{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:DQMP5NQQUELFW5AWGNIUY5SBZV","short_pith_number":"pith:DQMP5NQQ","canonical_record":{"source":{"id":"0912.0065","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T03:42:10Z","cross_cats_sorted":[],"title_canon_sha256":"f22687f02f603cf4aab827b6ed70887a4dbdd006c8ffd5313463ebd184f31fb5","abstract_canon_sha256":"96e4fd8c7ea9eeffcfdbccecd56222e215cf9be5fcb01ae66afe2c0b496742db"},"schema_version":"1.0"},"canonical_sha256":"1c18feb610a1165b741633514c7641cd4edaf42606604278bff6a1ea8bc14aa2","source":{"kind":"arxiv","id":"0912.0065","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0065","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0065v4","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0065","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"DQMP5NQQUELF","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DQMP5NQQUELFW5AW","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DQMP5NQQ","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:DQMP5NQQUELFW5AWGNIUY5SBZV","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0065","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T03:42:10Z","cross_cats_sorted":[],"title_canon_sha256":"f22687f02f603cf4aab827b6ed70887a4dbdd006c8ffd5313463ebd184f31fb5","abstract_canon_sha256":"96e4fd8c7ea9eeffcfdbccecd56222e215cf9be5fcb01ae66afe2c0b496742db"},"schema_version":"1.0"},"canonical_sha256":"1c18feb610a1165b741633514c7641cd4edaf42606604278bff6a1ea8bc14aa2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:36.919826Z","signature_b64":"+Kcm1FC9/uZ6bK2dGC5kAd4vU2tZBiUzPhIj9On9A3oHOCXk0XdIHoRJXLasC20hLOiBJ2DlhI2I9y8EJ4rDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c18feb610a1165b741633514c7641cd4edaf42606604278bff6a1ea8bc14aa2","last_reissued_at":"2026-05-18T04:15:36.919390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:36.919390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0065","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y+npdMwqi0kszfAGuSgQJHIuLG4UDn9Oyu4wzWdBkFiC+9zCzhSZsmNBg4LDrUEHQ2WMT+c9HfBLyTjMw2nPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:05:39.945030Z"},"content_sha256":"2d576d754626f244b4a77eae1c7f5745cc7aace75a6fe1a795d94d28e17aaf43","schema_version":"1.0","event_id":"sha256:2d576d754626f244b4a77eae1c7f5745cc7aace75a6fe1a795d94d28e17aaf43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:DQMP5NQQUELFW5AWGNIUY5SBZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Michele Zanolin, Nicholas Makris, Salvatore Vitale","submitted_at":"2009-12-01T03:42:10Z","abstract_excerpt":"In this paper we describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from Gravitational wave signals. All the existing litterature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of a MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0065","kind":"arxiv","version":4},"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":"2026-05-18T04:15:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7wHZjOX1S/VjsjhzqPk1shTriBNf8FrCvH0fGigHmZ9778OaM09d6JZzaYvcZufXFVMcghpJo1lcgziXj0lDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:05:39.945771Z"},"content_sha256":"5db271b60c4fec98bd1ab23578a5973c1960f26e777dfe2549441605a771e85c","schema_version":"1.0","event_id":"sha256:5db271b60c4fec98bd1ab23578a5973c1960f26e777dfe2549441605a771e85c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQMP5NQQUELFW5AWGNIUY5SBZV/bundle.json","state_url":"https://pith.science/pith/DQMP5NQQUELFW5AWGNIUY5SBZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQMP5NQQUELFW5AWGNIUY5SBZV/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":"2026-06-09T10:05:39Z","links":{"resolver":"https://pith.science/pith/DQMP5NQQUELFW5AWGNIUY5SBZV","bundle":"https://pith.science/pith/DQMP5NQQUELFW5AWGNIUY5SBZV/bundle.json","state":"https://pith.science/pith/DQMP5NQQUELFW5AWGNIUY5SBZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQMP5NQQUELFW5AWGNIUY5SBZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DQMP5NQQUELFW5AWGNIUY5SBZV","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":"96e4fd8c7ea9eeffcfdbccecd56222e215cf9be5fcb01ae66afe2c0b496742db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T03:42:10Z","title_canon_sha256":"f22687f02f603cf4aab827b6ed70887a4dbdd006c8ffd5313463ebd184f31fb5"},"schema_version":"1.0","source":{"id":"0912.0065","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0065","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0065v4","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0065","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"DQMP5NQQUELF","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DQMP5NQQUELFW5AW","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DQMP5NQQ","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:5db271b60c4fec98bd1ab23578a5973c1960f26e777dfe2549441605a771e85c","target":"graph","created_at":"2026-05-18T04:15:36Z","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 describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from Gravitational wave signals. All the existing litterature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of a MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias","authors_text":"Michele Zanolin, Nicholas Makris, Salvatore Vitale","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T03:42:10Z","title":"Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0065","kind":"arxiv","version":4},"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":"sha256:2d576d754626f244b4a77eae1c7f5745cc7aace75a6fe1a795d94d28e17aaf43","target":"record","created_at":"2026-05-18T04:15:36Z","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":"96e4fd8c7ea9eeffcfdbccecd56222e215cf9be5fcb01ae66afe2c0b496742db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T03:42:10Z","title_canon_sha256":"f22687f02f603cf4aab827b6ed70887a4dbdd006c8ffd5313463ebd184f31fb5"},"schema_version":"1.0","source":{"id":"0912.0065","kind":"arxiv","version":4}},"canonical_sha256":"1c18feb610a1165b741633514c7641cd4edaf42606604278bff6a1ea8bc14aa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c18feb610a1165b741633514c7641cd4edaf42606604278bff6a1ea8bc14aa2","first_computed_at":"2026-05-18T04:15:36.919390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:36.919390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Kcm1FC9/uZ6bK2dGC5kAd4vU2tZBiUzPhIj9On9A3oHOCXk0XdIHoRJXLasC20hLOiBJ2DlhI2I9y8EJ4rDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:36.919826Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0065","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d576d754626f244b4a77eae1c7f5745cc7aace75a6fe1a795d94d28e17aaf43","sha256:5db271b60c4fec98bd1ab23578a5973c1960f26e777dfe2549441605a771e85c"],"state_sha256":"98874652e90c968aa1fa6946c741b3e67fc4d9e445481720f4465cdfea920270"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvVDpOM7Qot0dNG6Y+bWpoF0gQV1ChUtn0KqZhctBrfDw+hlBlDfelHTwpL8L0fONeL/qtcGKfOZ+S0ULM3ZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:05:39.950278Z","bundle_sha256":"cd36ba5fe00ed6a92fd9353c5e3415c775422640462f8d27c29a0cb5d4407b2a"}}