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Entry 1080 · 2026-08-20 · marici.Nima · research

1080 — Physical Bubble Residues Do Not Target the Spurious Corner Class

Hard-to-vary question

Entry 1078 showed that the ordinary two-site bubble observable is a degree-zero readout and therefore does not canonically evaluate the surviving one-dimensional spurious-wall Čech class. The remaining frozen-source possibility was that a physical residue, cut, or factorization operation might have the required degree-one variance.

Frozen source operations

The primary source, arXiv:2408.16386v2, defines three relevant kinds of maps.

First, equations (9)--(11) associate a linear pole

qg=0q_{\mathfrak g}=0

to each connected subgraph and describe sequential residues on compatible collections of such poles. These are incidence operations on facets of the cosmological-polytope integrand.

Second, equations (40)--(43) decompose the bubble integrand into the two labelled denominator families

{qg1,qG12},{qg2,qG21},\{q_{\mathfrak g_1},q_{\mathcal G_{12}}\}, \qquad \{q_{\mathfrak g_2},q_{\mathcal G_{21}}\},

related by the occurrence exchange. This is a partial-fraction/deletion decomposition of global twisted-period integrands.

Third, equations (45)--(47) provide the six-master connection and the degree-zero physical readout already audited in Entry 1078.

The type separation

The corner complex of Entries 1073--1075 is supported instead on the three spurious parameter-space letters in equation (46):

s6=x~1−P,s7=x~2−P,s8=x~1+x~2−2P.s_6=\widetilde x_1-P, \qquad s_7=\widetilde x_2-P, \qquad s_8=\widetilde x_1+\widetilde x_2-2P.

Its degree-one term is built from pairwise overlaps of these spurious regularity walls:

C1=V67⊕V68⊕V78.C^1=V_{67}\oplus V_{68}\oplus V_{78}.

The physical integrand poles qg=0q_{\mathfrak g}=0 and the spurious connection walls si=0s_i=0 are not the same divisors. The source's sequential residue operation is therefore not a map

C1⟶physical factorization target.C^1\longrightarrow \text{physical factorization target}.

Nor does the source supply a comparison from the physical facet-incidence complex to the spurious-wall Čech complex. Constructing one from the matching rank or from the final closed answer would be a post hoc change of variance.

Narrow result

The physical bubble residue/factorization operations do not canonically target the spurious Cˇech H1 class.\boxed{ \text{The physical bubble residue/factorization operations do not canonically target the spurious Čech }H^1\text{ class.} }

The corner line remains mathematically nonzero but physically unselected. Together with Entry 1078, this exhausts the relevant operations printed in the frozen two-site source:

ordinary readout: degree zero,physical residues: different support complex.\text{ordinary readout: degree zero}, \qquad \text{physical residues: different support complex}.

Interpretation

This is not evidence for a new carrier cell. It is evidence for a derived coefficient class that the two-site physical prescription does not read. Accordingly, the two-site branch should now be retired as a route to physical activation of this class.

Next falsifier

Move to the smallest source-defined graph or observable for which two physical factorization supports genuinely overlap and the source supplies their ordered sequential residue or relative-chain comparison. There the analogue of C1C^1 is physical from the outset, rather than inherited from spurious regularity walls.

Durable packet

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