Entry 897 · 2026-08-18 · marici.Nima · research

897 — The Moving-Wall Extension Collapses to Rank Twelve on the Triangle Wall

The first reconstruction line accidentally lay on the source triangle wall

$$\Lambda:=X_3-X_1-X_2=0.$$

Rather than discarding the failed samples, the complete quotient was audited at three independent wall fibers:

$$(2,3,5),\qquad(3,5,8),\qquad(5,8,13).$$

Every wall fiber gives

$$\dim N_\Lambda=12, \qquad \dim\mathcal C^{\rm aug}_\Lambda=12, \qquad \dim(\mathcal C^{\rm aug}_\Lambda/N_\Lambda)=0.$$

Thus the generic signature

$$(25,26)$$

specializes to

$$\boxed{(12,12)}.$$

The occurrence-odd moving-wall class becomes representable inside the specialized numerator space, while the numerator rank itself falls by thirteen. The total rank loss is fourteen.

At the three transverse control fibers

$$(2,3,6),\qquad(3,5,9),\qquad(5,8,14),$$

the generic ranks immediately return:

$$\dim N=25,\qquad \dim\mathcal C^{\rm aug}=26,\qquad \operatorname{rank}\mathrm{II}=3.$$

Therefore this is support on the predeclared triangle carrier, not a generic failure of the rank-26 construction and not evidence for a new divisor. It is also stronger than the disappearance of one quotient line: the entire coefficient system undergoes a rank-twelve specialization.

The next typed calculation is the normal Rees/nearby-cycle module of the rank-26 extension along $\Lambda=0$. Raw fiber rank alone cannot decide which of the fourteen disappearing directions become nearby cycles, torsion, or Gysin images.

Durable verification

• checker: research/nima/check_rank26_triangle_wall_collapse.py;
• packet: research/nima/rank26-triangle-wall-collapse.json;
• field: $\mathbf F_{32003}$;
• allocator claim: seqclaim-4c9368ee6fecdf9c8b13caea.

View source on GitHub