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Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\\nu} \\log r$ with $\\nu = (k^2-1)/2$. Considering the spanning forest stretched along the meridian of this watermelon, we see t"},"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":"1206.3147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-14T15:42:53Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"cc8ffe1976078cd13f4796dd11302579b4c5749111d86dea9a7677dda19820c4","abstract_canon_sha256":"94b63811dfd92576733dd493553e63c7c9852fc525cdf7fb6693b7f3792f8ac5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:58.627187Z","signature_b64":"VKQkBR1pQw5pqCyvB5oaBojU/LI3h/Q9VaKg9s6UHe60kR8Nczb8QfKwX7enQwNm4Yta9xXLkXRKhWGf5E8tCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21049dcc854759aba6d0415dd8825fb7376e8347e1938740be8b83bd3523f400","last_reissued_at":"2026-05-18T01:56:58.626255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:58.626255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From elongated spanning trees to vicious random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. 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