model that relates the degree of molecular connectivity to the heat capacity jump Δ c$_{p}$ . 15 Establishing such connec- tions between local-chemistry and thermodynamics for actual substances is difficult, however, hampering our ef- forts to make first principles estimates of the configura- tional entropy and, ultimately, the glass-forming ability of those substances. Indeed, since the viscosity is directly related to the average relaxation time, 16 the crystal nucleus growth, which is subject to viscous drag, 17 is determined by the configurational entropy s$_{c}$ per bead. The actual chemical identification of beads is relatively straightforward in molecular, but less so in covalently bonded compounds, where, for instance, the apparent bead often corresponds to a non-integer frac- tion of a stoichiometric unit. 2,18 We note that these chal- lenges are, of course, not unique to theories of the glass transition but equally pertain to quantitative descriptions of the ordinary liquid-to-crystal transition. Yet perhaps in reflection of these open questions, which we view as quantitative, many believe fragile and strong behaviors actually have distinct mechanisms. In an effort to develop a microscopic description of the configurational dynamics in specific substances, here we propose and work out several consequences of a novel quasi-continuum ansatz for local stress distribution that implements direct interactions in the activated regime semi-empirically, via the local elastic properties of the material. The ansatz incorporates the possibility of local, short-length motions that are similar in spirit to Einstein oscillators, but are strongly anharmonic and account ex- plicitly for the tensorial nature of the relation between local deformation and stress in solids. In particular, ex- plicitly treated is (high-frequency) shear resistance, which is characteristic of deeply supercooled liquids and, gener- ally, activated liquid transport. This fully tensorial treat- ment of stress may be viewed, among other things, as a systematic improvement on self-consistent scalar-phonon theories of aperiodic crystals. 1,19 The many-body effects that lead to the emergence of shear resistance in liquids at high densities do not lend themselves easily to perturbative treatments that use the uniform liquid as the reference state. In contrast, we use a fully mechanically stable state as the reference state, and then uniformly allow for local, short-length anhar- monic motions. Within this ansatz, a metastable , ape- riodic frozen-in stress pattern emerges self-consistently, whereby the bead size is identified as the typical length scale of the stress heterogeneity. This result implies that even in a covalently bonded material, the concept of a bead is entirely unambiguous. The frozen-in stress pattern is multiply degenerate , whereby the transitions between alternative configurations can be mapped onto the dynamics of a classical Heisenberg model with six- component spins. The six components correspond to the independent entries in the local frozen-in deforma- tion tensor. The average length of the spin emerges as 2 an order parameter for the aperiodic-to-periodic crystal transition. The transitions between different spin config- urations are rare events implying the corresponding liq- uid states are long-lived and thus supporting the view of liquids in the activated-transport regime as aperiodic crystals. In other words, we explicitly confirm the non- trivial notion of the RFOT theory that aperiodic molec- ular assemblies can exhibit multiple states and, at the same time, support shear. Already in a mean-field analysis of the spin model, we establish that the broken-symmetry state can exhibit a range of behaviors interpolating between frozen-in shear and uniform compression/dilation. These two limits cor- respond to a 5-component Heisenberg- and Ising-like fer- romagnets respectively. The resulting heat capacity vari- ations, together with the RFOT-derived intrinsic relation between thermodynamics and kinetics, as reflected in the m vs. Δ c$_{p}$ relation, implies that the spin model exhibits a broad range of fragile-to-strong behaviors during acti- vated rearrangements. The heat-capacity jump per bead of the corresponding liquid will also depend on the ul- traviolet cutoff of the theory, as specified by the bead size. We will observe that the fragility depends on the Poisson ratio of the material, but in a complicated, non- monotonic fashion. In any case, in view of the appar- ent broad range of strong-to-fragile behaviors exhibited in the present model, the present analysis strongly sug- gests the activated dynamics have the same mechanism in both strong and fragile liquids, consistent with the basic picture of the RFOT theory. A potential formal benefit of the present approach is that it is possible to map the activated-transport liquid regime onto a spin model on a fixed lattice, thus opening the possibility of applying to liquids the many computa- tional techniques developed in the context of spin models. Importantly, this mapping may provide a first principles basis for computing the configurational entropy for spe- cific substances and the rate of crystallization from the supercooled state, since elastic constants at the length scale of a bead, which are the input into the theory, can be determined by ab initio methods. Informal motivation. Consider a substance that can both crystallize and vitrify and assume for concreteness that the glass has a greater specific volume than the corre- sponding crystal, as is usually the case. A quenched melt or frozen glass of such a substance may be thus viewed as a result of the following action: Apply negative pressure to slowly expand the crystal until the lattice relaxes into one of the myriad available glass structures, and then re- lease the negative pressure. (We assume cracking does not occur.) The sample will remain in the metastable, glass state; the eventual transition to the lower free en- ergy, crystal state will occur by nucleation and is sub- ject to the surface tension between the two phases. In I. MICROSCOPIC ANSATZ FOR LOCAL STRESS DISTRIBUTION η = 2 k$_{B}$T πad 2 L 〈 τ 〉 ≃ 60 k$_{B}$T a 3 〈 τ 〉 , (2)