{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NRBRAI3JVXYRFYHIPF4L43JM7T","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":"f55a645087ee431809decd6de7d1e81da734a51401b2757a6cefd3eb92089be9","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-02-07T14:06:40Z","title_canon_sha256":"cbac050a41571513b0a2f655319ae89400606632e3d5db18d496b3bd65e82159"},"schema_version":"1.0","source":{"id":"1002.1450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1450","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1450v2","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1450","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"NRBRAI3JVXYR","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NRBRAI3JVXYRFYHI","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NRBRAI3J","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:fb0585b1a25b3969d67fe37c73853413b948f8d55b6c2016b7584d5e3a13dc31","target":"graph","created_at":"2026-05-18T04:24:45Z","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":"Normal dynamics in a quasi-one-dimensional channel of length L (\\to\\infty) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W D^(-{\\gamma}), for small D, where 0\\leq{\\gamma}<1. The initial spheres' density {\\rho} is non-uniform and scales with the distance (from the origin) l as, {\\rho} l^(-a), 0\\leqa\\leq1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement f","authors_text":"Ophir Flomenbom","cross_cats":["q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-02-07T14:06:40Z","title":"Dynamics of heterogeneous hard spheres in a file"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1450","kind":"arxiv","version":2},"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":"sha256:11d7efdcf9b3e7f0182a556cfe32a28421414622d8a8d5bf1d830961939bcbb5","target":"record","created_at":"2026-05-18T04:24:45Z","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":"f55a645087ee431809decd6de7d1e81da734a51401b2757a6cefd3eb92089be9","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-02-07T14:06:40Z","title_canon_sha256":"cbac050a41571513b0a2f655319ae89400606632e3d5db18d496b3bd65e82159"},"schema_version":"1.0","source":{"id":"1002.1450","kind":"arxiv","version":2}},"canonical_sha256":"6c43102369adf112e0e87978be6d2cfcdf1b76ade13e6cac339748d141da7e60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c43102369adf112e0e87978be6d2cfcdf1b76ade13e6cac339748d141da7e60","first_computed_at":"2026-05-18T04:24:45.355012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:45.355012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4TqARoP1P71y0QG8PSF4uxgzIlv0gZasDbPNMQV/eyayw3Nc7lq8x3qfI9BBsdJa8o2so6XmLU8D65lBPCTnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:45.355646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11d7efdcf9b3e7f0182a556cfe32a28421414622d8a8d5bf1d830961939bcbb5","sha256:fb0585b1a25b3969d67fe37c73853413b948f8d55b6c2016b7584d5e3a13dc31"],"state_sha256":"67eee888b07a5c7e2f43491a56e7c5b53c1e208dc501e3bc5a84ad10f64aeea8"}