{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I5A4GOGR355T4CCAYJZ7QNVMTX","short_pith_number":"pith:I5A4GOGR","canonical_record":{"source":{"id":"1609.00916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-09-04T10:52:20Z","cross_cats_sorted":[],"title_canon_sha256":"623fb8b4c19f5ee39c9f32c2e6a813a7c1a7ebc15a1a803887997645b8ebc5a2","abstract_canon_sha256":"6fb77219d8cce21aac1ba4d994bf5bc149b650b2f05f2434f54f10851746a14b"},"schema_version":"1.0"},"canonical_sha256":"4741c338d1df7b3e0840c273f836ac9dd3dd0b6836c689bde211e91e2e26f665","source":{"kind":"arxiv","id":"1609.00916","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00916","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00916v1","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00916","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"I5A4GOGR355T","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I5A4GOGR355T4CCA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I5A4GOGR","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I5A4GOGR355T4CCAYJZ7QNVMTX","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-09-04T10:52:20Z","cross_cats_sorted":[],"title_canon_sha256":"623fb8b4c19f5ee39c9f32c2e6a813a7c1a7ebc15a1a803887997645b8ebc5a2","abstract_canon_sha256":"6fb77219d8cce21aac1ba4d994bf5bc149b650b2f05f2434f54f10851746a14b"},"schema_version":"1.0"},"canonical_sha256":"4741c338d1df7b3e0840c273f836ac9dd3dd0b6836c689bde211e91e2e26f665","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:19.547380Z","signature_b64":"c9aZz09u7Lg2a1evbQY7lihKyB+qMO/1eeLxY/WdrjUISSp7rro7ch7A+Pr0+DCF+0b4PA+Mv3FhBti9HC7zBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4741c338d1df7b3e0840c273f836ac9dd3dd0b6836c689bde211e91e2e26f665","last_reissued_at":"2026-05-18T01:06:19.546708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:19.546708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00916","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":"2026-05-18T01:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VjiGj3y1cTpEMi48/SyQQMoOJ67+sQt/Woj8h3koaqQKnVkBiSp1qO9tx9lh40APfoHwWznLGKbyFO3zXL24CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:22:45.077470Z"},"content_sha256":"4e3ae6f428029274d62b7e6fc9649bfc04ec554028475c8c2a31ffcf7bcedb40","schema_version":"1.0","event_id":"sha256:4e3ae6f428029274d62b7e6fc9649bfc04ec554028475c8c2a31ffcf7bcedb40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I5A4GOGR355T4CCAYJZ7QNVMTX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A correction to collision rates of droplets in turbulent flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Huang Zhang, Qianfeng Liu","submitted_at":"2016-09-04T10:52:20Z","abstract_excerpt":"This paper makes a correction to the collision rates of small droplets in turbulent fluid derived by Saffman and Turner(1956). Not only the distortion but also the rotation of the fluid is taken into account between two close droplets. A rotation reference is fixed on one drop, and the fluxes of the other drops moving towards the fixed one are carried out based on this new reference. The behaviors of turbulent flow are analyzed within the smallest eddies under the rotation reference, and a correction is made to the collision rates by multiplying a factor sqrt(2)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00916","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":"2026-05-18T01:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QwfG6+2+MnCCe2GEatAOt/toF763gRT1HmbOFP/4FhW5svfLJoKf23fV8oLshXmBFhHSLLTpwEa0xdl3b1pCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:22:45.077821Z"},"content_sha256":"e89aab8a23cf8da3eba3ffed6c25c5367600673e0255788538c556d5c65ecba4","schema_version":"1.0","event_id":"sha256:e89aab8a23cf8da3eba3ffed6c25c5367600673e0255788538c556d5c65ecba4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I5A4GOGR355T4CCAYJZ7QNVMTX/bundle.json","state_url":"https://pith.science/pith/I5A4GOGR355T4CCAYJZ7QNVMTX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I5A4GOGR355T4CCAYJZ7QNVMTX/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":"2026-06-28T08:22:45Z","links":{"resolver":"https://pith.science/pith/I5A4GOGR355T4CCAYJZ7QNVMTX","bundle":"https://pith.science/pith/I5A4GOGR355T4CCAYJZ7QNVMTX/bundle.json","state":"https://pith.science/pith/I5A4GOGR355T4CCAYJZ7QNVMTX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I5A4GOGR355T4CCAYJZ7QNVMTX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I5A4GOGR355T4CCAYJZ7QNVMTX","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":"6fb77219d8cce21aac1ba4d994bf5bc149b650b2f05f2434f54f10851746a14b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-09-04T10:52:20Z","title_canon_sha256":"623fb8b4c19f5ee39c9f32c2e6a813a7c1a7ebc15a1a803887997645b8ebc5a2"},"schema_version":"1.0","source":{"id":"1609.00916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00916","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00916v1","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00916","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"I5A4GOGR355T","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I5A4GOGR355T4CCA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I5A4GOGR","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:e89aab8a23cf8da3eba3ffed6c25c5367600673e0255788538c556d5c65ecba4","target":"graph","created_at":"2026-05-18T01:06:19Z","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":"This paper makes a correction to the collision rates of small droplets in turbulent fluid derived by Saffman and Turner(1956). Not only the distortion but also the rotation of the fluid is taken into account between two close droplets. A rotation reference is fixed on one drop, and the fluxes of the other drops moving towards the fixed one are carried out based on this new reference. The behaviors of turbulent flow are analyzed within the smallest eddies under the rotation reference, and a correction is made to the collision rates by multiplying a factor sqrt(2).","authors_text":"Huang Zhang, Qianfeng Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-09-04T10:52:20Z","title":"A correction to collision rates of droplets in turbulent flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00916","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":"sha256:4e3ae6f428029274d62b7e6fc9649bfc04ec554028475c8c2a31ffcf7bcedb40","target":"record","created_at":"2026-05-18T01:06:19Z","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":"6fb77219d8cce21aac1ba4d994bf5bc149b650b2f05f2434f54f10851746a14b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-09-04T10:52:20Z","title_canon_sha256":"623fb8b4c19f5ee39c9f32c2e6a813a7c1a7ebc15a1a803887997645b8ebc5a2"},"schema_version":"1.0","source":{"id":"1609.00916","kind":"arxiv","version":1}},"canonical_sha256":"4741c338d1df7b3e0840c273f836ac9dd3dd0b6836c689bde211e91e2e26f665","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4741c338d1df7b3e0840c273f836ac9dd3dd0b6836c689bde211e91e2e26f665","first_computed_at":"2026-05-18T01:06:19.546708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:19.546708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c9aZz09u7Lg2a1evbQY7lihKyB+qMO/1eeLxY/WdrjUISSp7rro7ch7A+Pr0+DCF+0b4PA+Mv3FhBti9HC7zBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:19.547380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e3ae6f428029274d62b7e6fc9649bfc04ec554028475c8c2a31ffcf7bcedb40","sha256:e89aab8a23cf8da3eba3ffed6c25c5367600673e0255788538c556d5c65ecba4"],"state_sha256":"a545d4d24eefce0812c33559b36d6c5f706f20ef61986ba042bee2fc23379736"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//c7Iqz8zbdnie0kganLe8JaDOjfy0d6kQuVKe7+rXUA1eEEkFC9bR1GfAw4TghjBnQmEJIwxDieM4vI8Z3kDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T08:22:45.079829Z","bundle_sha256":"db1dacc805b3e298c1866635359e31cd535e8f80e7d664e404e77d0a3ed09673"}}