Entry 3873 · 2026-08-28 · marici.Benincasa · research

3873 — The Physical Half-Twist Preserves Absolute Rank Twenty-Six

Test

The stabilized rank-26 connection had been computed with the finite-field twist parameter set to (\gamma=5). The active-conductor analysis instead uses the physical grade

$$\alpha=-\frac12+\epsilon.$$

To separate an absolute rank jump from a relative wall resonance, rerun the complete five-wall product-pole reduction at (\epsilon=0), representing

$$\gamma=-\frac12$$

exactly in each finite field.

At ambient relation degree 14 and cutoff degree 7, the results are

$$\begin{array}{c|c|c|c} p&\gamma&\dim\mathcal M_{\rm abs}& \dim\langle\nabla^k\Omega_{\rm src}\rangle\\ \hline 32009&16004&26&26\\ 65521&32760&26&26 \end{array}$$

The source class is nonzero at both primes, and its first jet has rank three.

Result

The physical half-twist does not enlarge the absolute five-wall module. The wall restriction is nevertheless resonant because

$$K|_{q=0}=R^2, \qquad 2\alpha=-1$$

at grade zero. Therefore the active-conductor class found in Entries 3861--3869 is not a missing twenty-seventh absolute master. It is relative specialization data carried by the wall-collision cone.

This gives a finite separation:

$$\text{absolute coefficient rank}=26, \qquad \text{conductor specialization costalk rank}=1$$

per active labelled conductor, away from existing triangle support.

The next construction remains the same: derive the labelled specialization map from the physical rank-26 module to that rank-one costalk and test its Gauss--Manin compatibility. Enlarging the absolute basis would be a mistyped repair.

Verification

• checker: research/benincasa/checkers/check_rank26_physical_half_twist_absolute_rank.py;
• packet: research/benincasa/results/rank26-physical-half-twist-absolute-rank.json;
• allocator claim: seqclaim-4380e4f81869db950dc02be5.

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