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We show that the existence of such a \"blow-up\" of $\\bar{H}: \\bar{\\cal{G}} \\rightarrow \\bar{\\cal{G}}$ relative to a given family of \"local\" graph-of-groups isomorphisms $H_{i}: \\cal{G}_{i} \\rightarrow \\cal{G}_{i}$ depends crucially on the $H_{i}$-conjugacy class of the correction term $\\delta(\\bar{E}_{i})$ for any edge $\\bar{E}_{i}$ of $\\bar{\\cal{G}}$, where $H$-congjugacy is a new but natural concept introduced here. As an application we obtain a criterion"},"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":"1512.00542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-02T01:51:23Z","cross_cats_sorted":[],"title_canon_sha256":"30f8614f76ea4c04ddc46e047e907e545537563425eed8e2f7848ff23330d27c","abstract_canon_sha256":"395d3b32f1f2f0fd00e30001b45f407fbd97d5bceb4ebb11a8c486c21331e05e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:29.461862Z","signature_b64":"StlIMRkxPCj7iF/fT8HOlOiQ2GovByniVK7eo9mtJBtCYMYHuMX0j7tk19ePZXSwHIvRO9mBdGfuOi+0C6BYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8a409c86edd5d6c9fe4569efda18eb29ed7927c77a305a07383c0d1be70c9c1","last_reissued_at":"2026-05-18T00:25:29.461177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:29.461177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quotient and blow-up of automorphisms of graphs of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kaidi Ye","submitted_at":"2015-12-02T01:51:23Z","abstract_excerpt":"In this paper we study the quotient and \"blow-up\" of graph-of-groups $\\cal{G}$ and of their automorphisms $H: \\cal{G} \\rightarrow \\cal{G}$. 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