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Kurili\\'c, Stevo Todor\\v{c}evi\\'c","submitted_at":"2014-11-12T11:23:51Z","abstract_excerpt":"Let $G$ be a countable graph containing a copy of the countable random graph (Erd\\H{o}s-R\\'enyi graph, Rado graph), $Emb (G)$ the monoid of its self-embeddings, ${\\mathbb P} (G)=\\{f[G]: f\\in Emb (G)\\}$ the set of copies of $G$ contained in $G$, and ${\\mathcal I}_G$ the ideal of subsets of $G$ which do not contain a copy of $G$. We show that the poset $< {\\mathbb P} (G), \\subset>$, the algebra $P (G)/{\\mathcal I}_G$, and the inverse of the right Green's pre-order $< Emb (G),\\preceq ^R >$ have the 2-localization property. The Boolean completions of these pre-orders are isomorphic and satisfy the"},"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":"1411.3144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-12T11:23:51Z","cross_cats_sorted":[],"title_canon_sha256":"0e3fffdee328973e0fcf5418f884f51bb5a51c109550c386df1edf544e94d23d","abstract_canon_sha256":"9d3ee04d8b41124188bffd17ce18ef31599db31074ce9ade74c81bbb0a2600fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:32.015855Z","signature_b64":"woitVXaHOUF3BgF/XQaFQxgBzgAA/QcoptFYPMuLT2STBWv9lC19WXO7k5MSVkIf9exqFwzTu2qGTEec9XudAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2a8f36dd68cc70276d7e42eaac18dd63d81e0940ac3c0269be71874786a4ed6","last_reissued_at":"2026-05-18T00:34:32.015467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:32.015467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Copies of the Random Graph: the 2-localization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milo\\v{s} S. 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