THE UNIVERSAL SANDBOX: S, B, E as a Cross-Domain Topology for Phase Transitions, and the Phenomenological Exception of the Social Case

What this paper establishes: the three-dimensional state space (S, B, E) introduced in the Longevity Asymmetry Corpus as a representation of civilizational stability is not a domain-specific model but a universal topology for phase transitions. Every scientific domain that studies critical transitions — cosmology (vacuum metastability), statistical mechanics (phase transitions), chemistry (transition state theory), mathematics (dynamical systems and catastrophe theory), ecology (regime shifts), and information theory (channel capacity) — has independently developed its own language for the same underlying geometry. S (system state integrity), B (barrier/buffer capacity), and E (entropy/disorder accumulation) name the three axes that all these theories implicitly inhabit. This paper demonstrates the mapping for six domains and isolates the one structural feature making the social/civilizational application categorically different from every physical application: the nature of the driving force. In five of the six physical domains, the A5-analog is stochastic and undirected — thermal fluctuations, quantum tunneling, random perturbations; ecology occupies an intermediate position, since a portion of ecosystem stressor load is human-driven rather than purely physical, and the paper treats this explicitly rather than absorbing it into a false uniformity. In the social case, A5 is constitutive attachment (愛別離苦): phenomenologically loaded, directed, and biologically constant. This distinction has two consequences. First, only in the social case is the driving force itself permanently irreducible — physical and even most ecological interventions can target the driving force directly (cooling a system, increasing signal-to-noise ratio, regulating a stressor), while no institutional design can reduce A5 itself, which forces all social intervention onto the barrier B alone. Second, the meaning of Σ-crossing differs categorically: vacuum decay destroys physics without moral content; sandbox collapse destroys governance with full moral content. The paper also introduces the S-B independence insight — a system with high S (near attractor) but low B (thin basin boundary) is categorically more dangerous than single-variable stability measures can detect — and demonstrates it across all six domains. Cross-domain comparison reveals that the social case at June 2026 (S ≈ 0.68, B ≈ 0.35, E ≈ 0.41) occupies the most dangerous quadrant of the S-B plane, that its F2 window is the shortest of any domain analyzed, and that the Governance Paradox has no physical analog in any other domain.