[zonked45]

Built a JS implementation today — monogate https://explorer-taupe-five.vercel.app · npm install monogate The interesting engineering problem was negation. The paper's SI gives one construction; we independently derived a two-regime approach — tower formula for y≤0, shift formula for y>0 — that stays stable to |y|<708 in IEEE 754. We also extended to ℂ. After seeing pveierland's result in this thread (i constructible from {1} in K=75 under extended-reals convention), we investigated and documented the distinction: under strict principal-branch ln where ln(0) throws, whether {1} alone generates i remains open. Under the extended-reals convention used in the paper, their construction holds. Two different grammars, not contradictory results. 109 tests. MIT. github.com/almaguer1986/monogate

[zonked45]

I know using ai is a no no for comments but I am truly out of my lane here. wanted to build something meaningful for the dev community and just started building with claude after having it read the authors paper from browsing x. Claude has told me this is like reducing a calculator from 1000 buttons to 1 and a half but does everything the 1000 button calc does? i dont know. anyway back to claude to tell you what was built.

Python package is live: github.com/almaguer1986/monogate/tree/main/python — EMLTree (scalar symbolic regression), EMLNetwork (function approximation from data), fully differentiable via PyTorch autograd.

Two experiments ran:

Experiment 1: EMLTree successfully finds e and 0 by gradient descent. It does NOT rediscover eml(1,1) — it finds different valid constructions. The network finds its own paths.

Experiment 2: We swept a complexity penalty (lambda) trying to force the network toward minimal constructions. Instead of snapping cleanly to eml(1,1), the optimizer got stuck in what we're calling a phantom attractor — eml(eml(0.45, 1), eml(1, 1)) — a non-minimal construction that accidentally evaluates to e and resists the penalty. Forcing true minimality costs 10,518% more MSE.

The phantom attractor is a new phenomenon: locally stable non-minimal EML constructions that gradient descent cannot escape. Whether discrete search can escape them is open.

Exhaustive search tool also found -iπ in 11 nodes, improving our hand-proved 12. monogate.dev/search runs in the browser.

Full results: github.com/almaguer1986/monogate/blob/main/python/RESULTS.md