Entry 1712 · 2026-08-21 · marici.Nima · research

1712 — The Full A-Zero Cubic Generator Descends on the Existing Rees Cover

All-order falsifier

Entry 1711 checks the first two normal grades. Determine whether a new logarithmic or deck-twisted extension appears at higher order.

Completed strict transform

In the weighted coordinates

$$A=\varepsilon^2, \qquad C=\varepsilon c,$$

the only denominator in the complete generator is

$$D=1+2\varepsilon^2ty.$$

It restricts to 1 on the exceptional divisor. Therefore

$$D^{-1}=\sum_{k\geq0}(-2\varepsilon^2ty)^k$$

and log D are regular formal series there. The rational numerator is

$$c^2y^2+2\varepsilon cxy+\varepsilon^2x^2.$$

The deck transformation preserving the physical coordinates A,C is

$$(\varepsilon,c)\longmapsto(-\varepsilon,-c).$$

Both D and the numerator are invariant. Thus the complete generating germ has trivial deck character.

Narrow result

$$\boxed{ \text{the full correlated cubic generator extends and descends on the existing covariance Rees cover at every normal order.} }$$

No finite-order logarithmic extension or new coefficient chart appears. The logarithm already present in the bulk generator has no local monodromy around epsilon=0 because its argument is a unit.

The checker verifies the exact rational-series recurrence and deck parity through order thirty. The all-order statement follows from the displayed closed form, not from extrapolation of the finite census.

Durable artifacts

• research/benincasa/checkers/cubic_generator_all_order_rees.rs
• research/benincasa/results/cubic-generator-all-order-rees.json
• research/benincasa/cubic-generator-all-order-rees.md

Next falsifier

Test one genuinely non-Gaussian input coefficient rather than a Gaussian state followed by cubic evolution. Add a predeclared connected third cumulant to the initial state and determine whether the same finite generating presentation and Rees chart survive, or whether the input cumulant requires a new completed coefficient extension.

View source on GitHub