Extreme-Value Electro-Chemo-Mechanics of Lithium Solid-Electrolyte Interfaces

Extreme-value electro-chemo-mechanics (EVECM) establishes a unified theoretical and computational framework for predicting how lithium solid-electrolyte interfaces respond to changes in electrode area, charging history and material architecture. The framework connects local fracture, active-defect populations, instrument response and intervention through one evolving material state, with shared energy and lithium-inventory balances. Developed through the human-directed collective research of semiAIfoundry Research, it brings physical derivation, computational verification and engineering design into a single account of defect-driven reliability. The scientific results resolve three coupled problems. First, a pressure-referenced transport and fracture kernel generates event-specific reliability distributions with protocol memory. Finite dwell can select an interior most-dangerous flaw size within the admissible range of the access-limited reduced model, with τ(ad) ≃1.82td in the fully ohmic linear limit. This shifts reliability assessment from the largest flaw alone to the protocol-selected initiating population. Confinement and creep calculations specify the measurable conditions for pressure retention, and exact collective-instability criteria explain how stored inventory can sustain extension after current interruption. Second, a reciprocal elastic closure derives transformation opening, chemical work and local intensity from the same retained field. It establishes ensemble reversal between assistance and shielding, intensity growth during pressure relaxation, and constant-toughness retained-wake instability. An illustrative garnet-scale mapping places the latter near a 105 µm slit half-length with 0.45 µm retained patches. Third, electrical, isotope and optical operators yield conservation witnesses, conductance certificates and capacity bounds that test mechanisms without fitting unknown reaction histories. Applied to published garnet observations, a contracted-wake interpretation of a 75% far-field intensity deficit requires Vf|θT|√hw ≳ 1.7 ×10−5 m1/2 under the stated steady-wake model. A separate residence-time analysis turns the current trend into a test of conversion relative to lithium supply. Sharp storage and throughput bounds expose the tradeoff between accommodating inventory and delivering useful charge. The engineering contribution translates these results into shared-population diagnosis, censoring-aware manufacturing qualification, accommodation and formation gates, and validity-aware assurance. Common-continuation qualification requires one observation-adapted policy to satisfy the risk contract across compatible models. Exact counterexamples establish why statewise safety, one-step diagnostic scores and horizon-independent decision partitions can fail. A reproducible normalized population calculation completes the chain from finite-dwell initiation and area scaling to service-constrained action selection. Residual-stress manufacture and conditional filament interruption extend the architecture to additional physical interventions. These achievements supply quantitative design laws, implementable decision structures and discriminating experimental tests for reliability-aware battery engineering. Physical operating envelopes and cell-level benefits are the targets of the independently calibrated, held-out validation campaigns specified in the compendium. Keywords: solid-state batteries; lithium metal; garnet electrolyte; fracture; extreme-value statistics; first passage; transformation mechanics; electrochemical impedance; observability; lithium creep; information-state qualification; sequential diagnostics; manufacturing assurance.