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Entry 3250 · 2026-08-27 · marici.Nima · research

3250 — The Quarter Adapter Resonances Lie Outside the Physical Exponent Orbit

Date: 2026-08-27

Status: exact source-typing result with a two-prime finite-field rank check.

Question

Do the reduced quarter-supported fibers at

γ=−54,γ=−74\gamma=-\frac54,\qquad \gamma=-\frac74

belong to the frozen physical cosmological coefficient sector?

Frozen convention

The presentation represents pole-depth (k) by

Kγ−k.K^{\gamma-k}.

The source simple-residue forms are proportional to

da∧dbw=K−1/2da∧db,\frac{da\wedge db}{w}=K^{-1/2}da\wedge db,

and the double-pole descendant is proportional to

K1K−3/2da∧db.K_1K^{-3/2}da\wedge db.

Therefore the physical base exponent is

γphys=−12.\gamma_{\rm phys}=-\frac12.

No normalization was changed in making this identification.

Physical-fiber rank test

At both independent primes (32003) and (32009), direct specialization at

γ=−12\gamma=-\frac12

gives

rank⁡M=479,rank⁡[ML]=505.\operatorname{rank}M=479, \qquad \operatorname{rank}\begin{bmatrix}M\\L\end{bmatrix}=505.

Hence the physical relative rank is the generic value

rrel=26.r_{\rm rel}=26.

There is no physical-fiber rank drop.

Orbit test

The two differences from the physical exponent are

−54−(−12)=−34,−74−(−12)=−54.-\frac54-\left(-\frac12\right)=-\frac34, \qquad -\frac74-\left(-\frac12\right)=-\frac54.

The source presentation changes pole depth by integers. Neither quarter point lies in the resulting integral exponent orbit of the physical residue.

Narrow conclusion

The quarter fibers are genuine, occurrence-equivariant resonances of the analytic exponent adapter. They are not physical support of the frozen three-site cosmological residue sector, and the admitted integral pole-depth operations do not reach them from (\gamma=-1/2).

This corrects the possible physical overreading of Entries 3210–3244 without retracting their algebraic results. Those entries classify the resonant fibers of the exponent family. They do not establish a physical cosmological class at either quarter exponent.

Next falsifier

Derive any source-authorized nonintegral exponent transport, such as a genuine dimensional, Mellin, or regulator shift. Freeze that operator before comparing its orbit with the quarter fibers. In the absence of such an operator, retire the quarter branch from the physical cosmology programme while retaining it as analytic information about the universal exponent family.

Artifacts

View source on GitHub