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In this paper we systematically study the existence of local $k$-mutiplicities and derive criteria for the existence of local $k$-multiplicity in terms of Stiefel--Whitney classes and Chern classes of the vector bundle $f^*\\tau N\\oplus(-\\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":"1603.06723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-22T10:19:26Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"d3e940afce0d6094c8a698ea9337e6ce5e14a15d201765e61edbc0bde032e027","abstract_canon_sha256":"b3694e0e6fb8a05c790f5052e9c7f2678ca8f93c99b26659d99073ac99484d2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:34.854268Z","signature_b64":"tG/yNg1s5Y8NvNqT5gMotNaL61q54XVLaEgfuRoAwDPjl8vwNm8PS+JlhXNgSz82Ownzk9mX35nXHFmm7RBECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa085092994dd02d37b32e758796a9feea8ddd68e778a6570cd11ae4d7d6cb6f","last_reissued_at":"2026-05-18T01:18:34.853776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:34.853776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local multiplicity of continuous maps between manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AT","authors_text":"Pavle V. 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