{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DLACNTBO2ZBASVU5A2X4BUKTTT","short_pith_number":"pith:DLACNTBO","schema_version":"1.0","canonical_sha256":"1ac026cc2ed64209569d06afc0d1539cc3a32cefa82aa392e0d095897543e83d","source":{"kind":"arxiv","id":"1107.0324","version":1},"attestation_state":"computed","paper":{"title":"Residence time and collision statistics for exponential flights: the rod problem revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alain Mazzolo, Andrea Zoia, Eric Dumonteil","submitted_at":"2011-07-01T20:16:39Z","abstract_excerpt":"Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\\em rod problem} (a 1d system), and disc"},"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":"1107.0324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-07-01T20:16:39Z","cross_cats_sorted":[],"title_canon_sha256":"451ce7d48e431184f7e6781b1314ff9869d33d213234843a3e66a0654d2f54e1","abstract_canon_sha256":"d5163e16c8301201b8eef10f61ddc5ce5cd7c5cdf4af979f9d12ad5fe7efc174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:17.798454Z","signature_b64":"a0LBLfKyWdwrfW/5GPDBtoCX1GFu7zKGv5TpUAyB+nIthcUaoUjBSJ36fWuOj0SF0PnXlU02WIGU7YR1THzKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ac026cc2ed64209569d06afc0d1539cc3a32cefa82aa392e0d095897543e83d","last_reissued_at":"2026-05-18T04:14:17.797892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:17.797892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Residence time and collision statistics for exponential flights: the rod problem revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alain Mazzolo, Andrea Zoia, Eric Dumonteil","submitted_at":"2011-07-01T20:16:39Z","abstract_excerpt":"Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\\em rod problem} (a 1d system), and disc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0324","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":"1107.0324","created_at":"2026-05-18T04:14:17.797984+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.0324v1","created_at":"2026-05-18T04:14:17.797984+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0324","created_at":"2026-05-18T04:14:17.797984+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLACNTBO2ZBA","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLACNTBO2ZBASVU5","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLACNTBO","created_at":"2026-05-18T12:26:26.731475+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/DLACNTBO2ZBASVU5A2X4BUKTTT","json":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT.json","graph_json":"https://pith.science/api/pith-number/DLACNTBO2ZBASVU5A2X4BUKTTT/graph.json","events_json":"https://pith.science/api/pith-number/DLACNTBO2ZBASVU5A2X4BUKTTT/events.json","paper":"https://pith.science/paper/DLACNTBO"},"agent_actions":{"view_html":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT","download_json":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT.json","view_paper":"https://pith.science/paper/DLACNTBO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.0324&json=true","fetch_graph":"https://pith.science/api/pith-number/DLACNTBO2ZBASVU5A2X4BUKTTT/graph.json","fetch_events":"https://pith.science/api/pith-number/DLACNTBO2ZBASVU5A2X4BUKTTT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT/action/storage_attestation","attest_author":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT/action/author_attestation","sign_citation":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT/action/citation_signature","submit_replication":"https://pith.science/pith/DLACNTBO2ZBASVU5A2X4BUKTTT/action/replication_record"}},"created_at":"2026-05-18T04:14:17.797984+00:00","updated_at":"2026-05-18T04:14:17.797984+00:00"}