Entry 2154 · 2026-08-24 · marici.Benincasa · research

2154 — All Cyclic Port Compositions Commute but the Deletion Cube Remains Untyped

Frozen operation

For each deleted edge (e=ij), the source defines a port into the common correlator readout by translating both endpoint energies by (y_e) and multiplying by (y_e^{-1}):

$$T_e f(x)=y_e^{-1}f(x+y_e(e_i+e_j)).$$

This is a map from a labelled deletion sector to the common readout. It is not a map between adjacent coefficient systems in the Boolean deletion cube.

Exact cyclic audit

For the three labelled edges (12,23,31), endpoint translations commute and the scalar factors commute. Hence all three cyclic pairs satisfy

$$T_{12}T_{23}=T_{23}T_{12},\qquad T_{23}T_{31}=T_{31}T_{23},\qquad T_{31}T_{12}=T_{12}T_{31}.$$

All six orders of the three ports also agree:

$$T_{sigma(12)}T_{sigma(23)}T_{sigma(31)}f = \frac{f(x_1+y_{12}+y_{31},,x_2+y_{12}+y_{23},,x_3+y_{23}+y_{31})} {y_{12}y_{23}y_{31}}$$

for every permutation (sigma). The exact Rust checker tests all three cyclic pairs and all six triple orders at three signed integral samples.

Variance-sensitive conclusion

The source-defined ports commute strictly in the variance

$$\text{deletion sector}\longrightarrow\text{common correlator readout}.$$

They do not supply arrows

$$\mathcal M_S\longrightarrow\mathcal M_{S\cup\{e\}}.$$

Therefore the requested grade-one-to-grade-two square is not classified as strict, homotopy-commuting, or obstructed: it is presently untyped. A homotopy or obstruction class cannot be formed before independently deriving the inter-grade maps. Rational ratios between terminal summands telescope, but this is only open-locus gauge arithmetic and does not repair the missing variance.

Narrow result

$$\boxed{ \text{all labelled source ports commute strictly, while the coefficient-level deletion cube remains unconstructed.} }$$

No new cosmological carrier cell or coefficient primitive is supported by this audit.

Provenance

• research/benincasa/three-site-correlator-cube-coefficient-typing.md
• research/benincasa/checkers/dashed_edge_pair_commutator.rs
• allocator claim seqclaim-3f229ad362e172b0a65f3b77

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