{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VTXSQVRIXS6H7D6EHCD3THYWLT","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":"7c4aeed0b158d4c3d8854f503b906dd748033fbb63f359552f74934eb2f574d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-16T12:54:25Z","title_canon_sha256":"c78a19f267ed76cdba1d2cccdf22e430c51400c01e81af5c6a1b66f5d8f5efd1"},"schema_version":"1.0","source":{"id":"1608.04578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04578","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04578v1","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04578","created_at":"2026-05-18T01:08:36Z"},{"alias_kind":"pith_short_12","alias_value":"VTXSQVRIXS6H","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VTXSQVRIXS6H7D6E","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VTXSQVRI","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:35e2f406a93fe3c0ef9b987f9f4937a3a46febe7d1d4235610ea3b8224b5d50f","target":"graph","created_at":"2026-05-18T01:08:36Z","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":"In this note we derive an exact formula for the Green's function of the random walk on different subspaces of the discrete lattice (orthants, including the half space, and the strip) without killing on the boundary in terms of the Green's function of the simple random walk on $\\mathbb{Z}^d$, $d\\ge 3$.","authors_text":"Alberto Chiarini, Alessandra Cipriani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-16T12:54:25Z","title":"A note on the Green's function for the transient random walk without killing on the half lattice, orthant and strip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04578","kind":"arxiv","version":1},"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":"sha256:9d8bede77620bc9ddc9a9dd5fc6f611d8090d54c3c3bcfc02b75a1f468bea630","target":"record","created_at":"2026-05-18T01:08:36Z","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":"7c4aeed0b158d4c3d8854f503b906dd748033fbb63f359552f74934eb2f574d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-16T12:54:25Z","title_canon_sha256":"c78a19f267ed76cdba1d2cccdf22e430c51400c01e81af5c6a1b66f5d8f5efd1"},"schema_version":"1.0","source":{"id":"1608.04578","kind":"arxiv","version":1}},"canonical_sha256":"acef285628bcbc7f8fc43887b99f165cc2d413d30360cc0b1bcc70bb1f48c4d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acef285628bcbc7f8fc43887b99f165cc2d413d30360cc0b1bcc70bb1f48c4d2","first_computed_at":"2026-05-18T01:08:36.810304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:36.810304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wotBjDO9zccssocM0QB+woD+Lbu/WQEve+q9Gru7RmVnSv5qUMSjMiRbJfMFmE5A4wuTWHxi/dFJzjUafwDwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:36.810839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d8bede77620bc9ddc9a9dd5fc6f611d8090d54c3c3bcfc02b75a1f468bea630","sha256:35e2f406a93fe3c0ef9b987f9f4937a3a46febe7d1d4235610ea3b8224b5d50f"],"state_sha256":"a67a62f3bee40ca50360fdde892952254547276bd32c85a74c5bcdd5ddb2a5ca"}