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An extension of the argument to graphs of the form $\\overline{P_{\\Delta(G)+2}\\sqcup G}$ where $P_{\\Delta(G)+2}$ is a path and $G$ is a simple connected graph it is possible to find an orthogonal representation of $\\overline{P_{\\Delta(G)+2}\\sqcup G}$ in $\\mathbb{R}^{\\Delta(G)+1}$. As a consequence we prove delta conjecture."},"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":"1806.06851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-16T04:38:45Z","cross_cats_sorted":[],"title_canon_sha256":"531312063b1159e07eba41c3fdd53091038ff1a5832078b568217186e1ca7a8c","abstract_canon_sha256":"92f2c524cc373c456ad238376b7b0179b4cbee244644c2615ae3b2ee6dec1bf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:58.305359Z","signature_b64":"o3zgy+MlAPTWBBdn8JUwl8RM8jjCiQFN0lKKfanPBZDgg6/pUjdnecl9ZTHFvZrVKOrmyJNkgxh2VpeSq+KHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8c9e4d7bedcbf633667d2b65633ae20f34394e74514b9d79bb5461771f16545","last_reissued_at":"2026-05-18T00:12:58.304704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:58.304704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Proof of Delta Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pedro D\\'iaz Navarro","submitted_at":"2018-06-16T04:38:45Z","abstract_excerpt":"By finding orthogonal representation for a family of simple connected called $\\delta$-graphs it is possible to show that $\\delta$-graphs satisfy delta conjecture. 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