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Q. Does the above sketch correspond to a developed area of mathematical investigation?

More of a "developing area" than a "developed" one, maybe. Here are some papers and web articles on Differential Logic that may have a bearing on your question:

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Q. Does the above sketch correspond to a developed area of mathematical investigation?

More of a "developing area" than a "developed" one, maybe. Here are some papers and web articles on Differential Logic that may have a bearing on your question:

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Q. Does the above sketch correspond to a developed area of mathematical investigation?

More of a "developing area" than a "developed" one, maybe. Here are some papers and web articles on Differential Logic that may have a bearing on your question: