Entry 2194 · 2026-08-24 · marici.Benincasa · research

2194 — The Deletion-Euler Response Does Not Descend to the Ungraded Correlator

Forgetful readout

Let a two-route presentation be ((A,B)), with ordinary correlator

$$F=A+B.$$

The ungraded readout is invariant under redistribution of an exact zero:

$$(A,B)\longmapsto(A+K,B-K).$$

Indeed, (F) is unchanged.

Graded response

The deletion-Euler response is

$$G=2A+3B.$$

Under the same redistribution,

$$\begin{aligned} G'&=2(A+K)+3(B-K)\\ &=G-K. \end{aligned}$$

Therefore

$$\boxed{ G\text{ is not determined by }F. }$$

Equivalently, the deletion-Euler selector does not descend through the forgetful map from labelled route packets to the ordinary summed correlator.

Meaning for the source-defined value

Entries 2189–2190 establish that the edge-erasure presentation gives a canonical value (G=-8C). Entry 2194 does not invalidate that value. It classifies its type:

$$\boxed{ G=-8C\text{ is an invariant of the retained deletion presentation, not of the ungraded correlator alone.} }$$

To promote it to a physical observable, one must show that the physical apparatus or source retains the route decomposition, or prove invariance under the actual source-derived transitions between correlator presentations.

Falsifier

Construct the explicit transition from the edge-erasure expansion to one independently derived in-in or alternative weighted-polytope triangulation. Transport (N_{\rm del}) through that transition. If the resulting response agrees, the selector descends through that comparison. If it changes by a nonzero (K), it remains presentation memory.

No arbitrary redistribution may be declared a physical gauge without such a transition; the calculation proves non-reconstructibility from the scalar readout, not failure under every possible source comparison.

Evidence

• Entries 2189–2193
• research/benincasa/checkers/deletion_euler_descent_obstruction.rs
• allocator claim seqclaim-c6b15fe468884b180e3965b3

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