{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SIVSMZCLWNRTOXSQ3O4X4KNLLT","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":"2afa72702f021dbe515d97670a3e409d988b0e4b955e0243333124bf8f2cc584","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-16T22:17:52Z","title_canon_sha256":"e26fe179bf3010157cc05efb5e95f7bb3fa5a76b22484c6b66943d3adb4a4312"},"schema_version":"1.0","source":{"id":"1801.05496","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05496","created_at":"2026-05-18T00:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05496v3","created_at":"2026-05-18T00:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05496","created_at":"2026-05-18T00:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"SIVSMZCLWNRT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SIVSMZCLWNRTOXSQ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SIVSMZCL","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:bdca882232f958bf9f319c84d0c362518b4701e55e93c5fb852641b3daee40f7","target":"graph","created_at":"2026-05-18T00:17:32Z","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":"$M$-Lipschitz mappings of graphs (or equivalently graph-indexed random walks) are a generalization of standard random walk on $\\mathbb{Z}$. For $M \\in \\N$, an \\emph{$M$-Lipschitz mapping} of a connected rooted graph $G = (V,E)$ is a mapping $f: V \\to \\Z$ such that root is mapped to zero and for every edge $(u,v) \\in E$ we have $|f(u) - f(v)| \\le M$.\n  We study two natural problems regarding graph-indexed random walks. - Computing the maximum range of a graph-indexed random walk for a given graph. - Deciding if we can extend a partial GI random walk into a full GI random walk for a given graph.","authors_text":"Jan Bok","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-16T22:17:52Z","title":"Algorithmic aspects of $M$-Lipschitz mappings of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05496","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":"sha256:6dde7ba55af45d6b963a3fcc15dc5c97eb09d3b232fe2c4de180d594006321cd","target":"record","created_at":"2026-05-18T00:17:32Z","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":"2afa72702f021dbe515d97670a3e409d988b0e4b955e0243333124bf8f2cc584","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-16T22:17:52Z","title_canon_sha256":"e26fe179bf3010157cc05efb5e95f7bb3fa5a76b22484c6b66943d3adb4a4312"},"schema_version":"1.0","source":{"id":"1801.05496","kind":"arxiv","version":3}},"canonical_sha256":"922b26644bb363375e50dbb97e29ab5cec509b0388b32649abcb9d22bbf1a02b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"922b26644bb363375e50dbb97e29ab5cec509b0388b32649abcb9d22bbf1a02b","first_computed_at":"2026-05-18T00:17:32.907308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:32.907308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dGlnDk9aFW9nW6bZWVLbXjejkeMhnpmqoNzWfVCqmw2SOrtcwKtTUyojcAPRgC1HIsaHLXWdWn15I1avW7CdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:32.907879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.05496","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dde7ba55af45d6b963a3fcc15dc5c97eb09d3b232fe2c4de180d594006321cd","sha256:bdca882232f958bf9f319c84d0c362518b4701e55e93c5fb852641b3daee40f7"],"state_sha256":"daeefea5227d053ce9e749e840bb637e893f47efa35811c2f382194f0775e218"}