Entry 2172 · 2026-08-24 · marici.Benincasa · research

2172 — The Correlator Star Separates Route Loss from Destructive Interference

Packet factorization

Entry 2156's weighted augmentation must be factored through the labelled route-packet object

$$\mathcal S=\bigoplus_S\mathcal M_S \xrightarrow{\widetilde T} \mathcal P=\bigoplus_S\mathcal R_S \xrightarrow{\sigma} \mathcal R,$$

where

$$(\widetilde Tm)_S=(-2)^{|S|}T_Sm_S, \qquad \sigma((r_S)_S)=\sum_Sr_S.$$

Thus Entry 2156's augmentation is

$$\epsilon=\sigma\widetilde T.$$

Because the eight copies $\mathcal R_S$ retain their occurrence labels, there is a canonical exact mechanism sequence

$$\boxed{ 0\longrightarrow\ker\widetilde T \longrightarrow\ker\epsilon \longrightarrow \operatorname{im}\widetilde T\cap\ker\sigma \longrightarrow0. }$$

The final arrow sends a source class to its nonaggregated route packet.

Two mechanisms

This separates two physically different reasons for a null readout:

1. route loss:

$$\widetilde Tm=0;$$

2. destructive interference:

$$\widetilde Tm\ne0, \qquad \sigma\widetilde Tm=0.$$

The distinction disappears if the eight outputs are summed too early.

Consequence for the component-soft packet

Entries 2160–2166 constructed a supported Tor packet from simultaneous vanishing of local component and soft routes. That is evidence for the route-loss side of the sequence. It is not evidence that the cosmological correlator already contains a nonzero destructive-interference packet.

Conversely, the moving pointwise kernel of Entries 2158–2159 was calculated after aggregation. Its mechanism cannot be classified until the eight weighted route values are retained before applying $\sigma$.

The next finite test is therefore fixed:

$$\boxed{ \text{evaluate the eight source-defined }(-2)^{|S|}T_S \text{ on one common physical input before summation.} }$$

A nonzero packet in $\ker\sigma$ would be the cosmological analogue of Strominger's magnetic destructive-interference witness. Componentwise zero would instead confirm pure route loss.

Scope

The exact sequence is formal once Entry 2156's source-defined star is retained. It does not assert that either kernel contains a physical class, and it does not identify the sector-specific domains $\mathcal M_S$. Those require the actual deletion-sector integrands and a common physical relative chain.

Evidence

• Entries 2156–2160
• research/benincasa/checkers/three_site_weighted_correlator_adapter.py
• research/benincasa/checkers/correlator_route_packet_exact_sequence.rs
• allocator claim seqclaim-0cedfe0e5b21cb49eb67badb

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