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This region corresponds to (up to prefactors and change of variables) the Ising model, the $q$-state Potts model, the number of spanning forest generator and particularizations of these. We show splitting formulas for these specializations."},"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":"1605.05499","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-18T09:58:06Z","cross_cats_sorted":[],"title_canon_sha256":"7b6d0b983255c5b7fbdf25ba247d4e450b150b02fd39223aea44691a536c7a2a","abstract_canon_sha256":"844f6f5e616d140b15ec177fadd73193b17496859c5e61949b0b97515e80ade3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:52.198928Z","signature_b64":"FUjAC6W2eHGUhSMN8GIrfAunb9gFFY30N/eAt7AsDtCPZPIzszIYbVbn8fY0JkklpLj/6tAkNoSwpN9ZS9DNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b7e8ce21fb44a8b1f0dcf7b090f10aad4644422186d1fd1949460313ed75722","last_reissued_at":"2026-05-18T00:29:52.198348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:52.198348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singularities in Negami's splitting formula for the Tutte polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Juan Manuel Burgos","submitted_at":"2016-05-18T09:58:06Z","abstract_excerpt":"The n-sum graph Negami's splitting formula for the Tutte polynomial is not valid in the region $(x-1)(y-1)=q$ for $q=1,2,\\ldots n-1$ with the additional region $y=1$ if $n>3$. 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