{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YDGJWXIMUWT4QPNVR4EOUP6XIH","short_pith_number":"pith:YDGJWXIM","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"},"canonical_sha256":"c0cc9b5d0ca5a7c83db58f08ea3fd741c9d2c726d931e7933a08dba2aa46e43f","source":{"kind":"arxiv","id":"1309.0603","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0603","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0603v2","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0603","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"YDGJWXIMUWT4","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YDGJWXIMUWT4QPNV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YDGJWXIM","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YDGJWXIMUWT4QPNVR4EOUP6XIH","target":"record","payload":{"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"},"canonical_sha256":"c0cc9b5d0ca5a7c83db58f08ea3fd741c9d2c726d931e7933a08dba2aa46e43f","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"},"source_kind":"arxiv","source_id":"1309.0603","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QTCjanXsgTawune3fLooXVX8gaPdNt/X6SfxffSl3MogvkJLZI5czD4nW1r1PZW+WGX5qw/i+kzJVjITIjVMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:24:52.431211Z"},"content_sha256":"74e0d66df18e2d903c1ce7fb09badbd83e2d32bd1dd36ca2b0ab9c8cac0244dd","schema_version":"1.0","event_id":"sha256:74e0d66df18e2d903c1ce7fb09badbd83e2d32bd1dd36ca2b0ab9c8cac0244dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YDGJWXIMUWT4QPNVR4EOUP6XIH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"arXbDat0VQK5IFm8bPwbiQXL7oJop1ju90fjZ99tjs7ezQAbHIcKcE+/qtHG5CunDJQy6yKoxexLzT0tEOIuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:24:52.431605Z"},"content_sha256":"64d2ac5e3e654ffab5bf7787d792a231dcdbd93340a1193752036c4123824c88","schema_version":"1.0","event_id":"sha256:64d2ac5e3e654ffab5bf7787d792a231dcdbd93340a1193752036c4123824c88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/bundle.json","state_url":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/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":"2026-05-27T12:24:52Z","links":{"resolver":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH","bundle":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/bundle.json","state":"https://pith.science/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDGJWXIMUWT4QPNVR4EOUP6XIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YDGJWXIMUWT4QPNVR4EOUP6XIH","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":"1c2be49903a7913d6e4265f17212bf62111761a318e41cc5ce9827baaa4c9489","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-03T08:04:42Z","title_canon_sha256":"8f6a30303a4032f8b7b9f02789ed56def53abb52ca09c831bb6b9b5e7b56f933"},"schema_version":"1.0","source":{"id":"1309.0603","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0603","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0603v2","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0603","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"YDGJWXIMUWT4","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YDGJWXIMUWT4QPNV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YDGJWXIM","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:64d2ac5e3e654ffab5bf7787d792a231dcdbd93340a1193752036c4123824c88","target":"graph","created_at":"2026-05-18T03:14:08Z","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":"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","authors_text":"Magdalena Lema\\'nska, Monika Rosicka, Rita Zuazua","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-03T08:04:42Z","title":"Graphs with $C_3_-free vertices are not universal fixers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0603","kind":"arxiv","version":2},"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":"sha256:74e0d66df18e2d903c1ce7fb09badbd83e2d32bd1dd36ca2b0ab9c8cac0244dd","target":"record","created_at":"2026-05-18T03:14:08Z","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":"1c2be49903a7913d6e4265f17212bf62111761a318e41cc5ce9827baaa4c9489","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-03T08:04:42Z","title_canon_sha256":"8f6a30303a4032f8b7b9f02789ed56def53abb52ca09c831bb6b9b5e7b56f933"},"schema_version":"1.0","source":{"id":"1309.0603","kind":"arxiv","version":2}},"canonical_sha256":"c0cc9b5d0ca5a7c83db58f08ea3fd741c9d2c726d931e7933a08dba2aa46e43f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0cc9b5d0ca5a7c83db58f08ea3fd741c9d2c726d931e7933a08dba2aa46e43f","first_computed_at":"2026-05-18T03:14:08.164064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:08.164064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HLEHz4x29Bu2EtGyELjtpNPW0nwj9V/nrAJi9kYv/qbqvd4x4VUwoK7vuiLaWLRA9NBQ3mtxUVLmLpUJMtczBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:08.164452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0603","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74e0d66df18e2d903c1ce7fb09badbd83e2d32bd1dd36ca2b0ab9c8cac0244dd","sha256:64d2ac5e3e654ffab5bf7787d792a231dcdbd93340a1193752036c4123824c88"],"state_sha256":"7fcaa1f798ceab45d951f40070e1ab2823616baedb2316394f6ee09023de2b91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pKnfeuO3G81ZY0pU+ivIvoGAIkj+awyCEu4UCNvrPqa4rjCVFzPCPPQ38AbGl1oKYgQr6iNXUu+QjSJvLyxGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:24:52.434615Z","bundle_sha256":"7e26dfc88f152332bc5175495c8e6fdb456c7cb1c45e26edf41420eea242784f"}}