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The Factorial Conjecture in dimension $m$ asserts that if a polynomial $f$ in $m$ variables $X_i$ over $\\C$ is such that ${\\cal L}(f^k)=0$ for all $k\\geq 1$, then $f=0$, where ${\\cal L}$ is the $\\C$-linear map from $\\C[X_1,...,X_m]$ to $\\C$ defined by ${\\cal L}(X_1^{l_1}... X_m^{l_m})=l_1!... l_m!$. The Rigidity Conjecture asserts that a univariate polynomial map $a(X)$ with complex coefficients of degree at most $m+1$ such that $a(X)=X$ mod $X^2$, is equal to $X$ if $m$ consecutive c"},"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":"1304.3956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-14T23:51:43Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"121a9f04cd595ef9de666a0a71719abc51c1efb86792defb542c5826d39fe595","abstract_canon_sha256":"3ae95d02df49aac811aa01cdae128a11d374b83893eb4cd177a1f0ac3b27327f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:53.676306Z","signature_b64":"cnxPuVO3FklzIB3vKoRJd+M5IQO+nWhvRh+md8pX6xOLDdE46nb7VouRsDLtYnOlCeYmzuc2SHDPjM8tFNj2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6fa20adc4f42c9f21d9ca035ea1d1f0c5f5d54d26a3fbac81bd819e20a7583c","last_reissued_at":"2026-05-18T03:24:53.675666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:53.675666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Strong Factorial Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Arno van den Essen, Eric Edo","submitted_at":"2013-04-14T23:51:43Z","abstract_excerpt":"In this paper we present an unexpected link between the Factorial Conjecture and Furter's Rigidity Conjecture. 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