{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DDOEZO5RGRARTMTVNCRWILNTSZ","short_pith_number":"pith:DDOEZO5R","canonical_record":{"source":{"id":"1301.4374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-18T13:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"a366eae82f411540266a3abecf31e348276aa8c2569421356329feca1e8caa12","abstract_canon_sha256":"6cd2cfffe459885d0380c4976b877f89013f6fbbe9a8966d9d176d52c23a869b"},"schema_version":"1.0"},"canonical_sha256":"18dc4cbbb1344119b27568a3642db396447d99c9b8336b73a98089dcc74efddf","source":{"kind":"arxiv","id":"1301.4374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4374","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4374v1","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4374","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"DDOEZO5RGRAR","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"DDOEZO5RGRARTMTV","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"DDOEZO5R","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DDOEZO5RGRARTMTVNCRWILNTSZ","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-18T13:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"a366eae82f411540266a3abecf31e348276aa8c2569421356329feca1e8caa12","abstract_canon_sha256":"6cd2cfffe459885d0380c4976b877f89013f6fbbe9a8966d9d176d52c23a869b"},"schema_version":"1.0"},"canonical_sha256":"18dc4cbbb1344119b27568a3642db396447d99c9b8336b73a98089dcc74efddf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:05.867329Z","signature_b64":"grm3wghAhYbdDSyM9hmFRGiXi1w+oxSsl6/zohVKSEiWCfHeTitUfla7IowE5/W/lgxCQI7nacKN5bfzgldTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18dc4cbbb1344119b27568a3642db396447d99c9b8336b73a98089dcc74efddf","last_reissued_at":"2026-05-18T01:52:05.866861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:05.866861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4374","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":"2026-05-18T01:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TChyx8uAgK6JyX3OJ9e1cHYnVzdrOP1tCFdqXUn512iJsqQ0jaZwZF1kU0cG94g9IdbUYuoXvw4RYKX4VCWuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:50:44.142674Z"},"content_sha256":"658ba51153f81ed603096aafbdc95161ce10cade9084fddd882fdf55656bebd5","schema_version":"1.0","event_id":"sha256:658ba51153f81ed603096aafbdc95161ce10cade9084fddd882fdf55656bebd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DDOEZO5RGRARTMTVNCRWILNTSZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Carlos Mejia-Monasterio, David S. Dean, Denis Boyer, Gleb Oshanin","submitted_at":"2013-01-18T13:14:11Z","abstract_excerpt":"In this paper we study the distribution function $P(u_{\\alpha})$ of the estimators $u_{\\alpha} \\sim T^{-1} \\int^T_0 \\, \\omega(t) \\, {\\bf B}^2_{t} \\, dt$, which optimise the least-squares fitting of the diffusion coefficient $D_f$ of a single $d$-dimensional Brownian trajectory ${\\bf B}_{t}$. We pursue here the optimisation further by considering a family of weight functions of the form $\\omega(t) = (t_0 + t)^{-\\alpha}$, where $t_0$ is a time lag and $\\alpha$ is an arbitrary real number, and seeking such values of $\\alpha$ for which the estimators most efficiently filter out the fluctuations. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4374","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":"2026-05-18T01:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRDIVypfkuL3Fd/RnEP1+e1MIHYj1dpATUn7cYj131f1sEuLsEt6WOZSUoExLUaHVPd9ndrAo9rZhkvb4MsfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:50:44.143026Z"},"content_sha256":"c627dbf642d6f6b97807a06de6b267e5adbb26cf53d8b970b4762c85661202b9","schema_version":"1.0","event_id":"sha256:c627dbf642d6f6b97807a06de6b267e5adbb26cf53d8b970b4762c85661202b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DDOEZO5RGRARTMTVNCRWILNTSZ/bundle.json","state_url":"https://pith.science/pith/DDOEZO5RGRARTMTVNCRWILNTSZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DDOEZO5RGRARTMTVNCRWILNTSZ/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":"2026-06-03T16:50:44Z","links":{"resolver":"https://pith.science/pith/DDOEZO5RGRARTMTVNCRWILNTSZ","bundle":"https://pith.science/pith/DDOEZO5RGRARTMTVNCRWILNTSZ/bundle.json","state":"https://pith.science/pith/DDOEZO5RGRARTMTVNCRWILNTSZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DDOEZO5RGRARTMTVNCRWILNTSZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DDOEZO5RGRARTMTVNCRWILNTSZ","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":"6cd2cfffe459885d0380c4976b877f89013f6fbbe9a8966d9d176d52c23a869b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-18T13:14:11Z","title_canon_sha256":"a366eae82f411540266a3abecf31e348276aa8c2569421356329feca1e8caa12"},"schema_version":"1.0","source":{"id":"1301.4374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4374","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4374v1","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4374","created_at":"2026-05-18T01:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"DDOEZO5RGRAR","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"DDOEZO5RGRARTMTV","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"DDOEZO5R","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:c627dbf642d6f6b97807a06de6b267e5adbb26cf53d8b970b4762c85661202b9","target":"graph","created_at":"2026-05-18T01:52:05Z","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":"In this paper we study the distribution function $P(u_{\\alpha})$ of the estimators $u_{\\alpha} \\sim T^{-1} \\int^T_0 \\, \\omega(t) \\, {\\bf B}^2_{t} \\, dt$, which optimise the least-squares fitting of the diffusion coefficient $D_f$ of a single $d$-dimensional Brownian trajectory ${\\bf B}_{t}$. We pursue here the optimisation further by considering a family of weight functions of the form $\\omega(t) = (t_0 + t)^{-\\alpha}$, where $t_0$ is a time lag and $\\alpha$ is an arbitrary real number, and seeking such values of $\\alpha$ for which the estimators most efficiently filter out the fluctuations. W","authors_text":"Carlos Mejia-Monasterio, David S. Dean, Denis Boyer, Gleb Oshanin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-18T13:14:11Z","title":"Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4374","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":"sha256:658ba51153f81ed603096aafbdc95161ce10cade9084fddd882fdf55656bebd5","target":"record","created_at":"2026-05-18T01:52:05Z","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":"6cd2cfffe459885d0380c4976b877f89013f6fbbe9a8966d9d176d52c23a869b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-18T13:14:11Z","title_canon_sha256":"a366eae82f411540266a3abecf31e348276aa8c2569421356329feca1e8caa12"},"schema_version":"1.0","source":{"id":"1301.4374","kind":"arxiv","version":1}},"canonical_sha256":"18dc4cbbb1344119b27568a3642db396447d99c9b8336b73a98089dcc74efddf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18dc4cbbb1344119b27568a3642db396447d99c9b8336b73a98089dcc74efddf","first_computed_at":"2026-05-18T01:52:05.866861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:05.866861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"grm3wghAhYbdDSyM9hmFRGiXi1w+oxSsl6/zohVKSEiWCfHeTitUfla7IowE5/W/lgxCQI7nacKN5bfzgldTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:05.867329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:658ba51153f81ed603096aafbdc95161ce10cade9084fddd882fdf55656bebd5","sha256:c627dbf642d6f6b97807a06de6b267e5adbb26cf53d8b970b4762c85661202b9"],"state_sha256":"43937a4ae6b6ee490eefdfd10cfadbdc4b6dc6bda6536b0897045e78debab929"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PvVEXWPiaCHFSIL+Afb6fLFIWO4Gtyq1NlGJPZv12GTVNsxGTQBdvpUugc5scP7577IyUd39h9/4ileH+WQoCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:50:44.145011Z","bundle_sha256":"a3b1c6d2c660a31df715c8e45ede71bedb8c2e17f889cbe0947023410fcf686d"}}