On The Adequacy of E → L^E → E As a "Replacement" For Doing Mathematics or Rather: How To Actually Use a Machine To Assist In It: A 1,179-Digit, 100+ proof Counterexample to Your Benchmark, Your Floats AND especially your Chat Bot. (2026)

Here is Brocard AND the class number one problem AND Moonshine AND the E8 lattice AND Zagier's congruent number triangle AND a 200-digit p-adic square root AND the exact rational value where your floating-point code hallucinates. And - there are - other ones. Image is a Categoric Sketch. ReF: 1. de Moura, L. & Ullrich, S. (2021). The Lean 4 Theorem Prover and Programming Language. In Automated Deduction – CADE 28, LNCS 12699, pp. 625–635. Springer. DOI: 10.1007/978-3-030-79876-5_37. 2. Gordon, M. J., Milner, A. J. & Wadsworth, C. P. (1979). Edinburgh LCF: A Mechanized Logic of Computation. Lecture Notes in Computer Science 78. Springer. DOI: 10.1007/3-540-09724-4. 3. Muller, J.-M. recurrence example; for an accessible exposition, see Christian Hill, Muller’s Recurrence (2017), describing the finite-precision instability and the exact limit \(5\). 4. Gowers, T. et al., eds. (2008). The Princeton Companion to Mathematics. Princeton University Press. Broad background reference for the surrounding mathematical corpus, including classical conjectures and structures such as Goldbach and Monstrous Moonshine. 5. Avigad, J., de Moura, L., Kong, S. & Ullrich, S. Theorem Proving in Lean 4. Official Lean documentation. Useful for the dependent type theory, propositions/proofs, tactics, and trusted reasoning model.