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For the maximum flow problem, we show that if the bunkbed graph $G\\times K_2$ has non-negative, reflection-symmetric edge capacities, then for any $u, v\\in V(G)$, the maximum flow strength from $(u,0)$ to $(v,0)$ in $G\\times K_2$ is at least as large as that from $(u,0)$ to $(v,1)$.\n  For the self-avoiding walk model on a bunkbed graph $G"},"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":"2502.06237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-02-10T08:16:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cfa340e16403731cef6dd7f12c0222de905eeaae5f808968775e091791290c49","abstract_canon_sha256":"ac5f9a81c8f09455d217d2b9fedc0a15c74b77dc666fe571979cfb9bf196e249"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:49.417215Z","signature_b64":"eercsTUkxqdckTgym2c6s4gPE4RrqfBtYc1rGH/yYxxiFL1Gx7mH4aNVzcodXIXsOzQYP5YlyhOi4i8CVi9gBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fb2b9d3564afd90160385c483bc1a74b53e27d6f6648c436c5ce05416ba3e2f","last_reissued_at":"2026-07-05T10:11:49.416675Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:49.416675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum flow and self-avoiding walk on bunkbed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Pengfei Tang","submitted_at":"2025-02-10T08:16:11Z","abstract_excerpt":"We consider two combinatorial models on bunkbed graphs: maximum flow and self-avoiding walks. 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