{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HG6A4ZYQSTJ2TQ7YACX73FODW2","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":"58c978f9b0ddd92ea217b123d0344c6912d42abc8ecc8e7a1bc60bc1ad78ccec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T10:10:55Z","title_canon_sha256":"8c8c64b50e2aabd4a21e77a813505d364b04e829524b5680947e0c4af160bf03"},"schema_version":"1.0","source":{"id":"1111.7106","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7106","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7106v2","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7106","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"HG6A4ZYQSTJ2","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HG6A4ZYQSTJ2TQ7Y","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HG6A4ZYQ","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:8119f76c96e0dab92ae666a142abfcee973be3e70da9c9a06e92cf4de22d91b6","target":"graph","created_at":"2026-05-18T03:43:52Z","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 reflection map, induced by the deterministic Skorohod problem on the nonnegative orthant, is applied to an $\\mathbb{R}^n$ valued function $X$ on $[0,\\infty)$ and then to $a+X$, where $a$ is a nonnegative constant vector. A question that has been open for over 15 years is under what conditions the difference between the two resulting regulated functions converges to zero for any choice of $a$ as time diverges. This in turn implies that if one imposes enough stochastic structure that ensures that the reflection map applied to a multidimensional process $X$ converges in distribution then it wil","authors_text":"Offer Kella, Sundareswaran Ramasubramanian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T10:10:55Z","title":"Asymptotic irrelevance of initial conditions for Skorohod reflection mapping on the nonnegative orthant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7106","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":"sha256:43334007d213e19424537afedec989d333cd62f9b5848f957dacb98bf2859adf","target":"record","created_at":"2026-05-18T03:43:52Z","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":"58c978f9b0ddd92ea217b123d0344c6912d42abc8ecc8e7a1bc60bc1ad78ccec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T10:10:55Z","title_canon_sha256":"8c8c64b50e2aabd4a21e77a813505d364b04e829524b5680947e0c4af160bf03"},"schema_version":"1.0","source":{"id":"1111.7106","kind":"arxiv","version":2}},"canonical_sha256":"39bc0e671094d3a9c3f800affd95c3b6a186100b0ce3a928ec0229d4761d56d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39bc0e671094d3a9c3f800affd95c3b6a186100b0ce3a928ec0229d4761d56d5","first_computed_at":"2026-05-18T03:43:52.747306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:52.747306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pzpp9IvTJwwIWBoG0EW0qWVGhmra1st9Vd7syHvGoDqgTM0ahNm54xvQQkC34jaI7ADLkSizTM9jTi6uVvyXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:52.747826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7106","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43334007d213e19424537afedec989d333cd62f9b5848f957dacb98bf2859adf","sha256:8119f76c96e0dab92ae666a142abfcee973be3e70da9c9a06e92cf4de22d91b6"],"state_sha256":"7ebfc27f9124151fb8813d9fa9fa6086e621da3af413929d069af00ec2cfc2ef"}