Ceramic superconductors (cuprates, pnictides, etc.) exhibit universal features in both T c max and in their planar lattice disordering measured by EXAFS, as reflected by three phase transitions. The two highest temperature transitions are known to be associated with formation of Jahn-Teller pseudogaps and superconductive gaps, with corresponding Landau order parameters, but no new gap is associated with the third transition below T c, and its origin is mysterious. It is argued that the third subT c transition is a dopant glass transition, which is remarkably similar to topological transitions previously observed in chalcogenide and oxide alloy network glasses (like window glass).EXAFS ͉ superconductivity ͉ topological C onventional metals achieve high superconductive transition temperatures by means of strong electron-phonon interactions, which provide an attractive interaction for Cooper pairs that overcomes Coulomb repulsion. In ceramic materials (oxides, halides, pnictides), one would expect to find strong ionic charges, little screening, and correspondingly strong Coulomb interactions, which would make superconductivity unlikely. Moreover, enhancing the electron-phonon interactions usually leads to large Jahn-Teller lattice distortions, which convert metals into semiconductors or insulators. Yet in certain ceramic materials, nature has found a way to circumvent both of these unfavorable mechanisms and to produce not only superconductivity but even superconductivity at temperatures far higher than are usually found in metals, thus posing the greatest scientific paradox discovered in recent decades (1), with over 7000 research citations.Several theoretical mechanisms propose to resolve this paradox by invoking interactions other than the traditional attractive electron-phonon interactions, but so far there has been little evidence to support such models, apart from the fact that magnetic nanophases often coexist with superconductive nanophases in samples with Meissner filling factors that are never close to unity (and seldom reported). The simplest idea, which recommends itself as minimally complex, is that certain special ceramics (like the layered cuprates, with layered crystal structures chemically similar to ferroelastic perovskites) have very strong electron-phonon interactions, and that upon being doped, the resulting structures lose most of their magnetic nanophases and instead phase-separate into pseudogapped (charge density wave, CDW, or Jahn-Teller distorted) and metallic superconductive nanophases (2). These superlattice phases have long been described as ''stripes'' (dynamical or otherwise), but it is noteworthy that in the rare materials (such as La 2-x Sr x CuO 4 near x ϭ 1/8) where stripes have been observed by diffraction, T c has been either strongly depressed or reduced to zero. It appears that ordering of nanophases into superlattices describable by Landau order parameters is extremely unfavorable for superconductivity.The opposite of ''stripes'' (superlattice ordering) would be the very str...