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The problem is to determine whether there exists a sequence $S_1,\\ldots,S_n$ of feasible solutions, where $S_1=S_s$, $S_n=S_t$, $|S_i|\\leq k\\pm 1$, and each $S_{i+1}$ results from $S_i$, $1\\leq i<n$, by the addition or removal of a single vertex. We prove that for every nowhere dense class of graphs and for every integer $r\\geq 1$ there exists a polynomial $p_r$ such that the rec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.06775","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-21T07:05:10Z","cross_cats_sorted":[],"title_canon_sha256":"035ed08c9f28e7f4656a97a0d392f22c1e976efa3297f233c58bd7e937810701","abstract_canon_sha256":"2010f703dac583b1abca85ef22856af7cb168f331eb1d7fd3b685b0c71d99320"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:06.203577Z","signature_b64":"f/8YSv1yp9C9eBYXHb5YuA+J0+IUgghJlER9lVsTAf0wLiYl+uHBImKVoh9/R3ws1qqZ+WBaw+Hj22LQur8nDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1d1341fcbdb686b0fcdaab261ed4a543b3df937bcc9257fd648d5ab50bd9b3f","last_reissued_at":"2026-05-18T00:06:06.202839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:06.202839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconfiguration on nowhere dense graph classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Sebastian Siebertz","submitted_at":"2017-07-21T07:05:10Z","abstract_excerpt":"Let $\\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\\subseteq V(G)$ of $\\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to determine whether there exists a sequence $S_1,\\ldots,S_n$ of feasible solutions, where $S_1=S_s$, $S_n=S_t$, $|S_i|\\leq k\\pm 1$, and each $S_{i+1}$ results from $S_i$, $1\\leq i<n$, by the addition or removal of a single vertex. We prove that for every nowhere dense class of graphs and for every integer $r\\geq 1$ there exists a polynomial $p_r$ such that the rec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06775","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.06775","created_at":"2026-05-18T00:06:06.202948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06775v2","created_at":"2026-05-18T00:06:06.202948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06775","created_at":"2026-05-18T00:06:06.202948+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HITIH6L3NUG","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HITIH6L3NUGWD6N","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HITIH6L","created_at":"2026-05-18T12:30:55.937587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ","json":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ.json","graph_json":"https://pith.science/api/pith-number/2HITIH6L3NUGWD6NVKZGD3KKKQ/graph.json","events_json":"https://pith.science/api/pith-number/2HITIH6L3NUGWD6NVKZGD3KKKQ/events.json","paper":"https://pith.science/paper/2HITIH6L"},"agent_actions":{"view_html":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ","download_json":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ.json","view_paper":"https://pith.science/paper/2HITIH6L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06775&json=true","fetch_graph":"https://pith.science/api/pith-number/2HITIH6L3NUGWD6NVKZGD3KKKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/2HITIH6L3NUGWD6NVKZGD3KKKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ/action/storage_attestation","attest_author":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ/action/author_attestation","sign_citation":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ/action/citation_signature","submit_replication":"https://pith.science/pith/2HITIH6L3NUGWD6NVKZGD3KKKQ/action/replication_record"}},"created_at":"2026-05-18T00:06:06.202948+00:00","updated_at":"2026-05-18T00:06:06.202948+00:00"}