{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YG23N57PHMWL442AHWDE4SR7FJ","short_pith_number":"pith:YG23N57P","schema_version":"1.0","canonical_sha256":"c1b5b6f7ef3b2cbe73403d864e4a3f2a7a2adacc1400e431e5806c2dac737bcd","source":{"kind":"arxiv","id":"1702.08096","version":1},"attestation_state":"computed","paper":{"title":"On the free path length distribution for linear motion in an n-dimensional box","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel M{\\aa}nsson, P\\\"ar Kurlberg, Samuel Holmin","submitted_at":"2017-02-26T22:03:21Z","abstract_excerpt":"We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path lengths coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we give an explicit formula (piecewise real analytic) for the probability density function in dimension two and three.\n  In dimension two we also consider a closely related model where each particle is allowed to bou"},"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":"1702.08096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-26T22:03:21Z","cross_cats_sorted":[],"title_canon_sha256":"916c2dabecfe51aad6585a9b1c43937141ba7a065811c60aae696cb3de7abf09","abstract_canon_sha256":"d62ebfe9138bd45fdc49de11f1a3142cd57d043d0f9578942a988b35f73f8d74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:00.860103Z","signature_b64":"80NfnmOWL1WUMwrFTh9pNoRTUpVxhxk3iKr3XbNgDMSInVCnQYBV/smNKMy3wBhld74hONAXLIsaZvtXUGSdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1b5b6f7ef3b2cbe73403d864e4a3f2a7a2adacc1400e431e5806c2dac737bcd","last_reissued_at":"2026-05-18T00:01:00.859549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:00.859549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the free path length distribution for linear motion in an n-dimensional box","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel M{\\aa}nsson, P\\\"ar Kurlberg, Samuel Holmin","submitted_at":"2017-02-26T22:03:21Z","abstract_excerpt":"We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path lengths coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we give an explicit formula (piecewise real analytic) for the probability density function in dimension two and three.\n  In dimension two we also consider a closely related model where each particle is allowed to bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08096","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":"1702.08096","created_at":"2026-05-18T00:01:00.859642+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.08096v1","created_at":"2026-05-18T00:01:00.859642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08096","created_at":"2026-05-18T00:01:00.859642+00:00"},{"alias_kind":"pith_short_12","alias_value":"YG23N57PHMWL","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YG23N57PHMWL442A","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YG23N57P","created_at":"2026-05-18T12:31:56.362134+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/YG23N57PHMWL442AHWDE4SR7FJ","json":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ.json","graph_json":"https://pith.science/api/pith-number/YG23N57PHMWL442AHWDE4SR7FJ/graph.json","events_json":"https://pith.science/api/pith-number/YG23N57PHMWL442AHWDE4SR7FJ/events.json","paper":"https://pith.science/paper/YG23N57P"},"agent_actions":{"view_html":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ","download_json":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ.json","view_paper":"https://pith.science/paper/YG23N57P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.08096&json=true","fetch_graph":"https://pith.science/api/pith-number/YG23N57PHMWL442AHWDE4SR7FJ/graph.json","fetch_events":"https://pith.science/api/pith-number/YG23N57PHMWL442AHWDE4SR7FJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ/action/storage_attestation","attest_author":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ/action/author_attestation","sign_citation":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ/action/citation_signature","submit_replication":"https://pith.science/pith/YG23N57PHMWL442AHWDE4SR7FJ/action/replication_record"}},"created_at":"2026-05-18T00:01:00.859642+00:00","updated_at":"2026-05-18T00:01:00.859642+00:00"}