What does this research mean for the field?

A recursive fixed-input construction of higher Artin–Rédei rows on successive zero kernels can be realized through compatible Kummer lifts, utilizing the virtual-unit squareclass group at the degree-sixteen layer to achieve recursive correctness when the effective dual space is one-dimensional. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish a recursive, fixed-input construction of higher Artin–Rédei rows using the central complete quotient for real quadratic fields ramified at three primes.

September 2, 2026Open Access

Direct higher Artin–Rédei towers and the central complete quotient for real quadratic fields with three ramified primes

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Authors

KMKenshirou MoriwakiHokkaido Research Organization

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Implication

Theoretical study demonstrates a recursive Kummer lift construction of higher Artin–Rédei rows in real quadratic fields, indicating structural limits of unit-only approaches.

Key Points

To establish a recursive, fixed-input construction of higher Artin–Rédei rows using the central complete quotient for real quadratic fields ramified at three primes.
Analyzed odd, squarefree integers N ≡ 1 (mod 4) with three prime factors whose continued fractions of √N possess even periods.
Constructed degree-four and higher tower layers via compatible Kummer lifts, local filters, and the virtual-unit squareclass group.
Formulated a class-field–Kummer comparison framework and computationally evaluated direct row-space behavior for r4 = 1 and r4 > 1.
Proved the cyclic Kummer lift-sign criterion, finite and infinite local filters, and the virtual-unit exact sequence.
Demonstrated recursive correctness when the effective dual space is one-dimensional, showing that standard unit-only constructions fail at degree sixteen.
Confirmed that no uniform finite stopping depth holds, while bounding the r4 > 1 implementation to direct R8 row-space evaluation.

Cite This Study

Kenshirou Moriwaki (2026) studied this question.

synapsesocial.com/papers/6a97e2d9c562ede874ec72bf https://doi.org/10.5281/zenodo.22204644

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Implication

Theoretical study demonstrates a recursive Kummer lift construction of higher Artin–Rédei rows in real quadratic fields, indicating structural limits of unit-only approaches.

Direct higher Artin–Rédei towers and the central complete quotient for real quadratic fields with three ramified primes

Discussion

Member takes

Implication

Key Points

Cite This Study

Direct higher Artin–Rédei towers and the central complete quotient for real quadratic fields with three ramified primes

Discussion

Member takes

Implication

Key Points

Cite This Study

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