{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:4UY7X34X4YV3I2XIMJPNXN44QF","short_pith_number":"pith:4UY7X34X","canonical_record":{"source":{"id":"math/0610242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-10-07T10:02:36Z","cross_cats_sorted":[],"title_canon_sha256":"32668d7041bf260c373a1bb1441a4ff21209b597d4e35183d0602fa32158108c","abstract_canon_sha256":"a0b92839bbba3ab7e2896fa8df12faa251170710dcffb3c25efb916a9cddd2cc"},"schema_version":"1.0"},"canonical_sha256":"e531fbef97e62bb46ae8625edbb79c817f65e9cbcbacade774eba7aa3af21fa0","source":{"kind":"arxiv","id":"math/0610242","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0610242","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0610242v2","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610242","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"4UY7X34X4YV3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4UY7X34X4YV3I2XI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4UY7X34X","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:4UY7X34X4YV3I2XIMJPNXN44QF","target":"record","payload":{"canonical_record":{"source":{"id":"math/0610242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-10-07T10:02:36Z","cross_cats_sorted":[],"title_canon_sha256":"32668d7041bf260c373a1bb1441a4ff21209b597d4e35183d0602fa32158108c","abstract_canon_sha256":"a0b92839bbba3ab7e2896fa8df12faa251170710dcffb3c25efb916a9cddd2cc"},"schema_version":"1.0"},"canonical_sha256":"e531fbef97e62bb46ae8625edbb79c817f65e9cbcbacade774eba7aa3af21fa0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:00.060393Z","signature_b64":"y+9pA5ndAej958SR4r6yjW/EXKXNHn/YL2rgsAL1803lLSyOCRNloi/sM2bHJOiAaXLfi106JtKFSY7wZTuUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e531fbef97e62bb46ae8625edbb79c817f65e9cbcbacade774eba7aa3af21fa0","last_reissued_at":"2026-05-18T03:09:00.059660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:00.059660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0610242","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":"2026-05-18T03:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QDsnICc2ZZdk1VeJYZDa71tPhhYOSQ9GWHoVu1gL5vFqVy/iirvB0JHNSJ/P7JNHIyZUxUQ1XKyGYfaAI2uYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:16:52.485246Z"},"content_sha256":"6dcd296087ebf1406f03ffb3b136b9e9105bfd25a6b6aae2795a985d93af9d2f","schema_version":"1.0","event_id":"sha256:6dcd296087ebf1406f03ffb3b136b9e9105bfd25a6b6aae2795a985d93af9d2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:4UY7X34X4YV3I2XIMJPNXN44QF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Martin boundary of a reflected random walk on a half-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Irina Ignatiouk-Robert","submitted_at":"2006-10-07T10:02:36Z","abstract_excerpt":"The complete representation of the Martin compactification for reflected random walks on a half-space $\\Z^d\\times\\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the ``radial'' compactification obtained by Ney and Spitzer for the homogeneous random walks in $\\Z^d$ : convergence of a sequence of points $z_n\\in\\Z^{d-1}\\times\\N$ to a point of on the Martin boundary does not imply convergence of the sequence $z_n/|z_n|$ on the unit sphere $S^d$. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610242","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":"2026-05-18T03:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DbeHrDSsIneygfc0IZJQ0fFj49ermGJMFF+Zj5yVbTzkdT9YrQpVdFtxsLom+pWQt9ACLAkJV6MnDuf9Gs4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:16:52.485639Z"},"content_sha256":"212045b392979652af029d11d7b90d0793f72cca2721fda89e934c908faaa064","schema_version":"1.0","event_id":"sha256:212045b392979652af029d11d7b90d0793f72cca2721fda89e934c908faaa064"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4UY7X34X4YV3I2XIMJPNXN44QF/bundle.json","state_url":"https://pith.science/pith/4UY7X34X4YV3I2XIMJPNXN44QF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4UY7X34X4YV3I2XIMJPNXN44QF/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":"2026-06-23T21:16:52Z","links":{"resolver":"https://pith.science/pith/4UY7X34X4YV3I2XIMJPNXN44QF","bundle":"https://pith.science/pith/4UY7X34X4YV3I2XIMJPNXN44QF/bundle.json","state":"https://pith.science/pith/4UY7X34X4YV3I2XIMJPNXN44QF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4UY7X34X4YV3I2XIMJPNXN44QF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4UY7X34X4YV3I2XIMJPNXN44QF","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":"a0b92839bbba3ab7e2896fa8df12faa251170710dcffb3c25efb916a9cddd2cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-10-07T10:02:36Z","title_canon_sha256":"32668d7041bf260c373a1bb1441a4ff21209b597d4e35183d0602fa32158108c"},"schema_version":"1.0","source":{"id":"math/0610242","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0610242","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0610242v2","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610242","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"4UY7X34X4YV3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4UY7X34X4YV3I2XI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4UY7X34X","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:212045b392979652af029d11d7b90d0793f72cca2721fda89e934c908faaa064","target":"graph","created_at":"2026-05-18T03:09:00Z","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 complete representation of the Martin compactification for reflected random walks on a half-space $\\Z^d\\times\\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the ``radial'' compactification obtained by Ney and Spitzer for the homogeneous random walks in $\\Z^d$ : convergence of a sequence of points $z_n\\in\\Z^{d-1}\\times\\N$ to a point of on the Martin boundary does not imply convergence of the sequence $z_n/|z_n|$ on the unit sphere $S^d$. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method","authors_text":"Irina Ignatiouk-Robert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-10-07T10:02:36Z","title":"Martin boundary of a reflected random walk on a half-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610242","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":"sha256:6dcd296087ebf1406f03ffb3b136b9e9105bfd25a6b6aae2795a985d93af9d2f","target":"record","created_at":"2026-05-18T03:09:00Z","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":"a0b92839bbba3ab7e2896fa8df12faa251170710dcffb3c25efb916a9cddd2cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-10-07T10:02:36Z","title_canon_sha256":"32668d7041bf260c373a1bb1441a4ff21209b597d4e35183d0602fa32158108c"},"schema_version":"1.0","source":{"id":"math/0610242","kind":"arxiv","version":2}},"canonical_sha256":"e531fbef97e62bb46ae8625edbb79c817f65e9cbcbacade774eba7aa3af21fa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e531fbef97e62bb46ae8625edbb79c817f65e9cbcbacade774eba7aa3af21fa0","first_computed_at":"2026-05-18T03:09:00.059660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:00.059660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y+9pA5ndAej958SR4r6yjW/EXKXNHn/YL2rgsAL1803lLSyOCRNloi/sM2bHJOiAaXLfi106JtKFSY7wZTuUCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:00.060393Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0610242","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dcd296087ebf1406f03ffb3b136b9e9105bfd25a6b6aae2795a985d93af9d2f","sha256:212045b392979652af029d11d7b90d0793f72cca2721fda89e934c908faaa064"],"state_sha256":"c21a649179612e9417cb186507ffac9f850fd60fe105a4aa14260bb291034dbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h+tP7GhVKdSM5MLfHGkEukQ1kPP3KfW5MszyxLPXPnQsDctRxM++tHKTtOD05Huip4gpG/6R6I4h0hTOIpCeBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:16:52.487562Z","bundle_sha256":"ccfa3e93397ad5ca20f6783aa30fd474a9e64b7966194ea6844bf269f9944160"}}