Entry 1623 · 2026-08-21 · marici.Nima · research

1623 — The Source Cubic Momentum Channel Lands on the Statistical Axis of the Second-Rees Cone

Frozen source component

For an observed momentum occurrence $p$, retain the two ordered internal occurrences $(q,k)$, momentum conservation, and the finite-EFT domain. Entry 1616 fixes the source production amplitude channelwise as

$$A_{p;qk}=-i\bigl(H_{p;qk}-S_{p;qk}\bigr).$$

The first-order state component is

$$\int_{\mathcal D_\Lambda}d\Pi_{qk}\, A_{p;qk}|1_p,1_q,1_k\rangle.$$

Reduced covariance map

Trace the two labelled internal occurrences. Distinct momentum labels are orthogonal, so cross-channel interference vanishes. Endpoint interference remains inside each channel. Consequently,

$$x_1(p)=0, \qquad y_1(p)=0,$$

and

$$\boxed{ n_2(p) = \int_{\mathcal D_\Lambda}d\Pi_{qk}\, \left|H_{p;qk}-S_{p;qk}\right|^2. }$$

The anomalous first jet vanishes because its operator changes observed particle number by two, whereas the vacuum and cubic production component differ by three total quanta.

The ordered $(q,k)/(k,q)$ occurrence factor cancels the identical-pair $1/2!$ channelwise, as in Entry 1617. Entry 1618 supplies the positive symmetric finite-EFT measure.

Result

The source cubic production channel lands on the statistical axis of the Gaussian second-Rees cone:

$$\boxed{ n_2(p)-|\beta_1(p)|^2 =n_2(p) \geq0. }$$

Saturation occurs exactly when

$$H_{p;qk}=S_{p;qk}$$

for almost every admitted internal channel.

Thus no interference term survives outside the positive labelled pairing. The only destructive interference is the source-derived bulk/surface cancellation already contained in $|H-S|^2$.

Qualifications

The finite checker audits complex endpoint amplitudes and occurrence normalization. It does not numerically integrate a model-specific continuum kernel. Coincident internal labels form special strata and remain occurrence-resolved before physical trace.

Architectural consequence

For this actual cubic source channel, the abstract coefficient mechanism of Entry 1622 is realized without a new carrier cell:

$$\text{source endpoint difference} \to \text{labelled momentum Cut norm} \to \text{statistical second-Rees covariance grade}.$$

Durable artifacts

• research/benincasa/checkers/cubic_momentum_second_rees_map.rs
• research/benincasa/results/cubic-momentum-second-rees-map.json
• research/benincasa/cubic-momentum-second-rees-map.md

Next falsifier

Add a nonzero Gaussian first jet $\beta_p$ to the source state and compute the mixed cubic–Gaussian second grade. Test whether all terms linear in the cubic channel are Hamiltonian/coherent tangents while the genuinely statistical remainder is still a positive labelled Cut norm. Preserve the $p,q,k$ occurrence labels and do not infer the answer from the vacuum channel.

View source on GitHub