{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z56MIS775SZ7LRI4YXS6SQ5LTZ","short_pith_number":"pith:Z56MIS77","canonical_record":{"source":{"id":"1406.0419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-02T15:42:39Z","cross_cats_sorted":[],"title_canon_sha256":"82564f95990d8fdfc8b1c1ef0ac954108a3e175b5bdfa7d7d403a2355f2b84c4","abstract_canon_sha256":"d0aaa47d91b735ec1cdbb67544b999d49b936ec74829776b9c62f961cbef7d06"},"schema_version":"1.0"},"canonical_sha256":"cf7cc44bffecb3f5c51cc5e5e943ab9e7092cf46896dcdf412bc06846926ae53","source":{"kind":"arxiv","id":"1406.0419","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0419","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0419v2","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0419","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z56MIS775SZ7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z56MIS775SZ7LRI4","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z56MIS77","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z56MIS775SZ7LRI4YXS6SQ5LTZ","target":"record","payload":{"canonical_record":{"source":{"id":"1406.0419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-02T15:42:39Z","cross_cats_sorted":[],"title_canon_sha256":"82564f95990d8fdfc8b1c1ef0ac954108a3e175b5bdfa7d7d403a2355f2b84c4","abstract_canon_sha256":"d0aaa47d91b735ec1cdbb67544b999d49b936ec74829776b9c62f961cbef7d06"},"schema_version":"1.0"},"canonical_sha256":"cf7cc44bffecb3f5c51cc5e5e943ab9e7092cf46896dcdf412bc06846926ae53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:59.361273Z","signature_b64":"JyUWj3KnSpsn+fvz9Ro+XQcDM0UQZ2kgv8TUrO2jTbaaJ3N44OmSUW/mVy1vQoz+vcIH7HYgpsa//wk2fnPfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf7cc44bffecb3f5c51cc5e5e943ab9e7092cf46896dcdf412bc06846926ae53","last_reissued_at":"2026-05-18T02:38:59.360916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:59.360916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.0419","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GB9HlNZq94cbPd2eEejbwRbUEiFKvDeAvWVAmfBqBTcFUdkMZ7K95c4wTA5nPHcVw+GuPrtCoqHqpVGLVOkXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:12:26.667621Z"},"content_sha256":"ebad0dafebe1f94a5a9a46abd913d598b4259e2c70a4543266eb5c5b51a01866","schema_version":"1.0","event_id":"sha256:ebad0dafebe1f94a5a9a46abd913d598b4259e2c70a4543266eb5c5b51a01866"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z56MIS775SZ7LRI4YXS6SQ5LTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Winding statistics of a Brownian particle on a ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alain Comtet, Anupam Kundu, Satya N. Majumdar","submitted_at":"2014-06-02T15:42:39Z","abstract_excerpt":"We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal properties of Brownian walker, we find exact analytical expressions of these distributions. This method serves as an alternative to the standard path integral techniques which are not always easily adaptable for certain observables. For large t, we show that these distributions have Gaussian scaling forms. We also compute large deviation functions associated to thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0419","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygz5TLQ62rOqtIbnPgplAAqzAQVil1AzVayKY+hmcBg7LmcFhaoL2gM3kNTUDmN0m0usfj2FyoxdQNhfPhB+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:12:26.667973Z"},"content_sha256":"a28f8bc6ddd3b4c7efa7ef099a39cda0c521cb7b0ba3e397dff208bba9eb61ba","schema_version":"1.0","event_id":"sha256:a28f8bc6ddd3b4c7efa7ef099a39cda0c521cb7b0ba3e397dff208bba9eb61ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z56MIS775SZ7LRI4YXS6SQ5LTZ/bundle.json","state_url":"https://pith.science/pith/Z56MIS775SZ7LRI4YXS6SQ5LTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z56MIS775SZ7LRI4YXS6SQ5LTZ/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":"2026-06-04T14:12:26Z","links":{"resolver":"https://pith.science/pith/Z56MIS775SZ7LRI4YXS6SQ5LTZ","bundle":"https://pith.science/pith/Z56MIS775SZ7LRI4YXS6SQ5LTZ/bundle.json","state":"https://pith.science/pith/Z56MIS775SZ7LRI4YXS6SQ5LTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z56MIS775SZ7LRI4YXS6SQ5LTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z56MIS775SZ7LRI4YXS6SQ5LTZ","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":"d0aaa47d91b735ec1cdbb67544b999d49b936ec74829776b9c62f961cbef7d06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-02T15:42:39Z","title_canon_sha256":"82564f95990d8fdfc8b1c1ef0ac954108a3e175b5bdfa7d7d403a2355f2b84c4"},"schema_version":"1.0","source":{"id":"1406.0419","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0419","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0419v2","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0419","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z56MIS775SZ7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z56MIS775SZ7LRI4","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z56MIS77","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:a28f8bc6ddd3b4c7efa7ef099a39cda0c521cb7b0ba3e397dff208bba9eb61ba","target":"graph","created_at":"2026-05-18T02:38:59Z","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":"We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal properties of Brownian walker, we find exact analytical expressions of these distributions. This method serves as an alternative to the standard path integral techniques which are not always easily adaptable for certain observables. For large t, we show that these distributions have Gaussian scaling forms. We also compute large deviation functions associated to thes","authors_text":"Alain Comtet, Anupam Kundu, Satya N. Majumdar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-02T15:42:39Z","title":"Winding statistics of a Brownian particle on a ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0419","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:ebad0dafebe1f94a5a9a46abd913d598b4259e2c70a4543266eb5c5b51a01866","target":"record","created_at":"2026-05-18T02:38:59Z","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":"d0aaa47d91b735ec1cdbb67544b999d49b936ec74829776b9c62f961cbef7d06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-02T15:42:39Z","title_canon_sha256":"82564f95990d8fdfc8b1c1ef0ac954108a3e175b5bdfa7d7d403a2355f2b84c4"},"schema_version":"1.0","source":{"id":"1406.0419","kind":"arxiv","version":2}},"canonical_sha256":"cf7cc44bffecb3f5c51cc5e5e943ab9e7092cf46896dcdf412bc06846926ae53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf7cc44bffecb3f5c51cc5e5e943ab9e7092cf46896dcdf412bc06846926ae53","first_computed_at":"2026-05-18T02:38:59.360916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:59.360916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JyUWj3KnSpsn+fvz9Ro+XQcDM0UQZ2kgv8TUrO2jTbaaJ3N44OmSUW/mVy1vQoz+vcIH7HYgpsa//wk2fnPfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:59.361273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0419","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebad0dafebe1f94a5a9a46abd913d598b4259e2c70a4543266eb5c5b51a01866","sha256:a28f8bc6ddd3b4c7efa7ef099a39cda0c521cb7b0ba3e397dff208bba9eb61ba"],"state_sha256":"84f1b770ab3463efb1352959b01e6166544920454927b1f5f163bd5a332e9dfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hMJ7e43EZJqtWQvGtrZc8qkzLjE0x1ix25wmsoSDmsgzMZoY+BEl//Lgnf9qRecFiHemUWyzXrXjaZY+JU9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:12:26.678714Z","bundle_sha256":"23cfb041b28aa611f3ff0ccc22bb551251c97c2815b740535b8dff2dc9d5ff45"}}