{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:J6ZVWH4JS6KEY7WXK2GOGJQLM4","short_pith_number":"pith:J6ZVWH4J","schema_version":"1.0","canonical_sha256":"4fb35b1f8997944c7ed7568ce3260b670dcff9264b482c3270240cd14877e5cd","source":{"kind":"arxiv","id":"0909.0955","version":1},"attestation_state":"computed","paper":{"title":"Correlation Dimension of Inertial Particles in Random Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Bernhard Mehlig, Kristian Gustavsson, Michael Wilkinson","submitted_at":"2009-09-04T20:39:10Z","abstract_excerpt":"We obtain an implicit equation for the correlation dimension of dynamical systems in terms of an integral over a propagator. We illustrate the utility of this approach by evaluating the correlation dimension for inertial particles suspended in a random flow. In the limit where the correlation time of the flow field approaches zero, taking the short-time limit of the propagator enables the correlation dimension to be determined from the solution of a partial differential equation. We develop the solution as a power series in a dimensionless parameter which represents the strength of inertial ef"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0909.0955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2009-09-04T20:39:10Z","cross_cats_sorted":[],"title_canon_sha256":"261312fb43e23d00bc7d0002d4a76cc2df46da60b1010864bab73f24ed19b2cc","abstract_canon_sha256":"4f2cbb6c1ad990bc753c8d5d12c101344f860e6bafa644c4f13c2113644b8f0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:59.583151Z","signature_b64":"uaCczPbFJIT+4qSSzqUkYQjurzQ/B1P0BWGGQVFiEvGYfjvjJsamuKboJPJhGNSUZ7xbF9+UsB3bcR+vpj6QBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fb35b1f8997944c7ed7568ce3260b670dcff9264b482c3270240cd14877e5cd","last_reissued_at":"2026-05-18T02:11:59.582290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:59.582290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlation Dimension of Inertial Particles in Random Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Bernhard Mehlig, Kristian Gustavsson, Michael Wilkinson","submitted_at":"2009-09-04T20:39:10Z","abstract_excerpt":"We obtain an implicit equation for the correlation dimension of dynamical systems in terms of an integral over a propagator. We illustrate the utility of this approach by evaluating the correlation dimension for inertial particles suspended in a random flow. In the limit where the correlation time of the flow field approaches zero, taking the short-time limit of the propagator enables the correlation dimension to be determined from the solution of a partial differential equation. We develop the solution as a power series in a dimensionless parameter which represents the strength of inertial ef"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0955","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0909.0955","created_at":"2026-05-18T02:11:59.582454+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.0955v1","created_at":"2026-05-18T02:11:59.582454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0955","created_at":"2026-05-18T02:11:59.582454+00:00"},{"alias_kind":"pith_short_12","alias_value":"J6ZVWH4JS6KE","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"J6ZVWH4JS6KEY7WX","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"J6ZVWH4J","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4","json":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4.json","graph_json":"https://pith.science/api/pith-number/J6ZVWH4JS6KEY7WXK2GOGJQLM4/graph.json","events_json":"https://pith.science/api/pith-number/J6ZVWH4JS6KEY7WXK2GOGJQLM4/events.json","paper":"https://pith.science/paper/J6ZVWH4J"},"agent_actions":{"view_html":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4","download_json":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4.json","view_paper":"https://pith.science/paper/J6ZVWH4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.0955&json=true","fetch_graph":"https://pith.science/api/pith-number/J6ZVWH4JS6KEY7WXK2GOGJQLM4/graph.json","fetch_events":"https://pith.science/api/pith-number/J6ZVWH4JS6KEY7WXK2GOGJQLM4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4/action/storage_attestation","attest_author":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4/action/author_attestation","sign_citation":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4/action/citation_signature","submit_replication":"https://pith.science/pith/J6ZVWH4JS6KEY7WXK2GOGJQLM4/action/replication_record"}},"created_at":"2026-05-18T02:11:59.582454+00:00","updated_at":"2026-05-18T02:11:59.582454+00:00"}