DQIS — Addendum I: Temporal Stratification of Tail Dependence Risk

Abstract

DQIS — Addendum I: Tail Dependence — What the Correlation Coefficient Does Not Tell You (V23, August 2026). Companion to Consolidated Framework V39 and Objections Register V38. The mathematical supplement covering the one place where the central claim is soft: channels that look independent on average can still fail together in exactly the situations that matter. It answers three questions. Does the measured correlation bound the risk? No — at one fixed Kendall τ the escape probability moves across seven orders of magnitude with the assumed dependence structure. Is joint failure in the tail real, or a modelling worry? It is real, and it is measured here for the first time on this panel: five of six channels sit in the low tail together 1.5× more often than independence predicts at the median and 4× at the lower quartile, growing monotonically as one goes deeper into the tail — the opposite of what would happen if the channels became independent at the extremes. What follows? We report the worst dependence structure we could construct rather than the middle one, and state the result as a declared edge of a band, never as a prediction. Further chapters distinguish evolutionary from environmental co-failure and explain why only the second is operative in the early interception window the framework targets; derive the observation floor before the device may decide, set by a safety criterion — fewer than one healthy cell killed across the body — declared before looking at escape, which it makes worse; give the memory imprint's computed optimum half-life and the reason "as long as possible" is wrong, together with the order-of-magnitude gap between what the imprint must span and the best duration measured in vivo; and list the assumptions one line each, marked as to whether each is the worst case, including the ones that are not. Two thresholds share the number 0.20 and are separated explicitly, because conflating them is the most reliable way to misread this framework: the channel admission gate, which is ours, and the worst published per-channel sensor error, which is from the literature. Prior-art deposit, not a peer-reviewed publication. No laboratory validation. Not clinical guidance. Contact: dqis.research@proton.meRelated documents: - DQIS Consolidated Framework (main document): https://zenodo.org/records/21128521- Register of Scientific Objections v35.0: https://zenodo.org/records/21128725