{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:L2Q6L3L5SVZXBNEA66KPGD73NA","short_pith_number":"pith:L2Q6L3L5","canonical_record":{"source":{"id":"1112.4817","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2011-12-20T20:17:44Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"48fe0d29f6bd624827319033027e1d9914c78cb8007ae7cf2a756197ae5f7782","abstract_canon_sha256":"511d267febf40d7c179e8ba96a56fc2f6409ab2dbedaae38b33ab216f992d016"},"schema_version":"1.0"},"canonical_sha256":"5ea1e5ed7d957370b480f794f30ffb682b0953f827f9d25b686363a921b31e83","source":{"kind":"arxiv","id":"1112.4817","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4817","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4817v4","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4817","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"L2Q6L3L5SVZX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L2Q6L3L5SVZXBNEA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L2Q6L3L5","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:L2Q6L3L5SVZXBNEA66KPGD73NA","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4817","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2011-12-20T20:17:44Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"48fe0d29f6bd624827319033027e1d9914c78cb8007ae7cf2a756197ae5f7782","abstract_canon_sha256":"511d267febf40d7c179e8ba96a56fc2f6409ab2dbedaae38b33ab216f992d016"},"schema_version":"1.0"},"canonical_sha256":"5ea1e5ed7d957370b480f794f30ffb682b0953f827f9d25b686363a921b31e83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:48.153650Z","signature_b64":"K3GmvU4mPk5oQb6MBAXo5IlSq9AAVwryliGQW8X0qqM9v8R6cvJ7sIXqrdBzsTHBkbdVMXiPYhdFqzBkvnz1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ea1e5ed7d957370b480f794f30ffb682b0953f827f9d25b686363a921b31e83","last_reissued_at":"2026-05-18T03:36:48.153166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:48.153166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4817","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W91T2aFzYDZc1VnKtJ/s/OVPJ/ExvQSopbihbm6a+/IbSF/Jio4tA7yzUEXPAA6kdC94uMlKG1+dYuB+1APMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:32:44.218233Z"},"content_sha256":"18ac5bdbeb2288881c96faba758e825793921e05333b4217f9ef19538978a709","schema_version":"1.0","event_id":"sha256:18ac5bdbeb2288881c96faba758e825793921e05333b4217f9ef19538978a709"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:L2Q6L3L5SVZXBNEA66KPGD73NA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Size-independence of statistics for boundary collisions of random walks and its implications for spin-polarized gases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.atom-ph","authors_text":"Alexander K. Petukhov, Dominique J. Bicout, Efim Kats, Robert S.Whitney","submitted_at":"2011-12-20T20:17:44Z","abstract_excerpt":"A bounded random walk exhibits strong correlations between collisions with a boundary. For an one-dimensional walk, we obtain the full statistical distribution of the number of such collisions in a time t. In the large t limit, the fluctuations in the number of collisions are found to be size-independent (independent of the distance between boundaries). This occurs for any inter-boundary distance, including less and greater than the mean-free-path, and means that this boundary effect does not decay with increasing system-size. As an application, we consider spin-polarized gases, such as 3-Heli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4817","kind":"arxiv","version":4},"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":"2026-05-18T03:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TdY03oLtHxemig9bVQ7WfLbHQLcGXyQQj4FrJ1akK0d+JpTAqrlZ6mThsUCM3YKMrvotFo8CUrylqzI0Sb80DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:32:44.218985Z"},"content_sha256":"0454ce522546cf4d2c8173955f71b9e4659f8fd1021c5a9a4cd717f4e180e506","schema_version":"1.0","event_id":"sha256:0454ce522546cf4d2c8173955f71b9e4659f8fd1021c5a9a4cd717f4e180e506"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2Q6L3L5SVZXBNEA66KPGD73NA/bundle.json","state_url":"https://pith.science/pith/L2Q6L3L5SVZXBNEA66KPGD73NA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2Q6L3L5SVZXBNEA66KPGD73NA/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":"2026-06-09T09:32:44Z","links":{"resolver":"https://pith.science/pith/L2Q6L3L5SVZXBNEA66KPGD73NA","bundle":"https://pith.science/pith/L2Q6L3L5SVZXBNEA66KPGD73NA/bundle.json","state":"https://pith.science/pith/L2Q6L3L5SVZXBNEA66KPGD73NA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2Q6L3L5SVZXBNEA66KPGD73NA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:L2Q6L3L5SVZXBNEA66KPGD73NA","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":"511d267febf40d7c179e8ba96a56fc2f6409ab2dbedaae38b33ab216f992d016","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2011-12-20T20:17:44Z","title_canon_sha256":"48fe0d29f6bd624827319033027e1d9914c78cb8007ae7cf2a756197ae5f7782"},"schema_version":"1.0","source":{"id":"1112.4817","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4817","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4817v4","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4817","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"L2Q6L3L5SVZX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L2Q6L3L5SVZXBNEA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L2Q6L3L5","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:0454ce522546cf4d2c8173955f71b9e4659f8fd1021c5a9a4cd717f4e180e506","target":"graph","created_at":"2026-05-18T03:36:48Z","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":"A bounded random walk exhibits strong correlations between collisions with a boundary. For an one-dimensional walk, we obtain the full statistical distribution of the number of such collisions in a time t. In the large t limit, the fluctuations in the number of collisions are found to be size-independent (independent of the distance between boundaries). This occurs for any inter-boundary distance, including less and greater than the mean-free-path, and means that this boundary effect does not decay with increasing system-size. As an application, we consider spin-polarized gases, such as 3-Heli","authors_text":"Alexander K. Petukhov, Dominique J. Bicout, Efim Kats, Robert S.Whitney","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2011-12-20T20:17:44Z","title":"Size-independence of statistics for boundary collisions of random walks and its implications for spin-polarized gases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4817","kind":"arxiv","version":4},"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":"sha256:18ac5bdbeb2288881c96faba758e825793921e05333b4217f9ef19538978a709","target":"record","created_at":"2026-05-18T03:36:48Z","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":"511d267febf40d7c179e8ba96a56fc2f6409ab2dbedaae38b33ab216f992d016","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2011-12-20T20:17:44Z","title_canon_sha256":"48fe0d29f6bd624827319033027e1d9914c78cb8007ae7cf2a756197ae5f7782"},"schema_version":"1.0","source":{"id":"1112.4817","kind":"arxiv","version":4}},"canonical_sha256":"5ea1e5ed7d957370b480f794f30ffb682b0953f827f9d25b686363a921b31e83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ea1e5ed7d957370b480f794f30ffb682b0953f827f9d25b686363a921b31e83","first_computed_at":"2026-05-18T03:36:48.153166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:48.153166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K3GmvU4mPk5oQb6MBAXo5IlSq9AAVwryliGQW8X0qqM9v8R6cvJ7sIXqrdBzsTHBkbdVMXiPYhdFqzBkvnz1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:48.153650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4817","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18ac5bdbeb2288881c96faba758e825793921e05333b4217f9ef19538978a709","sha256:0454ce522546cf4d2c8173955f71b9e4659f8fd1021c5a9a4cd717f4e180e506"],"state_sha256":"7bab1665603e46ba82b0b6a56f789663589e64c821aad6cc9376c6110cd7d5e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkHPJFxgwylch8ogSHirvNK7LWxiRyns5bANx/iCkjSXGv3Em0uhm1GdFQFDxWU8c/0YyxbnhA9e4KcXkPvxCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:32:44.222903Z","bundle_sha256":"d639fc3d59fee9e6b79583eb0d8b0e4abec4244c965f3dedbef13ef2fbc03247"}}