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For a bijective function $\\pi:V(G)\\mapsto V (G')$, we define the prism $\\pi G$ of $G$ as follows: $V(\\pi G)=V(G)\\cup V(G')$ and $E(\\pi G)=E(G)\\cup E(G')\\cup M_{\\pi}$, where $M_{\\pi}=\\{u\\pi (u): u\\in V(G)\\}$. Let $\\gamma(G)$ be the domination number of $G$. If $\\gamma(\\pi G)=\\gamma(G)$ for any bijective function $\\pi$, then $G$ is called a universal fix"},"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":"1309.0603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-03T08:04:42Z","cross_cats_sorted":[],"title_canon_sha256":"8f6a30303a4032f8b7b9f02789ed56def53abb52ca09c831bb6b9b5e7b56f933","abstract_canon_sha256":"1c2be49903a7913d6e4265f17212bf62111761a318e41cc5ce9827baaa4c9489"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:08.164452Z","signature_b64":"HLEHz4x29Bu2EtGyELjtpNPW0nwj9V/nrAJi9kYv/qbqvd4x4VUwoK7vuiLaWLRA9NBQ3mtxUVLmLpUJMtczBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0cc9b5d0ca5a7c83db58f08ea3fd741c9d2c726d931e7933a08dba2aa46e43f","last_reissued_at":"2026-05-18T03:14:08.164064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:08.164064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphs with $C_3_-free vertices are not universal fixers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Magdalena Lema\\'nska, Monika Rosicka, Rita Zuazua","submitted_at":"2013-09-03T08:04:42Z","abstract_excerpt":"A non-isolated vertex $x\\in V(G)$ is called $C_{3}$-free if $x$ belongs to no triangle of $G$. In \\cite{BMW} Burger, Mynhardt and Weakley introduced the idea of universal fixers. Let $G=(V,E)$ be a graph with $n$ vertices and $G'$ a copy of $G$. For a bijective function $\\pi:V(G)\\mapsto V (G')$, we define the prism $\\pi G$ of $G$ as follows: $V(\\pi G)=V(G)\\cup V(G')$ and $E(\\pi G)=E(G)\\cup E(G')\\cup M_{\\pi}$, where $M_{\\pi}=\\{u\\pi (u): u\\in V(G)\\}$. Let $\\gamma(G)$ be the domination number of $G$. If $\\gamma(\\pi G)=\\gamma(G)$ for any bijective function $\\pi$, then $G$ is called a universal fix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0603","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":"1309.0603","created_at":"2026-05-18T03:14:08.164119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0603v2","created_at":"2026-05-18T03:14:08.164119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0603","created_at":"2026-05-18T03:14:08.164119+00:00"},{"alias_kind":"pith_short_12","alias_value":"YDGJWXIMUWT4","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YDGJWXIMUWT4QPNV","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YDGJWXIM","created_at":"2026-05-18T12:28:06.772260+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/YDGJWXIMUWT4QPNVR4EOUP6XIH","json":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH.json","graph_json":"https://pith.science/api/pith-number/YDGJWXIMUWT4QPNVR4EOUP6XIH/graph.json","events_json":"https://pith.science/api/pith-number/YDGJWXIMUWT4QPNVR4EOUP6XIH/events.json","paper":"https://pith.science/paper/YDGJWXIM"},"agent_actions":{"view_html":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH","download_json":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH.json","view_paper":"https://pith.science/paper/YDGJWXIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0603&json=true","fetch_graph":"https://pith.science/api/pith-number/YDGJWXIMUWT4QPNVR4EOUP6XIH/graph.json","fetch_events":"https://pith.science/api/pith-number/YDGJWXIMUWT4QPNVR4EOUP6XIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/action/storage_attestation","attest_author":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/action/author_attestation","sign_citation":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/action/citation_signature","submit_replication":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/action/replication_record"}},"created_at":"2026-05-18T03:14:08.164119+00:00","updated_at":"2026-05-18T03:14:08.164119+00:00"}