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A library of eyes in Go, I: a life-and-death definition consistent with bent-4

In the game of Go we develop a consistent procedural definition of the status of life and death problems. This computationally efficient procedure determines the number of external ko threats that are necessary and sufficient to win, and in the case of positions of the type of bent-4-in-the-corner it finds that they are unconditionally dead in agreement with common practice. A rigorous definition of the status of life and death problems became necessary for building a library of monolithic eyes (i.e. eyes surrounded by only one chain). It is also needed for comparisons of life and death programs when solving automatically thousands of problems to analyse whether different results obtained by different programs are due to different status definitions or due to bugs.