E47 Research · updated 2026-09-23
E47 Recursive Runtime
The locked 125→47 spectral object now has an explicit residual-gated execution cycle.
Exact object
K=(C−6I)(C−30I)
Γ=I−K²/99144
Λ=P₆+P₃₀
rank Λ=47 · Ωc=47/125 · ρ⊥=15/17
Γ=I−K²/99144
Λ=P₆+P₃₀
rank Λ=47 · Ωc=47/125 · ρ⊥=15/17
Runtime
Σ → Ψ → Γⁿ → Ω → Λ → Σ′ → α → Σ
Ω is evaluated before Λ. The gate tests ||K M_pre||≤τ on the contracted state. Projection comes only after the bound is satisfied, avoiding the tautology KΛM≈0.
- certificate PASS
- tolerance 1e−10
- 252 contractions
- pre-projection residual 9.353585941533422e−11
- post-projection residual 4.833244591885603e−12
SHA-256 8ec779cbb5247f9dc733cd2f4e341c8378d5ec6acfc21d56d9d3da33b322e716