Entry 1668 · 2026-08-21 · marici.Nima · research

1668 — The Independent Gaussian Wick Cut Defect Descends with Cardinality Weighting

Pushed-forward falsifier

Entry 1667 closes the abstract three-block associator before internal pushforward. Test whether Entry 1650's concrete scalar-cubic Wick defect remains natural after the fixed-$\hbar$, cardinality-weighted normalization of Entry 1666.

For an internal occurrence of variance $\nu$,

$$[C,D](p_1q_3)=-\nu q_2.$$

For $N$ independent internal occurrences, set

$$Q_N=\frac1{\sqrt N}\sum_iq_i.$$

Its variance is

$$\nu_N=\operatorname{Var}(Q_N) =\frac1N\sum_i\nu_i.$$

If blocks of sizes $m,n$ have collective variances $\nu_m,\nu_n$, the cardinality-weighted merger gives

$$\nu_{m+n} =\frac{m\nu_m+n\nu_n}{m+n}.$$

Every binary merger tree therefore yields the same leaf average. The exact rational checker verifies:

$$36\text{ variance patterns}, \qquad 247{,}500\text{ ordered binary bracketings},$$

through twelve internal occurrences.

Narrow result

$$\boxed{ \text{the independent Gaussian Wick Cut defect is natural under cardinality-weighted fixed-}\hbar\text{ merge.} }$$

No new support-sensitive correction or ternary carrier cell appears at this grade. The variance is sector-specific coefficient data transported by the existing occurrence cardinality.

This statement assumes independence between the merged internal blocks. It does not erase Entry 1652's correlated conditional-pushforward correction.

Durable artifacts

• research/benincasa/checkers/cardinality_weighted_wick_cut.rs
• research/benincasa/results/cardinality-weighted-wick-cut.json
• research/benincasa/cardinality-weighted-wick-cut.md

Next falsifier

Admit a nonzero cross-covariance between two internal blocks. Derive its exact transport under cardinality-weighted merge and compare nested conditioning in both merger orders. Determine whether the full covariance matrix suffices for strict descent or whether the first conditional coherence carries additional support data.

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