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Then any x\\in H_{n-k}(X,Q) can be written in the form \\[ x=\\sum_{\\sigma\\in\\del_X, \\dim\\sigma=k}\\mu(x,\\sigma)[V(\\sigma)]. \\] A question occurs whether there is some canonical way to express \\mu(x,\\sigma). Morelli gave an answer when X is non-singular and at least for x= \\T_{n-k}(X) the Tod"},"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":"1308.2439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-12T00:12:22Z","cross_cats_sorted":[],"title_canon_sha256":"4f63436fd64f894f4c5034b790ad8ee283c1c0b25e7180e3d63f7fbfd359c1b5","abstract_canon_sha256":"a6e8d987ce090a8c959434da805de3de8b956a81e4be438c7b4e4518b5854875"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:07.402294Z","signature_b64":"fnjScRlJ92oFnEoJPyZAUor+zu0iB46sLZkkzK9KaGszysOciuJ2xE9fhWACnOlbef/s3JNP6p/HDclznMg8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4544e033e1e3ace5a154b8e54d4f040cfb2518bfe81ff9b0fe8430f9eb58e2bf","last_reissued_at":"2026-05-18T03:16:07.401657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:07.401657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Morelli type expression of cohomology classes of torus orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Akio Hattori","submitted_at":"2013-08-12T00:12:22Z","abstract_excerpt":"Let X be a complete toric variety of dimension n and \\del the fan in a lattice N associated to X. 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