{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BJPJKFWDGOBFWZABC4QX6AY6M5","short_pith_number":"pith:BJPJKFWD","canonical_record":{"source":{"id":"1202.3482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-16T00:59:11Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"257d30a2ac6007008432732c2651e1b7ee7d993f5e61138e7ac20381303bc833","abstract_canon_sha256":"715b94504f3125085714a82f6e4474bbf42d712248741a99ac015b99d6ed978d"},"schema_version":"1.0"},"canonical_sha256":"0a5e9516c333825b640117217f031e676a8fae9514dd179d91ed28a2e1b53954","source":{"kind":"arxiv","id":"1202.3482","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3482","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3482v2","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3482","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"BJPJKFWDGOBF","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BJPJKFWDGOBFWZAB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BJPJKFWD","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BJPJKFWDGOBFWZABC4QX6AY6M5","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-16T00:59:11Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"257d30a2ac6007008432732c2651e1b7ee7d993f5e61138e7ac20381303bc833","abstract_canon_sha256":"715b94504f3125085714a82f6e4474bbf42d712248741a99ac015b99d6ed978d"},"schema_version":"1.0"},"canonical_sha256":"0a5e9516c333825b640117217f031e676a8fae9514dd179d91ed28a2e1b53954","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:05.671592Z","signature_b64":"y6cKFlR13ALXzLwy99wrqoE2HZS68qerlz7YdtgqeHjZUUaQXQd386GJfNh7wpNpvuVKd5ndYDCQPasHqnk8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a5e9516c333825b640117217f031e676a8fae9514dd179d91ed28a2e1b53954","last_reissued_at":"2026-05-18T02:28:05.671224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:05.671224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3482","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":"2026-05-18T02:28:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6ZVOgXx32NbVvq658kE/87s4kQGeIZ63Cwkb7YvZfdv3p6awMym/LhNPyevJElZdGapxivLXRTEBDHzJ9vpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:04:54.504501Z"},"content_sha256":"855e92caab97064c82deb7c56188cb75808b9b82313c96c88b6bcb481831dd86","schema_version":"1.0","event_id":"sha256:855e92caab97064c82deb7c56188cb75808b9b82313c96c88b6bcb481831dd86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BJPJKFWDGOBFWZABC4QX6AY6M5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The local geometry of finite mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Elisabeth Gassiat (LM-Orsay), Ramon van Handel","submitted_at":"2012-02-16T00:59:11Z","abstract_excerpt":"We establish that for q>=1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of mixture classes. Our local geometry theorem yields a bound on the (bracketing) metric entropy of a class of normalized densities, from which a local entropy bound is deduced by a general slicing procedure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3482","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":"2026-05-18T02:28:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y5oQIeWz2lsjj448yjzmwREuKQKFewput2kury87TG3dxe8d6RoGzk6maeZQsG+jRkAUYOD3ngaZSaVoNfohDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:04:54.505221Z"},"content_sha256":"3afa8a6ef98f48458c076961de3fbaca2ed736f47d8d4d5788c698f18276b575","schema_version":"1.0","event_id":"sha256:3afa8a6ef98f48458c076961de3fbaca2ed736f47d8d4d5788c698f18276b575"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJPJKFWDGOBFWZABC4QX6AY6M5/bundle.json","state_url":"https://pith.science/pith/BJPJKFWDGOBFWZABC4QX6AY6M5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJPJKFWDGOBFWZABC4QX6AY6M5/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":"2026-06-08T19:04:54Z","links":{"resolver":"https://pith.science/pith/BJPJKFWDGOBFWZABC4QX6AY6M5","bundle":"https://pith.science/pith/BJPJKFWDGOBFWZABC4QX6AY6M5/bundle.json","state":"https://pith.science/pith/BJPJKFWDGOBFWZABC4QX6AY6M5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJPJKFWDGOBFWZABC4QX6AY6M5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BJPJKFWDGOBFWZABC4QX6AY6M5","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":"715b94504f3125085714a82f6e4474bbf42d712248741a99ac015b99d6ed978d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-16T00:59:11Z","title_canon_sha256":"257d30a2ac6007008432732c2651e1b7ee7d993f5e61138e7ac20381303bc833"},"schema_version":"1.0","source":{"id":"1202.3482","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3482","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3482v2","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3482","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"BJPJKFWDGOBF","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BJPJKFWDGOBFWZAB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BJPJKFWD","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:3afa8a6ef98f48458c076961de3fbaca2ed736f47d8d4d5788c698f18276b575","target":"graph","created_at":"2026-05-18T02:28:05Z","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":"We establish that for q>=1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of mixture classes. Our local geometry theorem yields a bound on the (bracketing) metric entropy of a class of normalized densities, from which a local entropy bound is deduced by a general slicing procedure.","authors_text":"Elisabeth Gassiat (LM-Orsay), Ramon van Handel","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-16T00:59:11Z","title":"The local geometry of finite mixtures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3482","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":"sha256:855e92caab97064c82deb7c56188cb75808b9b82313c96c88b6bcb481831dd86","target":"record","created_at":"2026-05-18T02:28:05Z","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":"715b94504f3125085714a82f6e4474bbf42d712248741a99ac015b99d6ed978d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-16T00:59:11Z","title_canon_sha256":"257d30a2ac6007008432732c2651e1b7ee7d993f5e61138e7ac20381303bc833"},"schema_version":"1.0","source":{"id":"1202.3482","kind":"arxiv","version":2}},"canonical_sha256":"0a5e9516c333825b640117217f031e676a8fae9514dd179d91ed28a2e1b53954","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a5e9516c333825b640117217f031e676a8fae9514dd179d91ed28a2e1b53954","first_computed_at":"2026-05-18T02:28:05.671224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:05.671224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y6cKFlR13ALXzLwy99wrqoE2HZS68qerlz7YdtgqeHjZUUaQXQd386GJfNh7wpNpvuVKd5ndYDCQPasHqnk8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:05.671592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3482","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:855e92caab97064c82deb7c56188cb75808b9b82313c96c88b6bcb481831dd86","sha256:3afa8a6ef98f48458c076961de3fbaca2ed736f47d8d4d5788c698f18276b575"],"state_sha256":"48eec59fae504c8215b20222e52cd1c057d563d045977282c93a509d64f483e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7fp4EIbeZDoiQ0Bg/bJdzzT5H0f/iwUCmSc6QCDvvX3V07B14XKpmm8vFmGdCGBSUCfrpIOw07N7vCFqwgKiDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:04:54.509650Z","bundle_sha256":"0f39c02da0dd3d4213bb4d32d0c988927504f2a3f5427e0e6230eca92623868c"}}