{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:56H6RGV6TVMQANYNIG3CYTIOAY","short_pith_number":"pith:56H6RGV6","canonical_record":{"source":{"id":"1204.2763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-12T16:04:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ef7a4307df4727d332a5856c6203f41ce425a7659be2731b01a88d075842904e","abstract_canon_sha256":"df1789f673333163b89bc23c51f9570f48b493646b9bf41015a262bd8ba3a58f"},"schema_version":"1.0"},"canonical_sha256":"ef8fe89abe9d5900370d41b62c4d0e0602176380c846526eb4b9f6853ab9c8d0","source":{"kind":"arxiv","id":"1204.2763","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2763","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2763v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2763","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"56H6RGV6TVMQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"56H6RGV6TVMQANYN","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"56H6RGV6","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:56H6RGV6TVMQANYNIG3CYTIOAY","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-12T16:04:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ef7a4307df4727d332a5856c6203f41ce425a7659be2731b01a88d075842904e","abstract_canon_sha256":"df1789f673333163b89bc23c51f9570f48b493646b9bf41015a262bd8ba3a58f"},"schema_version":"1.0"},"canonical_sha256":"ef8fe89abe9d5900370d41b62c4d0e0602176380c846526eb4b9f6853ab9c8d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:03.592891Z","signature_b64":"ErH90lz1Qd++GFvzfUO23Y4gePgxqffI03got+0csXAEi2mYeQaeHIHGYA0wIqW69QvvZzgt4OqK1wFhrDRWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef8fe89abe9d5900370d41b62c4d0e0602176380c846526eb4b9f6853ab9c8d0","last_reissued_at":"2026-05-18T03:58:03.592420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:03.592420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2763","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":"2026-05-18T03:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qkt2ZgD5FXUNdadLUXY+iZagxN+KMDypuRijcB1C1asKIsPKHfn0jbJ3IW6Yz+Nn4PmFrg6A4YNs3xi5f3cMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:35:06.638622Z"},"content_sha256":"200ec2cd5a5128defbce4b6e1640fc02f1c28591bbfeffd1182bcbb460da7b2a","schema_version":"1.0","event_id":"sha256:200ec2cd5a5128defbce4b6e1640fc02f1c28591bbfeffd1182bcbb460da7b2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:56H6RGV6TVMQANYNIG3CYTIOAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Cram\\'er-Rao inequality for non differentiable models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Paul Rochet, Thibault Espinasse","submitted_at":"2012-04-12T16:04:39Z","abstract_excerpt":"We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\\'er-Rao bound, although it does not require the differentiability of the model. Moreover, we show our efficiency bound to be always greater than the Cram\\'er-Rao bound in smooth models, thus providing a sharper result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2763","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":""},"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":"2026-05-18T03:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHheGDuFbAMLDcTKuMUTGwa2kRwwyBDY2Afmf+lhw5Uyj2IqGL8RI1UGRyH8GG+vBFLIl3ejHHuSv8erzLnIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:35:06.639262Z"},"content_sha256":"19a968f23e3b4f3e3668acb3c43e4b81df4f4c7930749fc37bc7c9e47df313a0","schema_version":"1.0","event_id":"sha256:19a968f23e3b4f3e3668acb3c43e4b81df4f4c7930749fc37bc7c9e47df313a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/56H6RGV6TVMQANYNIG3CYTIOAY/bundle.json","state_url":"https://pith.science/pith/56H6RGV6TVMQANYNIG3CYTIOAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/56H6RGV6TVMQANYNIG3CYTIOAY/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":"2026-05-30T06:35:06Z","links":{"resolver":"https://pith.science/pith/56H6RGV6TVMQANYNIG3CYTIOAY","bundle":"https://pith.science/pith/56H6RGV6TVMQANYNIG3CYTIOAY/bundle.json","state":"https://pith.science/pith/56H6RGV6TVMQANYNIG3CYTIOAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/56H6RGV6TVMQANYNIG3CYTIOAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:56H6RGV6TVMQANYNIG3CYTIOAY","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":"df1789f673333163b89bc23c51f9570f48b493646b9bf41015a262bd8ba3a58f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-12T16:04:39Z","title_canon_sha256":"ef7a4307df4727d332a5856c6203f41ce425a7659be2731b01a88d075842904e"},"schema_version":"1.0","source":{"id":"1204.2763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2763","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2763v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2763","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"56H6RGV6TVMQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"56H6RGV6TVMQANYN","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"56H6RGV6","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:19a968f23e3b4f3e3668acb3c43e4b81df4f4c7930749fc37bc7c9e47df313a0","target":"graph","created_at":"2026-05-18T03:58:03Z","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 compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\\'er-Rao bound, although it does not require the differentiability of the model. Moreover, we show our efficiency bound to be always greater than the Cram\\'er-Rao bound in smooth models, thus providing a sharper result.","authors_text":"Paul Rochet, Thibault Espinasse","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-12T16:04:39Z","title":"A Cram\\'er-Rao inequality for non differentiable models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2763","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":"sha256:200ec2cd5a5128defbce4b6e1640fc02f1c28591bbfeffd1182bcbb460da7b2a","target":"record","created_at":"2026-05-18T03:58:03Z","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":"df1789f673333163b89bc23c51f9570f48b493646b9bf41015a262bd8ba3a58f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-12T16:04:39Z","title_canon_sha256":"ef7a4307df4727d332a5856c6203f41ce425a7659be2731b01a88d075842904e"},"schema_version":"1.0","source":{"id":"1204.2763","kind":"arxiv","version":1}},"canonical_sha256":"ef8fe89abe9d5900370d41b62c4d0e0602176380c846526eb4b9f6853ab9c8d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef8fe89abe9d5900370d41b62c4d0e0602176380c846526eb4b9f6853ab9c8d0","first_computed_at":"2026-05-18T03:58:03.592420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:03.592420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ErH90lz1Qd++GFvzfUO23Y4gePgxqffI03got+0csXAEi2mYeQaeHIHGYA0wIqW69QvvZzgt4OqK1wFhrDRWCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:03.592891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:200ec2cd5a5128defbce4b6e1640fc02f1c28591bbfeffd1182bcbb460da7b2a","sha256:19a968f23e3b4f3e3668acb3c43e4b81df4f4c7930749fc37bc7c9e47df313a0"],"state_sha256":"336aae4eca9b6c69a48ed8e0bcdfd9df0006c26d795eae4f4063976b7469b585"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+bEDQogE0/sQ2oSciY10Kua11mB84KT4wYEHlQcRgZYvQr5HvVv1DjsNOvIaBJyWg7r/Bn3QqnhCKDOGcne9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:35:06.642665Z","bundle_sha256":"f99af2c4f2cc04f3dfe7758b269a97ae0c7787ba564812f7aa0c86abdebaec99"}}