{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ASXVFY7Y22PYV5MSEBREWCVHMR","short_pith_number":"pith:ASXVFY7Y","canonical_record":{"source":{"id":"1611.07712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-23T10:03:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e527d86bf5113e66c3f1e42282e004c07f1c8aa3704076505f580df474ffc5a7","abstract_canon_sha256":"5eae75c67dfda1ff8d8a4d2a4a1df8024e7aa9728025b01dd442ad2e5f889759"},"schema_version":"1.0"},"canonical_sha256":"04af52e3f8d69f8af59220624b0aa7644afff08178a3bde9c6d0e3467f5171c4","source":{"kind":"arxiv","id":"1611.07712","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07712","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07712v1","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07712","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"ASXVFY7Y22PY","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ASXVFY7Y22PYV5MS","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ASXVFY7Y","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ASXVFY7Y22PYV5MSEBREWCVHMR","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-23T10:03:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e527d86bf5113e66c3f1e42282e004c07f1c8aa3704076505f580df474ffc5a7","abstract_canon_sha256":"5eae75c67dfda1ff8d8a4d2a4a1df8024e7aa9728025b01dd442ad2e5f889759"},"schema_version":"1.0"},"canonical_sha256":"04af52e3f8d69f8af59220624b0aa7644afff08178a3bde9c6d0e3467f5171c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:00.029051Z","signature_b64":"2zeCnG+vuW38ic7aVv5uWVrVWctx+xeT1foKBx9awMPqfBW8EoDUXW33lNKnESsCBy0katvwyHtibA1WJwimAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04af52e3f8d69f8af59220624b0aa7644afff08178a3bde9c6d0e3467f5171c4","last_reissued_at":"2026-05-18T00:57:00.028573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:00.028573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07712","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":"2026-05-18T00:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PKEMrRzziMHPMoP0TlfpVbACrSAj4unFXNyxowMru00DEt6p+wf5o+//Wj1fcxqQWQ+73P9BEUfgkr/l1RicBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:10:20.770509Z"},"content_sha256":"2764ec270324561ce5e217140407d63e2f1f46d0d0f3a7b858d3f3a8390d10c3","schema_version":"1.0","event_id":"sha256:2764ec270324561ce5e217140407d63e2f1f46d0d0f3a7b858d3f3a8390d10c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ASXVFY7Y22PYV5MSEBREWCVHMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pearson information-based lower bound on Fisher information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dave Zachariah, Petre Stoica","submitted_at":"2016-11-23T10:03:05Z","abstract_excerpt":"The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either unknown or intractable. For this reason, it is of interest to develop useful lower bounds on the FIM. In this lecture note, we derive such a bound based on moment constraints. We call this bound the Pearson information matrix (PIM) and relate it to properties of a misspecified data distribution. Finally, we show that the inverse PIM coincides with the asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07712","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":"2026-05-18T00:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zcp9C9w402znExWIs9K5+VsQ+xHcfKpjLNmjCjGDhkOatAFLfXJg7fF2Tw8sH/fFbm7GWuMT9lVNi0HH+xWwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:10:20.771174Z"},"content_sha256":"a82dd8f2593f037127b79be57ca19f64181766418587e10930dc84098f85f34f","schema_version":"1.0","event_id":"sha256:a82dd8f2593f037127b79be57ca19f64181766418587e10930dc84098f85f34f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASXVFY7Y22PYV5MSEBREWCVHMR/bundle.json","state_url":"https://pith.science/pith/ASXVFY7Y22PYV5MSEBREWCVHMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASXVFY7Y22PYV5MSEBREWCVHMR/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":"2026-05-25T23:10:20Z","links":{"resolver":"https://pith.science/pith/ASXVFY7Y22PYV5MSEBREWCVHMR","bundle":"https://pith.science/pith/ASXVFY7Y22PYV5MSEBREWCVHMR/bundle.json","state":"https://pith.science/pith/ASXVFY7Y22PYV5MSEBREWCVHMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASXVFY7Y22PYV5MSEBREWCVHMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ASXVFY7Y22PYV5MSEBREWCVHMR","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":"5eae75c67dfda1ff8d8a4d2a4a1df8024e7aa9728025b01dd442ad2e5f889759","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-23T10:03:05Z","title_canon_sha256":"e527d86bf5113e66c3f1e42282e004c07f1c8aa3704076505f580df474ffc5a7"},"schema_version":"1.0","source":{"id":"1611.07712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07712","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07712v1","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07712","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"ASXVFY7Y22PY","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ASXVFY7Y22PYV5MS","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ASXVFY7Y","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:a82dd8f2593f037127b79be57ca19f64181766418587e10930dc84098f85f34f","target":"graph","created_at":"2026-05-18T00:57:00Z","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":"The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either unknown or intractable. For this reason, it is of interest to develop useful lower bounds on the FIM. In this lecture note, we derive such a bound based on moment constraints. We call this bound the Pearson information matrix (PIM) and relate it to properties of a misspecified data distribution. Finally, we show that the inverse PIM coincides with the asymp","authors_text":"Dave Zachariah, Petre Stoica","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-23T10:03:05Z","title":"Pearson information-based lower bound on Fisher information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07712","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":"sha256:2764ec270324561ce5e217140407d63e2f1f46d0d0f3a7b858d3f3a8390d10c3","target":"record","created_at":"2026-05-18T00:57:00Z","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":"5eae75c67dfda1ff8d8a4d2a4a1df8024e7aa9728025b01dd442ad2e5f889759","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-23T10:03:05Z","title_canon_sha256":"e527d86bf5113e66c3f1e42282e004c07f1c8aa3704076505f580df474ffc5a7"},"schema_version":"1.0","source":{"id":"1611.07712","kind":"arxiv","version":1}},"canonical_sha256":"04af52e3f8d69f8af59220624b0aa7644afff08178a3bde9c6d0e3467f5171c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04af52e3f8d69f8af59220624b0aa7644afff08178a3bde9c6d0e3467f5171c4","first_computed_at":"2026-05-18T00:57:00.028573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:00.028573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2zeCnG+vuW38ic7aVv5uWVrVWctx+xeT1foKBx9awMPqfBW8EoDUXW33lNKnESsCBy0katvwyHtibA1WJwimAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:00.029051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2764ec270324561ce5e217140407d63e2f1f46d0d0f3a7b858d3f3a8390d10c3","sha256:a82dd8f2593f037127b79be57ca19f64181766418587e10930dc84098f85f34f"],"state_sha256":"f6532465141cfeafc16d6ff0abd41db3f5cb75d590a7dcb8801fc51de56fed5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VooN7sqzU7CUNtdcQjgh7nI1TbAyV22vLO6XHzTJsG+hW4E8wxB66JyTI8vKuIlS4nrt+diR2wyJYlxNxSJBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:10:20.774515Z","bundle_sha256":"d41fb0965196eb78deec5c4087a945ab41d1361751f5bc4ac5d05694028b10b9"}}