What Do We Actually Know About Tau Ceti? Three Paradoxes, the Detection Completeness Principle, and Testable Predictions for the Nearest Sun-Like Planetary System

Tau Ceti (HD 10700, G8 V, 3.65 pc) is the nearest solitary Sun-like star and one of the most extensively observed stellar systems. Despite decades of study, no planet in the system is confirmed, and most of its architecture remains unconstrained. This paper identifies three genuine paradoxes (properties in tension with standard models), two observational puzzles, and two open questions. The three paradoxes are: (P1) the Detection Completeness Paradox — approximately 46% of the physically plausible mass–semi-major-axis parameter space lies below 10% detection completeness, and Earth-mass planets in the habitable zone are undetectable at the system's pole-on inclination; (P2) the Metallicity–Planet Formation Paradox — four super-Earth candidates exist despite [Fe/H] ≈ −0.5; (P3) the Disk Longevity Paradox, addressed through the Observational Asymmetry Theorem. The two observational puzzles are the near-pole-on geometry (i ≈ 7° ± 7°) and the unconfirmed status of all planet candidates. The two open questions concern a ~28° star–disk misalignment and the habitability implications of low stellar magnetic activity. The Detection Completeness Principle (DCP) is formalized as a quantitative framework, building on established injection-recovery methods (Cumming et al. 2008; Howard et al. 2010; Petigura et al. 2013) but applying them with explicit rigor to a single nearby system where pole-on geometry creates an unusually large gap between detection limits and physically interesting parameter space. The Observational Asymmetry Theorem proves that the canonical "ten times more debris than the Solar System" is an upper bound on the true mass ratio, not a measurement: the comparison excludes the Solar System's Oort cloud (estimated 2–100 Earth masses). Depending on the adopted Oort cloud mass, the true ratio ranges from 0.01 to 0.56 — the Tau Ceti system may contain less total small-body mass than the Solar System. For each paradox and puzzle, competing hypotheses are formulated with analytical models, toy numerical implementations, and falsifiable predictions organized by observational facility (ESPRESSO, Gaia DR4, ALMA, ELT/METIS). The paper includes three figures (detection completeness map, disk mass evolution model, metallicity–planet mass relation), all generated by reproducible Python code provided in the appendices. Tau Ceti is compared against a population of solar analogs to assess which properties are genuinely anomalous. Revised per two rounds of peer review. Companion paper to "Why Is Vega Metal-Poor and Rapidly Rotating? Four Hypotheses, One Laboratory" (Kriger, 2026). Keywords: Tau Ceti; exoplanets; debris disks; detection completeness; Oort cloud; observational asymmetry; solar analogs; habitability; analytical astrophysics; planet formation; stellar metallicity License: Creative Commons Attribution 4.0 International Author: Boris Kriger (ORCID: 0009-0001-0034-2903) Affiliations: Information Physics Institute, Gosport; Institute of Integrative and Interdisciplinary Research, Toronto