Here is a clearer comparison of open-weight SOTA-only models with GPT-5.6 added:
artificialanalysis.ai/?models=glm-5-3-flash%2Cdeepseek-v4-flash%2Cdeepseek-v4-flash-vision%2Cqwen3-8-flash-next%2Cqwen3-8-27b%2Cgpt-5-6-sol%2Cgpt-5-6-luna%2Cgpt-5-6-terra&intelligence=artificial-analysis-intelligence-index#intelligence-tabs

Yes, you can have your own GPT-5.6 equivalent at home.

And here is a list of open-weight models only (AA calls them "open-source", but they are mostly open-weight) (in the table click "Select all" to see the best straight away):
artificialanalysis.ai/models/open-source#artificial-analysis-intelligence-index

192 GB RAM is enough to fit one of these new SOTA AI MoE models:

• GLM-5.3-Flash (4-bit quant) (huggingface.co/unsloth/GLM-5.3-Flash-GGUF)
• DeepSeek V4 Flash 0731 (full weights are 162 GB, so it fits nicely and with full context!) (huggingface.co/unsloth/DeepSeek-V4-Flash-0731-GGUF)

Up to ~330B open-weight AI models (open-weight means you can download and run them locally) (there are more, you can search in the table):
artificialanalysis.ai/?models=qwen3-5-122b-a10b-non-reasoning%2Cglm-5-3-flash%2Cqwen3-5-122b-a10b%2Cmimo-v2-5-0424%2Cnemotron-3-5-lightning%2Cqwen3-6-27b-non-reasoning%2Cminimax-m2-7%2Cmuse-glimmer%2Cnvidia-nemotron-3-super-120b-a12b%2Cqwen3-8-27b-medium%2Cqwen3-6-35b-a3b-non-reasoning%2Cstep-3-7-flash%2Cinkling-small%2Csolar-open2-250b%2Cqwen3-6-35b-a3b%2Cqwen3-6-27b%2Cqwen3-8-flash-next%2Cqwen3-8-27b%2Cmotif-3%2Chy3%2Cg9v3-39a5b%2Cgemma-4-31b%2Cgemma-4-31b-non-reasoning%2Cmistral-medium-3-5%2Cling-3-0-flash%2Cgpt-oss-120b%2Cdeepseek-v4-flash%2Cdeepseek-v4-flash-vision&intelligence=artificial-analysis-intelligence-index