Four Impossibilities Are One: Heisenberg, Gödel, the Second Law, and the Coherence Channel Capacity

Four foundational impossibility results — Heisenberg’s uncertainty principle (1927), Gödel’s incompleteness theorems (1931), the second law of thermodynamics, and the closed-system impossibility theorem (Spektre corpus, 2026) — are shown to share identical structure. Each states: a closed system cannot simultaneously have full resolution in two conjugate directions. The common structure: the corrective channel F(t) has finite capacity — a bandwidth limit set by ℏ/2 at quantum scale, k_BT ln 2 at thermal scale, and the Gödel sentence at logical scale. Conjugate variables are complementary directions in coherence space, and the uncertainty product is the minimum coherence resource required for observation. ℏ/2 is K_crit at quantum scale. Uncertainty is not fundamental. Incompleteness is not fundamental. Entropy increase is not fundamental. They are all consequences of one thing: coherence channels are finite. Part of the Spektre research corpus.