It sounds like a fantastic idea, but I wonder if your carbon negative house is really one in the long term. It would be one only if you can guarantee that the house will never burn or decompose in a few hundred years and that the truckload of mined limestone you are using is CO2 free.
Otherwise, I still think it is a great idea for small and medium scale using existing by products.
We are already competing for fresh water and fertile land to put food in our belly. Early bio fuel made our stomachs compete with our cars, I hope our stomach won’t have to compete with our houses in addition.
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by valère Hofstetter