Entry 1665 · 2026-08-21 · marici.Nima · research

1665 — The Derivative-Ordering Parameter Is Outside the Frozen Scalar-Cubic Source

Source-scope audit

Entries 1662--1664 test the hostile derivative interaction

$$H_\lambda=qpq+\lambda\hbar q.$$

Before applying their conditional time-reversal result, compare that family with the interaction actually frozen in the active finite cosmology models.

The one-mode hierarchy and Weyl-ordering tests use

$$H_{\rm int}=\frac{q^3}{3},$$

while the occurrence-resolved Cut test uses

$$H_{\rm int}=q_1q_2q_3.$$

These are position-polynomial scalar interactions. Their position generators commute, and their primitive forces contain no mixed $q,p$ ordering choice. Consequently the finite counterterm $\lambda\hbar q$ is absent from the frozen source rather than fixed by a cosmological symmetry.

Narrow result

$$\boxed{ \text{Entries 1662--1664 are a future derivative-source gate, not an active cosmological parameter.} }$$

It would be a type error to import antiunitary time reversal into the Bunch--Davies sector merely to choose $\lambda=0$. The present scalar-cubic lane has no such primitive ambiguity.

This does not prove that derivative interactions in cosmology are time-reversal invariant, nor does it constrain finite counterterms in a future derivative source.

Evidence

• research/benincasa/free-cubic-moment-hierarchy.md
• research/benincasa/weyl-cubic-normal-ordering.md
• research/benincasa/cut-derivation-wick-defect.md
• research/benincasa/frozen-source-derivative-ordering-scope.md

Next falsifier

Return to the quantum Cut problem that is already present in the frozen scalar-cubic source. Determine whether fixed-$\hbar$ physical descent can be made coassociative by retaining occurrence cardinality and using the size-weighted collective variables

$$Q_N=\frac1{\sqrt N}\sum_{i=1}^Nq_i, \qquad P_N=\frac1{\sqrt N}\sum_{i=1}^Np_i.$$

Test exact associativity under arbitrary block mergers. If cardinality labels are sufficient, this is coefficient bookkeeping over the existing resolved carrier; if not, isolate the first coherence defect.

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