Attracting fixed points of Dedekind zeta functions

Every Dedekind zeta function has a unique fixed point on (1, infinity), but this point need not be repelling. We give certified attracting examples in a real quadratic field and four abelian fields, each with a certified repelling real two-cycle. Two arithmetic limits explain the phenomenon. For quadratic fields with increasingly many inert primes, the zeta functions tend to zeta(2s); allowing ramification at 2 changes the limit to (1+2^(-s))zeta(2s). For prime-power cyclotomic fields they tend to (1-p^(-s))^(-1). We prove explicit sufficient thresholds for attraction and show that the quadratic examples have a positive natural density, equal for positive and negative fundamental discriminants. This density is the probability of attraction in a random Euler-product model, whose fixed-point multiplier has a non-atomic distribution. We also give an exact criterion for the absence of real two-cycles, distinguish it from convexity of the second iterate, and exhibit two obstructions to extending the cyclotomic conclusion to arbitrary Z_p-extensions. Numerical enumerations and density estimates are separated from the proofs and the interval-arithmetic certificates. MSC 2020:Primary 11R42, 37E05; Secondary 11M06, 11R11, 11R18. Version 1.0.0 (2026-09-05). Archive contents (zip): LaTeX source, abstract, interval-arithmetic certificate programs (python-flint 0.9.0 / Arb) with replay logs, execution manifest and provenance, exact rational threshold checkers, PARI/GP scan snapshots and aggregation program, expository proof notes. See README.md and CHECKSUMS.txt.