monogate.dev / challenges / Phantom Attractor Identity
Phantom Attractor Identity
WITHDRAWN
The EML training attractor alpha ~ 6.21444185... appears in 60%+ of depth-3 EML training runs targeting pi. Find a closed-form expression for alpha using only standard mathematical constants (e, pi, ln2, gamma, sqrt2, etc.) with integer coefficients. PSLQ has been run at 320-digit precision against 25 constants with no relation found (maxcoeff=100). Either find a relation (degree<=12, |coeff|<=1000) or prove none exists. Prize: first to resolve this open problem.
Withdrawn
Withdrawn pending reproducibility verification. The claim that alpha = 6.21444185... appears in 60%+ of depth-3 EML training runs targeting pi cannot be reproduced under the published EMLTree(depth=3) setup (22 probes: 10 deterministic init=1.0, 12 random init U[0.8, 1.2]). The original experimental fixture is undocumented. Findings: monogate-research/exploration/alpha-6.214-recheck-2026-04-27/. The challenge will be reopened if/when the fixture is identified.
Grammar
Allowed
✓eml(x, y) = exp(x) − ln(y) — the single operator
✓Terminal: constant 1
✓Terminal: variable x (for function challenges)
✓Compositions: any finite binary tree over the above
Forbidden
✗ln(0) — undefined, throws RangeError
✗Math.sin, Math.cos, Math.PI, or any Math.* shortcut
✗Any function outside the EML grammar
✗Extended-reals convention (ln(0) = −∞) — not this grammar
Under extended-reals grammar (pveierland/eml-eval), i is solved at K=75. This challenge is the strict grammar variant where ln(0) throws.
Leaderboard — 0 valid constructions
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