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Gauss Bonnet is then parametrized, f_G(t) = sum_x F_(S(x))(t), and holds for all simplicial complexes G. The Gauss-Bonnet formula chi(G)=sum_x K(x) for Euler characteristic chi(G) is the special case t=-1. Dehn-Sommerville is equivalent to the reflection symmetry f_G(t)+(-1)^d f_G(-1-t)=0 which is equi"},"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":"1905.04831","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-13T02:18:03Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"56c971e98aa2dd77d6a1b036079d7900b4d2346dbb90ebe269f4c856b24d83b4","abstract_canon_sha256":"d9b927fe1eae46a088e13aedf59443242734d922afbafc58597aec79c6f041bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:23.357729Z","signature_b64":"MQOaQ6Pmof2w8QHQaYatL7h/4+nsQiu5Q2lGVoxoYPRksai8r+wURB4Zdmkj55rRDb48m0x4VVt4YXfM09J4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"becf3ace3ec6c2f391456a80a49fc01c63ea2d671986a813a816b195d312beda","last_reissued_at":"2026-05-17T23:46:23.356981Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:23.356981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dehn-Sommerville from Gauss-Bonnet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Oliver Knill","submitted_at":"2019-05-13T02:18:03Z","abstract_excerpt":"We give a zero curvature proof of Dehn-Sommerville for finite simple graphs. 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