{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WG7H7ULMSQ7UZ2TBLNM4K6F2YL","short_pith_number":"pith:WG7H7ULM","canonical_record":{"source":{"id":"2605.16247","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T17:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"3b2c734d6be43247ae329e10d1c9a9f99b6727664cc243f4d7247a50dbf7de17","abstract_canon_sha256":"d6edd67a7f5f5d34543da68ddfe1312af88cbc6846d583c9e0f56e44587d8fff"},"schema_version":"1.0"},"canonical_sha256":"b1be7fd16c943f4cea615b59c578bac2cbde4410393e80ec2f4e2ed9b58b6b01","source":{"kind":"arxiv","id":"2605.16247","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16247","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16247v1","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16247","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_12","alias_value":"WG7H7ULMSQ7U","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_16","alias_value":"WG7H7ULMSQ7UZ2TB","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_8","alias_value":"WG7H7ULM","created_at":"2026-05-20T00:02:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WG7H7ULMSQ7UZ2TBLNM4K6F2YL","target":"record","payload":{"canonical_record":{"source":{"id":"2605.16247","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T17:51:01Z","cross_cats_sorted":[],"title_canon_sha256":"3b2c734d6be43247ae329e10d1c9a9f99b6727664cc243f4d7247a50dbf7de17","abstract_canon_sha256":"d6edd67a7f5f5d34543da68ddfe1312af88cbc6846d583c9e0f56e44587d8fff"},"schema_version":"1.0"},"canonical_sha256":"b1be7fd16c943f4cea615b59c578bac2cbde4410393e80ec2f4e2ed9b58b6b01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:00.037252Z","signature_b64":"JeG+4PwKCDmeD5M5ren9/KpzQD+fVK1Yr6R8o2bOWYPpvN1di3O7SOukf8AhaDOOmRb9Mw5QNP2ESZXj6TAtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1be7fd16c943f4cea615b59c578bac2cbde4410393e80ec2f4e2ed9b58b6b01","last_reissued_at":"2026-05-20T00:02:00.036431Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:00.036431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.16247","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":"2026-05-20T00:02:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ttBOyv18lwrC6BwEsTXe/U0TPYwB7al7zDOE/B/HaYDCvSOgODmvSMK8nw2rxM0/eoHgeP5dsA0niBGQKjCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:32:47.735358Z"},"content_sha256":"cc862074bd9c54e54c85a69d33cfea92f36214a6ba16aa8af54df74b549ebec4","schema_version":"1.0","event_id":"sha256:cc862074bd9c54e54c85a69d33cfea92f36214a6ba16aa8af54df74b549ebec4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WG7H7ULMSQ7UZ2TBLNM4K6F2YL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brownian motion: non-equilibrium states from equilibrium trajectories -- recovering hydrodynamic regimes from prepared displacement measurements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Giuseppe Procopio, Jason Boynewicz, Massimiliano Giona, Michael C. Thumann","submitted_at":"2026-05-15T17:51:01Z","abstract_excerpt":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics,any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states. This property permits the unraveling of fine details of fluid-particle interactions at microscales defined by its non-equilibrium properties from the analysis of a single Brownian trajectory and to connect them to the hydrodynamics of the solvent fluid, simply considering the lower-order (second) moments of particle position in trapped conditions. In this way, the acceleration "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics, any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states, permitting the unraveling of fine details of fluid-particle interactions at microscales from the analysis of a single Brownian trajectory by considering the lower-order (second) moments of particle position in trapped conditions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The particle dynamics are strictly Markovian so that the Chapman-Kolmogorov equation applies directly to the equilibrium trajectory and allows its decomposition into non-equilibrium components (stated in the opening sentence of the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Equilibrium Brownian trajectories encode non-equilibrium hydrodynamic information through displacement moments, confirming a t^{5/2} scaling from fluid inertia and suggesting a possible t^4 scaling at shorter times due to velocity regularity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c00ce0e98f37b414d343ec1980f3a4a3b189b6696393be3c145b7a83a6e14f99"},"source":{"id":"2605.16247","kind":"arxiv","version":1},"verdict":{"id":"5088fff4-8eae-415a-af5a-1af3751f9c9a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:31:00.118073Z","strongest_claim":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics, any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states, permitting the unraveling of fine details of fluid-particle interactions at microscales from the analysis of a single Brownian trajectory by considering the lower-order (second) moments of particle position in trapped conditions.","one_line_summary":"Equilibrium Brownian trajectories encode non-equilibrium hydrodynamic information through displacement moments, confirming a t^{5/2} scaling from fluid inertia and suggesting a possible t^4 scaling at shorter times due to velocity regularity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The particle dynamics are strictly Markovian so that the Chapman-Kolmogorov equation applies directly to the equilibrium trajectory and allows its decomposition into non-equilibrium components (stated in the opening sentence of the abstract).","pith_extraction_headline":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16247/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.874053Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:40:52.987630Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"shingle_duplication","ran_at":"2026-05-19T17:49:42.181526Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:41.792340Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:23.092759Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T17:31:24.989746Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.602583Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T16:51:56.780943Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"cfa39a8a272320f9a07849171623ac9467f767b7198ea6550beb6896280a9298"},"references":{"count":63,"sample":[{"doi":"","year":null,"title":"001 0 . 01 0 . 1 1 10 100 1000 mxx(t) 1 10 t5 FIG. 2. mxx(t) = ⟨x2(t)|v(0) = 0 , R (0) = 0 ⟩ vs t expressed by eq. (35) for zero velocity and zero initial thermal force conditions for a GLE governed b","work_id":"fd79e7a7-4ac9-469a-a3d6-597681bd243b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"ﬁll the plane","work_id":"54dec1d7-de80-4e16-81f5-88885a0507d9","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1943,"title":"Chandrasekhar, Stochastic Problems in Physics and As tronomy, Rev","work_id":"f24cfc8b-7588-4dc0-8aef-352943688aa5","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1905,"title":"Einstein, ¨Uber die von der molekularkinetischen Theorie der W¨ rme gef orderte Bewegung von in ruhenden Fl¨ ussigkeiten suspendierten Teilchen,Ann","work_id":"5b257aa2-2cc8-4d6a-b641-3ca8c06b8b05","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1906,"title":"Einstein, Zur Theorie der Brownschen Bewegung Ann","work_id":"47786328-9fd1-4b04-be3c-1396fb0cefc7","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":63,"snapshot_sha256":"29b564e36f03d104f8bc6b020cf2fa9198e369f0d144172aa0afe398548d21a4","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f68c7242901a104537abba8b9c42725cecf3b5ce64d5549fcc7a17f90920a57d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"5088fff4-8eae-415a-af5a-1af3751f9c9a"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQ4y8OyeLgmG1iclpFgluFutVjA5ZciQqB9QN/gmk2VRkoe/SQi2KpjjAqqTR5oOCknn74+WvExe1+PDQpuHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:32:47.736603Z"},"content_sha256":"aab3aeff578ef2c08f06cf7af5501631fb930dbd81d295f369fd43a59601a613","schema_version":"1.0","event_id":"sha256:aab3aeff578ef2c08f06cf7af5501631fb930dbd81d295f369fd43a59601a613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WG7H7ULMSQ7UZ2TBLNM4K6F2YL/bundle.json","state_url":"https://pith.science/pith/WG7H7ULMSQ7UZ2TBLNM4K6F2YL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WG7H7ULMSQ7UZ2TBLNM4K6F2YL/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":"2026-06-02T19:32:47Z","links":{"resolver":"https://pith.science/pith/WG7H7ULMSQ7UZ2TBLNM4K6F2YL","bundle":"https://pith.science/pith/WG7H7ULMSQ7UZ2TBLNM4K6F2YL/bundle.json","state":"https://pith.science/pith/WG7H7ULMSQ7UZ2TBLNM4K6F2YL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WG7H7ULMSQ7UZ2TBLNM4K6F2YL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WG7H7ULMSQ7UZ2TBLNM4K6F2YL","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":"d6edd67a7f5f5d34543da68ddfe1312af88cbc6846d583c9e0f56e44587d8fff","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T17:51:01Z","title_canon_sha256":"3b2c734d6be43247ae329e10d1c9a9f99b6727664cc243f4d7247a50dbf7de17"},"schema_version":"1.0","source":{"id":"2605.16247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16247","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16247v1","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16247","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_12","alias_value":"WG7H7ULMSQ7U","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_16","alias_value":"WG7H7ULMSQ7UZ2TB","created_at":"2026-05-20T00:02:00Z"},{"alias_kind":"pith_short_8","alias_value":"WG7H7ULM","created_at":"2026-05-20T00:02:00Z"}],"graph_snapshots":[{"event_id":"sha256:aab3aeff578ef2c08f06cf7af5501631fb930dbd81d295f369fd43a59601a613","target":"graph","created_at":"2026-05-20T00:02:00Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics, any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states, permitting the unraveling of fine details of fluid-particle interactions at microscales from the analysis of a single Brownian trajectory by considering the lower-order (second) moments of particle position in trapped conditions."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The particle dynamics are strictly Markovian so that the Chapman-Kolmogorov equation applies directly to the equilibrium trajectory and allows its decomposition into non-equilibrium components (stated in the opening sentence of the abstract)."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Equilibrium Brownian trajectories encode non-equilibrium hydrodynamic information through displacement moments, confirming a t^{5/2} scaling from fluid inertia and suggesting a possible t^4 scaling at shorter times due to velocity regularity."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation."}],"snapshot_sha256":"c00ce0e98f37b414d343ec1980f3a4a3b189b6696393be3c145b7a83a6e14f99"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f68c7242901a104537abba8b9c42725cecf3b5ce64d5549fcc7a17f90920a57d"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.874053Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T18:40:52.987630Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"shingle_duplication","ran_at":"2026-05-19T17:49:42.181526Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:41.792340Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:23.092759Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"external_links","ran_at":"2026-05-19T17:31:24.989746Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.602583Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T16:51:56.780943Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.16247/integrity.json","findings":[],"snapshot_sha256":"cfa39a8a272320f9a07849171623ac9467f767b7198ea6550beb6896280a9298","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics,any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states. This property permits the unraveling of fine details of fluid-particle interactions at microscales defined by its non-equilibrium properties from the analysis of a single Brownian trajectory and to connect them to the hydrodynamics of the solvent fluid, simply considering the lower-order (second) moments of particle position in trapped conditions. In this way, the acceleration ","authors_text":"Giuseppe Procopio, Jason Boynewicz, Massimiliano Giona, Michael C. Thumann","cross_cats":[],"headline":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T17:51:01Z","title":"Brownian motion: non-equilibrium states from equilibrium trajectories -- recovering hydrodynamic regimes from prepared displacement measurements"},"references":{"count":63,"internal_anchors":0,"resolved_work":63,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"001 0 . 01 0 . 1 1 10 100 1000 mxx(t) 1 10 t5 FIG. 2. mxx(t) = ⟨x2(t)|v(0) = 0 , R (0) = 0 ⟩ vs t expressed by eq. (35) for zero velocity and zero initial thermal force conditions for a GLE governed b","work_id":"fd79e7a7-4ac9-469a-a3d6-597681bd243b","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"ﬁll the plane","work_id":"54dec1d7-de80-4e16-81f5-88885a0507d9","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Chandrasekhar, Stochastic Problems in Physics and As tronomy, Rev","work_id":"f24cfc8b-7588-4dc0-8aef-352943688aa5","year":1943},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Einstein, ¨Uber die von der molekularkinetischen Theorie der W¨ rme gef orderte Bewegung von in ruhenden Fl¨ ussigkeiten suspendierten Teilchen,Ann","work_id":"5b257aa2-2cc8-4d6a-b641-3ca8c06b8b05","year":1905},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Einstein, Zur Theorie der Brownschen Bewegung Ann","work_id":"47786328-9fd1-4b04-be3c-1396fb0cefc7","year":1906}],"snapshot_sha256":"29b564e36f03d104f8bc6b020cf2fa9198e369f0d144172aa0afe398548d21a4"},"source":{"id":"2605.16247","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:31:00.118073Z","id":"5088fff4-8eae-415a-af5a-1af3751f9c9a","model_set":{"reader":"grok-4.3"},"one_line_summary":"Equilibrium Brownian trajectories encode non-equilibrium hydrodynamic information through displacement moments, confirming a t^{5/2} scaling from fluid inertia and suggesting a possible t^4 scaling at shorter times due to velocity regularity.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation.","strongest_claim":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics, any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states, permitting the unraveling of fine details of fluid-particle interactions at microscales from the analysis of a single Brownian trajectory by considering the lower-order (second) moments of particle position in trapped conditions.","weakest_assumption":"The particle dynamics are strictly Markovian so that the Chapman-Kolmogorov equation applies directly to the equilibrium trajectory and allows its decomposition into non-equilibrium components (stated in the opening sentence of the abstract)."}},"verdict_id":"5088fff4-8eae-415a-af5a-1af3751f9c9a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cc862074bd9c54e54c85a69d33cfea92f36214a6ba16aa8af54df74b549ebec4","target":"record","created_at":"2026-05-20T00:02:00Z","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":"d6edd67a7f5f5d34543da68ddfe1312af88cbc6846d583c9e0f56e44587d8fff","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T17:51:01Z","title_canon_sha256":"3b2c734d6be43247ae329e10d1c9a9f99b6727664cc243f4d7247a50dbf7de17"},"schema_version":"1.0","source":{"id":"2605.16247","kind":"arxiv","version":1}},"canonical_sha256":"b1be7fd16c943f4cea615b59c578bac2cbde4410393e80ec2f4e2ed9b58b6b01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1be7fd16c943f4cea615b59c578bac2cbde4410393e80ec2f4e2ed9b58b6b01","first_computed_at":"2026-05-20T00:02:00.036431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:00.036431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JeG+4PwKCDmeD5M5ren9/KpzQD+fVK1Yr6R8o2bOWYPpvN1di3O7SOukf8AhaDOOmRb9Mw5QNP2ESZXj6TAtAg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:00.037252Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc862074bd9c54e54c85a69d33cfea92f36214a6ba16aa8af54df74b549ebec4","sha256:aab3aeff578ef2c08f06cf7af5501631fb930dbd81d295f369fd43a59601a613"],"state_sha256":"70e16c7c09109336c61337746863025a01857828b13cccca62dec16fc8d4c0c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CfqVkAE+Qx/yGsh0gAwNptSpVfVO45d5vPJnNcLhTi/4ZJjzFEgn1mqwGQ5XT5ETG6goakVxGa51aru7gDKMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:32:47.739454Z","bundle_sha256":"18b27e7ee99abf876ada8f62b9e357b7128e982d66fbac83dddff76f06ea1daf"}}