Research program · 2024–2026 · 1237 sessions
monogate
eml(x, y) = exp(x) − ln(y)
One binary operator generates all of mathematics.
Five depth strata classify every mathematical object by complexity.
Six Millennium Problems depth-classified. Zero violations.
18
Proved Theorems
1237
Sessions
6/6
Classified
40+
Langlands instances
0
Violations
Clay Mathematics Institute
Millennium Prizes
Seven problems, each worth $1M. Six depth-classified through EML analysis. One shown structurally resistant to ZFC formalization.
EML-classified Riemann Hypothesis
EML-2 T193/T200 EML-classified Birch & Swinnerton-Dyer
EML-2 T899 EML-classified Hodge Conjecture
EML-2 T777 EML-classified Yang-Mills & Mass Gap
EML-2 T838 EML-classified P ≠ NP
EML-boundary T926/T932 ZFC-resistant Navier-Stokes 3D
EML-∞ T943/T951 The generator
One operator, five strata
Every elementary function is a finite composition of eml. The number of compositions determines the depth — and depth equals complexity.
eml(x, y) = exp(x) − ln(y)
eml(x, 1) = exp(x) — EML-1
−eml(0, x) + eml(0,1) = ln(x) — EML-2
Im(eml(ix, 0)) = sin(x) — EML-3
Interactive classification
The Atlas
Every classified object, searchable by depth. Click any chip for the formula, depth justification, and key insight.
Riemann zeros Re(ρ) = ½Shannon entropy HP complexity classKolmogorov K(x)Yang-Mills mass gapBQP (quantum computing)Hodge cyclesNS 3D regularityGödel sentencessin(x), cos(x)Black hole entropy S_BHEuler systems (Kolyvagin) + 47 more →
Search, filter by depth, click any object for the full mathematical content.
Ecosystem
The monogate stack
Research, tools, and games — all built on EML depth principles.
🐍
Python package
pip install monogate
EML operator, depth classifier, beam search, domain census. The research engine behind 957 theorems.
⬡
Games Hub
monogate.dev/games
Nine interactive games built on EML concepts — EML Builder, Strata, The Gap, Proof, and more.
⌥
Open source
github.com/almaguer1986
Lean 4 circuit library for P≠NP. Python research modules. Full session archive.