{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NWU7DQ4KVAIQ7V45GNEWOYUZ7J","short_pith_number":"pith:NWU7DQ4K","canonical_record":{"source":{"id":"1703.00316","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-01T14:37:23Z","cross_cats_sorted":[],"title_canon_sha256":"deabec442faa3934db77992d8673224a189f0c2fbae7b71e99a2f170a3f32fdd","abstract_canon_sha256":"5da207ad3b370a860886e701853312979edc6b9d71252350b08c795f4121653a"},"schema_version":"1.0"},"canonical_sha256":"6da9f1c38aa8110fd79d3349676299fa6ac951c9ea195ec7329dcb0078c3ffb0","source":{"kind":"arxiv","id":"1703.00316","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00316","created_at":"2026-05-18T00:21:46Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00316v3","created_at":"2026-05-18T00:21:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00316","created_at":"2026-05-18T00:21:46Z"},{"alias_kind":"pith_short_12","alias_value":"NWU7DQ4KVAIQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWU7DQ4KVAIQ7V45","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWU7DQ4K","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NWU7DQ4KVAIQ7V45GNEWOYUZ7J","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00316","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-01T14:37:23Z","cross_cats_sorted":[],"title_canon_sha256":"deabec442faa3934db77992d8673224a189f0c2fbae7b71e99a2f170a3f32fdd","abstract_canon_sha256":"5da207ad3b370a860886e701853312979edc6b9d71252350b08c795f4121653a"},"schema_version":"1.0"},"canonical_sha256":"6da9f1c38aa8110fd79d3349676299fa6ac951c9ea195ec7329dcb0078c3ffb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:46.533360Z","signature_b64":"eLhtOYiOq6T4ouLjz03guZu2vGhs1bdTuO33/U2DRJo3u9prLJTH3TTBVzSZJAwb3HFQBtzWdy1OE3OkSsHdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6da9f1c38aa8110fd79d3349676299fa6ac951c9ea195ec7329dcb0078c3ffb0","last_reissued_at":"2026-05-18T00:21:46.532790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:46.532790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00316","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8hrFVHCvhi8vQtc0Ieee742AV0qp/AVOneiTDfjFwzQT4pk0vlryxVYxJkNybPQrEPVIJ8e6kvA9GGjIQ/1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:10:20.212186Z"},"content_sha256":"49e6cd1c065b22dbd3db9e2af41e2875e5461b997a9871952adbba8e1bd6e863","schema_version":"1.0","event_id":"sha256:49e6cd1c065b22dbd3db9e2af41e2875e5461b997a9871952adbba8e1bd6e863"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NWU7DQ4KVAIQ7V45GNEWOYUZ7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Arcsine Law for Markov Random Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabian Buckmann, Gerold Alsmeyer","submitted_at":"2017-03-01T14:37:23Z","abstract_excerpt":"The classic arcsine law for the number $N_{n}^{>}:=n^{-1}\\sum_{k=1}^{n}\\mathbf{1}_{\\{S_{k}>0\\}}$ of positive terms, as $n\\to\\infty$, in an ordinary random walk $(S_{n})_{n\\ge 0}$ is extended to the case when this random walk is governed by a positive recurrent Markov chain $(M_{n})_{n\\ge 0}$ on a countable state space $\\mathcal{S}$, that is, for a Markov random walk $(M_{n},S_{n})_{n\\ge 0}$ with positive recurrent discrete driving chain. More precisely, it is shown that $n^{-1}N_{n}^{>}$ converges in distribution to a generalized arcsine law with parameter $\\rho\\in [0,1]$ (the classic arcsine "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00316","kind":"arxiv","version":3},"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":"2026-05-18T00:21:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+bUyXI0fRJg/LcdRD3SOyDn1PjoSWVNOO91hqCGC1muEybXApLNXwtyhszIOYaMdFMdgI9p51ClpoOusObjLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:10:20.212842Z"},"content_sha256":"238a14f1b03233faecc8d0a6449f2f32a0417a685a4743e0ddd0dd5211575023","schema_version":"1.0","event_id":"sha256:238a14f1b03233faecc8d0a6449f2f32a0417a685a4743e0ddd0dd5211575023"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWU7DQ4KVAIQ7V45GNEWOYUZ7J/bundle.json","state_url":"https://pith.science/pith/NWU7DQ4KVAIQ7V45GNEWOYUZ7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWU7DQ4KVAIQ7V45GNEWOYUZ7J/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":"2026-05-30T23:10:20Z","links":{"resolver":"https://pith.science/pith/NWU7DQ4KVAIQ7V45GNEWOYUZ7J","bundle":"https://pith.science/pith/NWU7DQ4KVAIQ7V45GNEWOYUZ7J/bundle.json","state":"https://pith.science/pith/NWU7DQ4KVAIQ7V45GNEWOYUZ7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWU7DQ4KVAIQ7V45GNEWOYUZ7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NWU7DQ4KVAIQ7V45GNEWOYUZ7J","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":"5da207ad3b370a860886e701853312979edc6b9d71252350b08c795f4121653a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-01T14:37:23Z","title_canon_sha256":"deabec442faa3934db77992d8673224a189f0c2fbae7b71e99a2f170a3f32fdd"},"schema_version":"1.0","source":{"id":"1703.00316","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00316","created_at":"2026-05-18T00:21:46Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00316v3","created_at":"2026-05-18T00:21:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00316","created_at":"2026-05-18T00:21:46Z"},{"alias_kind":"pith_short_12","alias_value":"NWU7DQ4KVAIQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWU7DQ4KVAIQ7V45","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWU7DQ4K","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:238a14f1b03233faecc8d0a6449f2f32a0417a685a4743e0ddd0dd5211575023","target":"graph","created_at":"2026-05-18T00:21:46Z","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":"The classic arcsine law for the number $N_{n}^{>}:=n^{-1}\\sum_{k=1}^{n}\\mathbf{1}_{\\{S_{k}>0\\}}$ of positive terms, as $n\\to\\infty$, in an ordinary random walk $(S_{n})_{n\\ge 0}$ is extended to the case when this random walk is governed by a positive recurrent Markov chain $(M_{n})_{n\\ge 0}$ on a countable state space $\\mathcal{S}$, that is, for a Markov random walk $(M_{n},S_{n})_{n\\ge 0}$ with positive recurrent discrete driving chain. More precisely, it is shown that $n^{-1}N_{n}^{>}$ converges in distribution to a generalized arcsine law with parameter $\\rho\\in [0,1]$ (the classic arcsine ","authors_text":"Fabian Buckmann, Gerold Alsmeyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-01T14:37:23Z","title":"An Arcsine Law for Markov Random Walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00316","kind":"arxiv","version":3},"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":"sha256:49e6cd1c065b22dbd3db9e2af41e2875e5461b997a9871952adbba8e1bd6e863","target":"record","created_at":"2026-05-18T00:21:46Z","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":"5da207ad3b370a860886e701853312979edc6b9d71252350b08c795f4121653a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-01T14:37:23Z","title_canon_sha256":"deabec442faa3934db77992d8673224a189f0c2fbae7b71e99a2f170a3f32fdd"},"schema_version":"1.0","source":{"id":"1703.00316","kind":"arxiv","version":3}},"canonical_sha256":"6da9f1c38aa8110fd79d3349676299fa6ac951c9ea195ec7329dcb0078c3ffb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6da9f1c38aa8110fd79d3349676299fa6ac951c9ea195ec7329dcb0078c3ffb0","first_computed_at":"2026-05-18T00:21:46.532790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:46.532790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eLhtOYiOq6T4ouLjz03guZu2vGhs1bdTuO33/U2DRJo3u9prLJTH3TTBVzSZJAwb3HFQBtzWdy1OE3OkSsHdBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:46.533360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00316","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49e6cd1c065b22dbd3db9e2af41e2875e5461b997a9871952adbba8e1bd6e863","sha256:238a14f1b03233faecc8d0a6449f2f32a0417a685a4743e0ddd0dd5211575023"],"state_sha256":"73162949b8281ea513c313c5ca0f5eadc80dcb58ca081a916b097b91b522cfa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6oWwgRdQQiunM9f5TaZCbGXT5kklBZeRFwgdLXxkg8RyjKM8R1iL27oRNEyb4+rN8EE2O19eisny6hPs6bQTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:10:20.220007Z","bundle_sha256":"84240f134dc9eb26d56656b719c49b306f9c75c3e5c6d0137a142af3808bad39"}}