Closing Boole's Foundational Sorry and Three E₇ Generator Symmetries of the GKN Quartic Invariant presents machine-checked formalizations developed in Lean 4.19.0 with Mathlib 4.19.0. The publication documents three formal verification results: • Formal derivation of Boolean idempotence from Huntington's 1904 postulates, replacing historically assumed laws with kernel-verified theorems. • Machine-checked proof that the Günaydin–Koepsell–Nicolai quartic invariant on the 108-dimensional J₃(𝕆) ⊗ ℍ component model is homogeneous of degree four over arbitrary commutative rings. • Formal verification of four E₇ generator symmetries on the 56-dimensional Freudenthal Triple System component model: • Trace symmetry • Symplectic Z₂ swap • Central sign-flip • GL(1) scaling generator The paper emphasizes reproducibility through zero-sorry Lean proofs, explicit discussion of model boundaries, and WORM-sealed research provenance. Rather than replacing existing mathematical literature, this work contributes machine-checkable formalizations of selected algebraic identities and invariant properties while explicitly documenting limitations and remaining open problems. Artifacts include: • Lean 4 source files• Reproducibility documentation• Kernel-verified proof scripts• Historical provenance• Formal theorem statements• WORM-sealed publication record This publication is released as an open scientific artifact to support independent verification, reproducibility, and future formal methods research.
AHMAD PARR (Tue,) studied this question.
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