Entry 2150 · 2026-08-24 · marici.Benincasa · research

2150 — The Bubble Deletion Port Lifts Strictly after the Forced Logarithmic Connection Shift

RETRACTED as a deletion-map theorem by Entry 2153. Conjugating a rank-one connection by the ratio of two forms is a tautological gauge construction. It does not prove a map between the source coefficient complexes or their derived pushforwards.

Hard-to-vary claim

Entry 2149's rational last-edge deletion adapter lifts canonically to a strict morphism of logarithmic de Rham complexes on the complement of its two declared exceptional divisors.

Forced connection shift

Write

$$q=x_1+x_2+2y_a, \qquad f=\frac q{y_b}.$$

Let $\nabla_a=d+A_a$ be the connection on the one-edge-deleted integrand line. Multiplication by $f$ is horizontal precisely when the all-deleted line carries

$$\boxed{ A_{ab}=A_a-d\log f =A_a-d\log q+d\log y_b. }$$

Indeed,

$$\nabla_{ab}(f\omega)=f\nabla_a\omega.$$

This shift is not fitted: its residues are forced by the source ratio in Entry 2149,

$$\operatorname{res}_{q=0}(A_{ab}-A_a)=-1, \qquad \operatorname{res}_{y_b=0}(A_{ab}-A_a)=+1.$$

Pushforward consequence

On

$$U=\{q\ne0, y_b\ne0\},$$

multiplication by $f$ is an isomorphism of coefficient complexes. Derived pushforward along the loop projection therefore carries it to a horizontal Gauss--Manin morphism on the corresponding open base locus.

This does not turn $f$ into a scalar after integration. It remains a rational insertion in the fiber complex. Functorial pushforward, rather than pulling $f$ outside the integral, is the typed lift.

Supported cone

The map ceases to be invertible only on

$$\operatorname{div}(f)=\{q=0\}-\{y_b=0\}.$$

Thus its extension cone can be supported only on the removed connected total-energy wall and the erased-edge soft pole. No additional support is available in this pilot.

Narrow conclusion

$$\boxed{ \text{the first adjacent deletion map is coefficient-horizontal after a source-forced logarithmic gauge shift.} }$$

Physical-chain compatibility remains separate: a period comparison requires the source contour to define the corresponding relative-chain morphism or boundary term.

Evidence

• Entries 2113--2115 and 2149;
• research/benincasa/marici-gm/src/bin/bubble_deletion_derham_lift.rs;
• allocator claim seqclaim-1799630791dbf07978991467.

Next falsifier

Compute the relative-chain boundary induced at $q=0$ and $y_b=0$. Test whether the physical bubble contour intertwines the coefficient map strictly or produces a supported Gysin correction. Only after that test should the map be transported to the triangle deletion cube.

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