SWhat changed
Hensel proposed replacing aspects of ideal-prime factorization by local prime-power expansions analogous to power-series expansions of algebraic functions. His announcement describes algebraic numbers through expansions with finitely many negative terms, distinguishes unramified and ramified local parameters, and relates the resulting places and orders of zeros or poles to prime-ideal divisibility and ramification. It sets out a prime-adic local viewpoint rather than giving a complete proof of the announced foundation.
Scientific scope
Hensel proposed replacing aspects of ideal-prime factorization by local prime-power expansions analogous to power-series expansions of algebraic functions. His announcement describes algebraic numbers through expansions with finitely many negative terms, distinguishes unramified and ramified local parameters, and relates the resulting places and orders of zeros or poles to prime-ideal divisibility and ramification. It sets out a prime-adic local viewpoint rather than giving a complete proof of the announced foundation. The six-page note explicitly defers simple proofs to a forthcoming Mathematische Annalen paper. The stated root-count and expansion assertions are historical announcements, not independently validated general congruence-root theorems in this record. Digits may belong to a finite residue-field extension; ramified parameters are not always simply a root of p, and the note separately discusses the exceptional divisibility case. No claim that every algebraic number lies in Q_p, no arbitrary p-adic completeness theorem, full modern local-field classification, Hensel lifting lemma proof or local-global principle is certified here.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The six-page note explicitly defers simple proofs to a forthcoming Mathematische Annalen paper. The stated root-count and expansion assertions are historical announcements, not independently validated general congruence-root theorems in this record. Digits may belong to a finite residue-field extension; ramified parameters are not always simply a root of p, and the note separately discusses the exceptional divisibility case. No claim that every algebraic number lies in Q_p, no arbitrary p-adic completeness theorem, full modern local-field classification, Hensel lifting lemma proof or local-global principle is certified here.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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