Read the mathematical arguments.
Three selected TFPT arguments, with the definitions, formulas and reasoning on the page. Each reading edition keeps the original assumptions and links directly to its paper, source lines and cited verification code.
The E₈ discriminant glue theorem
The D₅ carrier lattice and the A₃ family lattice have compatible discriminant forms. Their diagonal order 4 glue gives an even unimodular lattice of rank 8. This is the lattice argument behind the TFPT E₈ construction.
One four point divisor, a carrier of 5 and a family rank of 3
The pair (5, 3) can be read from one geometric object. Four marked points on the projective line give a five dimensional meromorphic function space and three independent puncture cycles. The original argument then connects the function space to the carrier spinor.
Why the specified alpha equation has one positive root
The specified electromagnetic closure has exactly one positive simple root. The original convexity proof establishes this on the whole positive half line, without a numerical sign scan. It is a theorem about the stated function and its inputs.
Continue into the original documents
These pages select complete arguments from a larger publication set. The source library retains the remaining sections, evidence links and document filters. The knowledge atlas follows each result into its recorded assumptions and physical scope.