{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WUB4GXO7A2QLYON34MLTR2JUCQ","short_pith_number":"pith:WUB4GXO7","canonical_record":{"source":{"id":"1107.2340","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-12T16:26:44Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3f054c058f079114ffa318284bd9fe601d5a8cd4bd72a1173bf56ed3c60f0ea7","abstract_canon_sha256":"6f894085a26def45eb918fabd1bfe0eaf799bb02cc9a80eee6d376669a41042f"},"schema_version":"1.0"},"canonical_sha256":"b503c35ddf06a0bc39bbe31738e93414149371d88361c7d4fbeb07133403341f","source":{"kind":"arxiv","id":"1107.2340","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2340","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2340v3","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2340","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"WUB4GXO7A2QL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WUB4GXO7A2QLYON3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WUB4GXO7","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WUB4GXO7A2QLYON34MLTR2JUCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2340","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-12T16:26:44Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3f054c058f079114ffa318284bd9fe601d5a8cd4bd72a1173bf56ed3c60f0ea7","abstract_canon_sha256":"6f894085a26def45eb918fabd1bfe0eaf799bb02cc9a80eee6d376669a41042f"},"schema_version":"1.0"},"canonical_sha256":"b503c35ddf06a0bc39bbe31738e93414149371d88361c7d4fbeb07133403341f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:40.483392Z","signature_b64":"VU0h4ybpWBpuQK9mm8jQQbj5PwvwuehxT8/XKVaBgvwf0a48SWQeykLvNVSTc//crGuuWZpAZvN5es0eJF1WDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b503c35ddf06a0bc39bbe31738e93414149371d88361c7d4fbeb07133403341f","last_reissued_at":"2026-05-18T03:41:40.482568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:40.482568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2340","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":"2026-05-18T03:41:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HvsFKyRYbaxA6cDLGWhFGl5kjH5CshaA7NFJ3W5fUoT4Zb9d98ZwjaaJgs97g9HUjTyTxfgst/Y+MSmhxQy0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:51.547944Z"},"content_sha256":"e028c079dd4eff3423f99a32dad02a4fa43b287fb9354a2aff093d64c63f9c67","schema_version":"1.0","event_id":"sha256:e028c079dd4eff3423f99a32dad02a4fa43b287fb9354a2aff093d64c63f9c67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WUB4GXO7A2QLYON34MLTR2JUCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the functions counting walks with small steps in the quarter plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Irina Kurkova, Kilian Raschel","submitted_at":"2011-07-12T16:26:44Z","abstract_excerpt":"Models of spatially homogeneous walks in the quarter plane ${\\bf Z}_+^{2}$ with steps taken from a subset $\\mathcal{S}$ of the set of jumps to the eight nearest neighbors are considered. The generating function $(x,y,z)\\mapsto Q(x,y;z)$ of the numbers $q(i,j;n)$ of such walks starting at the origin and ending at $(i,j) \\in {\\bf Z}_+^{2}$ after $n$ steps is studied. For all non-singular models of walks, the functions $x \\mapsto Q(x,0;z)$ and $y\\mapsto Q(0,y;z)$ are continued as multi-valued functions on ${\\bf C}$ having infinitely many meromorphic branches, of which the set of poles is identifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2340","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":"2026-05-18T03:41:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qurQIfpYfYEw9ikOSY/EuPYFqKaNrb6nsA0H4qmuqlIZdUuY8ZHpyOWjsKB0PKpdHWvJMTXbNv2IZgH2V+gzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:51.548602Z"},"content_sha256":"b2f496881468dd6d252509fd07e8916dfef490daa9ec3e553c5b5140d7a8dad6","schema_version":"1.0","event_id":"sha256:b2f496881468dd6d252509fd07e8916dfef490daa9ec3e553c5b5140d7a8dad6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUB4GXO7A2QLYON34MLTR2JUCQ/bundle.json","state_url":"https://pith.science/pith/WUB4GXO7A2QLYON34MLTR2JUCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUB4GXO7A2QLYON34MLTR2JUCQ/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":"2026-05-27T11:19:51Z","links":{"resolver":"https://pith.science/pith/WUB4GXO7A2QLYON34MLTR2JUCQ","bundle":"https://pith.science/pith/WUB4GXO7A2QLYON34MLTR2JUCQ/bundle.json","state":"https://pith.science/pith/WUB4GXO7A2QLYON34MLTR2JUCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUB4GXO7A2QLYON34MLTR2JUCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WUB4GXO7A2QLYON34MLTR2JUCQ","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":"6f894085a26def45eb918fabd1bfe0eaf799bb02cc9a80eee6d376669a41042f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-12T16:26:44Z","title_canon_sha256":"3f054c058f079114ffa318284bd9fe601d5a8cd4bd72a1173bf56ed3c60f0ea7"},"schema_version":"1.0","source":{"id":"1107.2340","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2340","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2340v3","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2340","created_at":"2026-05-18T03:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"WUB4GXO7A2QL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WUB4GXO7A2QLYON3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WUB4GXO7","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:b2f496881468dd6d252509fd07e8916dfef490daa9ec3e553c5b5140d7a8dad6","target":"graph","created_at":"2026-05-18T03:41:40Z","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":"Models of spatially homogeneous walks in the quarter plane ${\\bf Z}_+^{2}$ with steps taken from a subset $\\mathcal{S}$ of the set of jumps to the eight nearest neighbors are considered. The generating function $(x,y,z)\\mapsto Q(x,y;z)$ of the numbers $q(i,j;n)$ of such walks starting at the origin and ending at $(i,j) \\in {\\bf Z}_+^{2}$ after $n$ steps is studied. For all non-singular models of walks, the functions $x \\mapsto Q(x,0;z)$ and $y\\mapsto Q(0,y;z)$ are continued as multi-valued functions on ${\\bf C}$ having infinitely many meromorphic branches, of which the set of poles is identifi","authors_text":"Irina Kurkova, Kilian Raschel","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-12T16:26:44Z","title":"On the functions counting walks with small steps in the quarter plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2340","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:e028c079dd4eff3423f99a32dad02a4fa43b287fb9354a2aff093d64c63f9c67","target":"record","created_at":"2026-05-18T03:41:40Z","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":"6f894085a26def45eb918fabd1bfe0eaf799bb02cc9a80eee6d376669a41042f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-12T16:26:44Z","title_canon_sha256":"3f054c058f079114ffa318284bd9fe601d5a8cd4bd72a1173bf56ed3c60f0ea7"},"schema_version":"1.0","source":{"id":"1107.2340","kind":"arxiv","version":3}},"canonical_sha256":"b503c35ddf06a0bc39bbe31738e93414149371d88361c7d4fbeb07133403341f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b503c35ddf06a0bc39bbe31738e93414149371d88361c7d4fbeb07133403341f","first_computed_at":"2026-05-18T03:41:40.482568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:40.482568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VU0h4ybpWBpuQK9mm8jQQbj5PwvwuehxT8/XKVaBgvwf0a48SWQeykLvNVSTc//crGuuWZpAZvN5es0eJF1WDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:40.483392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2340","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e028c079dd4eff3423f99a32dad02a4fa43b287fb9354a2aff093d64c63f9c67","sha256:b2f496881468dd6d252509fd07e8916dfef490daa9ec3e553c5b5140d7a8dad6"],"state_sha256":"282ac8a1c699916b5f540f5402b9f9f854131637ab16cef3b263bb5d9d2a041a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tX+BQsayEa4aGrcLwJC09jc32qbJ1ekmYHONvwysjBgRfOFDvFAktf3voV5XGpzPFy+klls5B/p3jHmzhQpwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:19:51.552088Z","bundle_sha256":"70b6e2d773efc4d32991e75b4ad8e993dc57a458118f0d5373be45f3be27631c"}}