{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:I6TCC75QZTMLPIXLN4SC5K2IWS","short_pith_number":"pith:I6TCC75Q","canonical_record":{"source":{"id":"0907.0250","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-01T22:06:33Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"6e7f73c602417d236e49a72410bbf0151fcc20f2649b41ee75d5061677ba988b","abstract_canon_sha256":"2c2a25c4e4b5d53be5d224617463860d0d2cf31f31bdef7234fdf4505714a953"},"schema_version":"1.0"},"canonical_sha256":"47a6217fb0ccd8b7a2eb6f242eab48b49e64dd044389f48c17fa4cde6cb8a29a","source":{"kind":"arxiv","id":"0907.0250","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0250","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0250v3","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0250","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"I6TCC75QZTML","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"I6TCC75QZTMLPIXL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"I6TCC75Q","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:I6TCC75QZTMLPIXLN4SC5K2IWS","target":"record","payload":{"canonical_record":{"source":{"id":"0907.0250","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-01T22:06:33Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"6e7f73c602417d236e49a72410bbf0151fcc20f2649b41ee75d5061677ba988b","abstract_canon_sha256":"2c2a25c4e4b5d53be5d224617463860d0d2cf31f31bdef7234fdf4505714a953"},"schema_version":"1.0"},"canonical_sha256":"47a6217fb0ccd8b7a2eb6f242eab48b49e64dd044389f48c17fa4cde6cb8a29a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:22.896838Z","signature_b64":"le3ImuCsICCj6z2pT3QkbjmehDmHuWOYrpyfTX2/xWKL1TFr0WVt8/eURwB8gQjAh3Jx+eYWFTTFV21FqgRGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47a6217fb0ccd8b7a2eb6f242eab48b49e64dd044389f48c17fa4cde6cb8a29a","last_reissued_at":"2026-05-18T03:06:22.896173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:22.896173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.0250","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJOgFxZr+oSu9jy3KE9nod6HkQ6ElRaB4XwQUMc/Ga7ypz41fNx+03BZBtAb069hmINRh7L+DTxh2Eu/I86UCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:47:00.069534Z"},"content_sha256":"9a3082ff32b862e09759d461a062c4d034bb20f38c2ddce874b36dd33a1629ca","schema_version":"1.0","event_id":"sha256:9a3082ff32b862e09759d461a062c4d034bb20f38c2ddce874b36dd33a1629ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:I6TCC75QZTMLPIXLN4SC5K2IWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Log-Concave Distributions as a Nearly Parametric Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Andre Huesler, Dominic Schuhmacher, Lutz Duembgen","submitted_at":"2009-07-01T22:06:33Z","abstract_excerpt":"In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence in total variation distance, (ii) convergence of arbitrary moments, and (iii) pointwise convergence of Laplace transforms. Hence the nonparametric model P_d has similar properties as parametric models such as, for instance, the family of all d-variate Gaussian distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0250","kind":"arxiv","version":3},"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":"2026-05-18T03:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YeC02Z1oRCk5j8LC6mamvVjoAQlE5YOjyZYnC2v+WV8eN7peysgPsdtzzY5Cb7DdhgE3XV26JmQHNoG8df4zCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:47:00.070223Z"},"content_sha256":"0f050f46106c30844379eea3fea9d6de791b9874d2e11d5f98894782e7ab113e","schema_version":"1.0","event_id":"sha256:0f050f46106c30844379eea3fea9d6de791b9874d2e11d5f98894782e7ab113e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6TCC75QZTMLPIXLN4SC5K2IWS/bundle.json","state_url":"https://pith.science/pith/I6TCC75QZTMLPIXLN4SC5K2IWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6TCC75QZTMLPIXLN4SC5K2IWS/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":"2026-05-29T22:47:00Z","links":{"resolver":"https://pith.science/pith/I6TCC75QZTMLPIXLN4SC5K2IWS","bundle":"https://pith.science/pith/I6TCC75QZTMLPIXLN4SC5K2IWS/bundle.json","state":"https://pith.science/pith/I6TCC75QZTMLPIXLN4SC5K2IWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6TCC75QZTMLPIXLN4SC5K2IWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:I6TCC75QZTMLPIXLN4SC5K2IWS","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":"2c2a25c4e4b5d53be5d224617463860d0d2cf31f31bdef7234fdf4505714a953","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-01T22:06:33Z","title_canon_sha256":"6e7f73c602417d236e49a72410bbf0151fcc20f2649b41ee75d5061677ba988b"},"schema_version":"1.0","source":{"id":"0907.0250","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0250","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0250v3","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0250","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"I6TCC75QZTML","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"I6TCC75QZTMLPIXL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"I6TCC75Q","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:0f050f46106c30844379eea3fea9d6de791b9874d2e11d5f98894782e7ab113e","target":"graph","created_at":"2026-05-18T03:06:22Z","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 this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence in total variation distance, (ii) convergence of arbitrary moments, and (iii) pointwise convergence of Laplace transforms. Hence the nonparametric model P_d has similar properties as parametric models such as, for instance, the family of all d-variate Gaussian distributions.","authors_text":"Andre Huesler, Dominic Schuhmacher, Lutz Duembgen","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-01T22:06:33Z","title":"Multivariate Log-Concave Distributions as a Nearly Parametric Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0250","kind":"arxiv","version":3},"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":"sha256:9a3082ff32b862e09759d461a062c4d034bb20f38c2ddce874b36dd33a1629ca","target":"record","created_at":"2026-05-18T03:06:22Z","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":"2c2a25c4e4b5d53be5d224617463860d0d2cf31f31bdef7234fdf4505714a953","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-01T22:06:33Z","title_canon_sha256":"6e7f73c602417d236e49a72410bbf0151fcc20f2649b41ee75d5061677ba988b"},"schema_version":"1.0","source":{"id":"0907.0250","kind":"arxiv","version":3}},"canonical_sha256":"47a6217fb0ccd8b7a2eb6f242eab48b49e64dd044389f48c17fa4cde6cb8a29a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47a6217fb0ccd8b7a2eb6f242eab48b49e64dd044389f48c17fa4cde6cb8a29a","first_computed_at":"2026-05-18T03:06:22.896173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:22.896173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"le3ImuCsICCj6z2pT3QkbjmehDmHuWOYrpyfTX2/xWKL1TFr0WVt8/eURwB8gQjAh3Jx+eYWFTTFV21FqgRGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:22.896838Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0250","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a3082ff32b862e09759d461a062c4d034bb20f38c2ddce874b36dd33a1629ca","sha256:0f050f46106c30844379eea3fea9d6de791b9874d2e11d5f98894782e7ab113e"],"state_sha256":"3f476678ba3f9856d5ee5e1ac5b3fb7ea4fa565b62f37d319b483a3a7ed1e352"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSpx/+p2628jkId7+NzGYmph6dqbDYpaGkZjYxWUhMnMJIkcYYWtxa30IBghzW7Bq9blcXlErH2+9aIacTPqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T22:47:00.073782Z","bundle_sha256":"dcb4096eeb83d66a725f47696c33f3983626a67396f3ae079250c06b0b8f494c"}}