Strategic financial markets can admit multiple approximate Nash equilibria with materially different liquidation and price-impact regimes. Returning one equilibrium cannot exclude a more stressed alternative, yet complete enclosure becomes expensive when the profitable deviator changes inside a search region. We propose EquiPartition, a learning-augmented branch-and-bound method based on player-adaptive deviation certificates. The certificate combines institution-specific unilateral-deviation atoms through state-dependent Bernstein weights, while an outward-rounded verifier alone authorizes exclusion. Inconclusive proposals undergo bounded repair or conservative subdivision, so prediction quality affects efficiency but not the complete $\epsilon$-Nash outer-enclosure guarantee. On the controlled and multi-institution synthetic one-period fire-sale markets, the finite recorded-reference audit retained all recorded high-precision reference-equilibrium components and found no accepted exclusion intersecting them. Relative to Nash-B&B, Predict+Repair reduced proof-tree nodes by 83.3% and 83.9%, unresolved volume by 75.8% and 69.0%, and mean capped runtime by 40.5% and 20.2%; it completed 113 of 120 multi-institution instances versus 103 for Nash-B&B. The same finite recorded-reference audit retained all recorded crisis components under the financial stress shifts. Runtime decomposition showed that amortized proposals avoided repeated neutral-start optimization and offset repair and verification costs. EquiPartition reduces proof fragmentation while preserving verifier-based completeness.

The adoption of provincial carbon-trading market-construction policies in China expanded rapidly before a five-year hiatus in new qualifying policies. This study examines how industrial-structure and GDP-feasibility learning cues relate to diffusion alongside pilot designation, regional competition, and media attention. Directed provincial-pair models cover the lagged-covariate period of 2013–2022 within a descriptive observation window of 2012–2022. Industrial-structure learning has a positive association in the additive model, and the highest signed-gap quartile differs positively from the lowest quartile, whereas GDP-feasibility learning is not supported. The industrial association becomes imprecise when national-market phases are included, and multiple-testing adjustments further qualify the evidence. Interaction estimates do not consistently support signal interference. The hiatus coincides with national-market construction and a changing population of nonadopters. Exploratory provincial scenarios also remain uncertain. These findings distinguish structural learning cues from economic-capacity cues while emphasizing that nationwide institutional change must be considered when interpreting provincial diffusion.