQ0xI48zZhg9aSaim5CpZfowoifwc51Hfhe6F4Sx2+WXuAJjLWEAu6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T18:43:58.205570Z"},"content_sha256":"669d3f89db93a1c951e1149339a572b0def0d96ba15f112d95e7d563db3b26fe","schema_version":"1.0","event_id":"sha256:669d3f89db93a1c951e1149339a572b0def0d96ba15f112d95e7d563db3b26fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KQ4AVDVXQZTH2GDZ2XRMKNF7C5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian Generalization Error of Poisson Mixture and Simplex Vandermonde Matrix Type Singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Kenichiro Sato, Sumio Watanabe","submitted_at":"2019-12-31T12:32:09Z","abstract_excerpt":"A Poisson mixture is one of the practically important models in computer science, biology, and sociology. However, the theoretical property has not been studied because the posterior distribution can not be approximated by any normal distribution. Such a model is called singular and it is known that Real Log Canonical Threshold (RLCT) is equal to the coefficient of the asymptotically main term of the Bayesian generalization error. In this paper, we derive RLCT of a simplex Vandermonde matrix type singularity which is equal to that of a Poisson mixture in general cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.13289","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/1912.13289/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":"2026-07-05T00:29:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IdqvUJ894BxgKE3y8Bgh6XxVjrbgeOddOskZT4Vrd8KtReHwYGMhc14CNn/E5MHYznGdpf9M5fUvL/hA3zf/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T18:43:58.206113Z"},"content_sha256":"fd3d1bef8e85bb6c9e41dc05a9b9df1da414ea631d244d12bfdf8bbfeda0d6b1","schema_version":"1.0","event_id":"sha256:fd3d1bef8e85bb6c9e41dc05a9b9df1da414ea631d244d12bfdf8bbfeda0d6b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQ4AVDVXQZTH2GDZ2XRMKNF7C5/bundle.json","state_url":"https://pith.science/pith/KQ4AVDVXQZTH2GDZ2XRMKNF7C5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQ4AVDVXQZTH2GDZ2XRMKNF7C5/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":"2026-08-11T18:43:58Z","links":{"resolver":"https://pith.science/pith/KQ4AVDVXQZTH2GDZ2XRMKNF7C5","bundle":"https://pith.science/pith/KQ4AVDVXQZTH2GDZ2XRMKNF7C5/bundle.json","state":"https://pith.science/pith/KQ4AVDVXQZTH2GDZ2XRMKNF7C5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQ4AVDVXQZTH2GDZ2XRMKNF7C5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KQ4AVDVXQZTH2GDZ2XRMKNF7C5","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":"73d4dc16abf9fc165030a8e82110eddaf90d0129b811fbdb0bf85c3632a04ddc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-12-31T12:32:09Z","title_canon_sha256":"bd5f66556d2781acbb63e7e1af006a2b059011e5d9f44621be5cbc3bcc1acff0"},"schema_version":"1.0","source":{"id":"1912.13289","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.13289","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"arxiv_version","alias_value":"1912.13289v1","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.13289","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"pith_short_12","alias_value":"KQ4AVDVXQZTH","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"KQ4AVDVXQZTH2GDZ","created_at":"2026-07-05T00:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"KQ4AVDVX","created_at":"2026-07-05T00:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:fd3d1bef8e85bb6c9e41dc05a9b9df1da414ea631d244d12bfdf8bbfeda0d6b1","target":"graph","created_at":"2026-07-05T00:29:07Z","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/1912.13289/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A Poisson mixture is one of the practically important models in computer science, biology, and sociology. However, the theoretical property has not been studied because the posterior distribution can not be approximated by any normal distribution. Such a model is called singular and it is known that Real Log Canonical Threshold (RLCT) is equal to the coefficient of the asymptotically main term of the Bayesian generalization error. In this paper, we derive RLCT of a simplex Vandermonde matrix type singularity which is equal to that of a Poisson mixture in general cases.","authors_text":"Kenichiro Sato, Sumio Watanabe","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-12-31T12:32:09Z","title":"Bayesian Generalization Error of Poisson Mixture and Simplex Vandermonde Matrix Type Singularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.13289","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":"sha256:669d3f89db93a1c951e1149339a572b0def0d96ba15f112d95e7d563db3b26fe","target":"record","created_at":"2026-07-05T00:29:07Z","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":"73d4dc16abf9fc165030a8e82110eddaf90d0129b811fbdb0bf85c3632a04ddc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-12-31T12:32:09Z","title_canon_sha256":"bd5f66556d2781acbb63e7e1af006a2b059011e5d9f44621be5cbc3bcc1acff0"},"schema_version":"1.0","source":{"id":"1912.13289","kind":"arxiv","version":1}},"canonical_sha256":"54380a8eb786667d1879d5e2c534bf17411c5f73f9821c73b13df34f1433198a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54380a8eb786667d1879d5e2c534bf17411c5f73f9821c73b13df34f1433198a","first_computed_at":"2026-07-05T00:29:07.548907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:29:07.548907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/ZRZ2tzhcTwnflJsmHGuwD7A7JOQxHdv3QzM7smAQRElFgzpyZhDjwG+OicVzvYWT6flWbyF1RLAYjzvoRqAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:29:07.549293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.13289","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:669d3f89db93a1c951e1149339a572b0def0d96ba15f112d95e7d563db3b26fe","sha256:fd3d1bef8e85bb6c9e41dc05a9b9df1da414ea631d244d12bfdf8bbfeda0d6b1"],"state_sha256":"0a7a0fc498e374f54a637e340618effd5c4472583e165f23ffac473fe36091ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8LJcSiIOZ6DdWJkgcKmvYVM9PW43fdyUGndOUNNhNxdPygBQw1vJtduW7ltShZ6O9eKaSB7U6XK4zqTTJAXtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T18:43:58.210553Z","bundle_sha256":"cc675504127a676ea9aa0e968f37771013a04924c6dc586cffb3679fa65eb2b4"}}