{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:R6I52MCFVRPI374ROXIAE7J4EC","short_pith_number":"pith:R6I52MCF","schema_version":"1.0","canonical_sha256":"8f91dd3045ac5e8dff9175d0027d3c20ad036daf258940f5e530fd18602f2dfb","source":{"kind":"arxiv","id":"1403.6642","version":2},"attestation_state":"computed","paper":{"title":"Escape Dynamics of Many Hard Disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hiroki Murata, Shin-ichi Sawada, Tooru Taniguchi","submitted_at":"2014-03-26T12:02:01Z","abstract_excerpt":"Many-particle effects in escapes of hard disks from a square box via a hole are discussed in a viewpoint of dynamical systems. Starting from $N$ disks in the box at the initial time, we calculate the probability $P_{n}(t)$ for at least $n$ disks to remain inside the box at time $t$ for $n=1,2,\\cdots,N$. At early times the probabilities $P_{n}(t)$, $n=2,3,\\cdots,N-1$, are described by superpositions of exponential decay functions. On the other hand, after a long time the probability $P_{n}(t)$ shows a power-law decay $\\sim t^{-2n}$ for $n\\neq 1$, in contrast to the fact that it decays with a di"},"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":"1403.6642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-03-26T12:02:01Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"a428fff4589dfb52d45b249c4f247a7d909fad2d0cbe2887e00c5fd9998b43c9","abstract_canon_sha256":"46f856e6529a5b00d697676ab228834bb9d3213d1d4eb4dc18fb65ffbd0fb03b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:32.109964Z","signature_b64":"WH6pwR4yj7fmsaTYg8uc7J7IjrnM7nbgZ+pWWebMnITnq53uvDfHyDAJEyIuslVjNkrjBV17cFerYlatUvdsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f91dd3045ac5e8dff9175d0027d3c20ad036daf258940f5e530fd18602f2dfb","last_reissued_at":"2026-05-18T02:30:32.109292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:32.109292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Escape Dynamics of Many Hard Disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hiroki Murata, Shin-ichi Sawada, Tooru Taniguchi","submitted_at":"2014-03-26T12:02:01Z","abstract_excerpt":"Many-particle effects in escapes of hard disks from a square box via a hole are discussed in a viewpoint of dynamical systems. Starting from $N$ disks in the box at the initial time, we calculate the probability $P_{n}(t)$ for at least $n$ disks to remain inside the box at time $t$ for $n=1,2,\\cdots,N$. At early times the probabilities $P_{n}(t)$, $n=2,3,\\cdots,N-1$, are described by superpositions of exponential decay functions. On the other hand, after a long time the probability $P_{n}(t)$ shows a power-law decay $\\sim t^{-2n}$ for $n\\neq 1$, in contrast to the fact that it decays with a di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6642","kind":"arxiv","version":2},"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":"1403.6642","created_at":"2026-05-18T02:30:32.109413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.6642v2","created_at":"2026-05-18T02:30:32.109413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6642","created_at":"2026-05-18T02:30:32.109413+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6I52MCFVRPI","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6I52MCFVRPI374R","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6I52MCF","created_at":"2026-05-18T12:28:46.137349+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/R6I52MCFVRPI374ROXIAE7J4EC","json":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC.json","graph_json":"https://pith.science/api/pith-number/R6I52MCFVRPI374ROXIAE7J4EC/graph.json","events_json":"https://pith.science/api/pith-number/R6I52MCFVRPI374ROXIAE7J4EC/events.json","paper":"https://pith.science/paper/R6I52MCF"},"agent_actions":{"view_html":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC","download_json":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC.json","view_paper":"https://pith.science/paper/R6I52MCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.6642&json=true","fetch_graph":"https://pith.science/api/pith-number/R6I52MCFVRPI374ROXIAE7J4EC/graph.json","fetch_events":"https://pith.science/api/pith-number/R6I52MCFVRPI374ROXIAE7J4EC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC/action/storage_attestation","attest_author":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC/action/author_attestation","sign_citation":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC/action/citation_signature","submit_replication":"https://pith.science/pith/R6I52MCFVRPI374ROXIAE7J4EC/action/replication_record"}},"created_at":"2026-05-18T02:30:32.109413+00:00","updated_at":"2026-05-18T02:30:32.109413+00:00"}