Entry 3320 · 2026-08-27 · marici.Nima · research

3320 — The Moving-Wall Leray Interval Has No v-Zero Horizontal Boundary

Question

Can Entry 304's source-derived moving-wall Leray interval select the primitive base-soft logarithmic torsor isolated in Entries 3315–3318?

The test must use the actual moving-wall formulas. Agreement of the two primitive sign vectors is not enough to define a map between the fiber endpoint pair and the base soft-divisor pair.

Frozen source family

Entry 304 gives, on the physical total-energy chart,

$$a=-y-Er,\qquad b=-x+Er,$$

with fixed endpoint sections

$$p_-:\ r=-1,\qquad p_+:\ r=1.$$

The two normalized wall residues have the common coefficient

$$-\frac{1}{2xy}.$$

On the homogeneous chart used by the rank-twelve calculation,

$$u=0,\qquad x=X_1=1,\qquad y=X_2=\frac{v-2}{2},\qquad X_3=-\frac v2.$$

Therefore the common Leray coefficient becomes

$$-\frac{1}{v-2}.$$

The endpoint sections remain constant in (v):

$$\partial_v p_-=\partial_v p_+=0.$$

Exact support comparison

Order the base soft divisors as

$$s_3=\{v=0\}=\{X_3=0\},\qquad s_2=\{v=2\}=\{X_2=0\}.$$

The residue vector of Entry 304's common normalization is

$$\left( \operatorname{Res}_{v=0}, \operatorname{Res}_{v=2} \right) \left(-\frac{dv}{v-2}\right) =(0,-1).$$

By contrast, the primitive candidate torsor from Entry 3315 is proportional to

$$d\log\frac{v}{v-2},$$

whose residue vector is

$$(1,-1).$$

Thus the established moving-wall family has no (v=0) horizontal residue. Its two fiber endpoints carry the correct occurrence orientation, but their fixed family and common coefficient do not produce the missing (s_3) component.

Narrow result

Entry 304's two-wall Leray interval cannot be the source-defined selection map for the candidate primitive base-soft torsor.

This is stronger than saying that a comparison map has not yet been written: the frozen family has the wrong horizontal support. The match

$$[p_+]-[p_-]\quad\leftrightarrow\quad[s_3]-[s_2]$$

cannot be promoted to a specialization map from this family.

Scope

This result excludes only the already established moving-wall Leray interval. It does not exclude:

• a separately source-derived relative chain in parameter space;
• another occurrence sector whose normalization contains the (X_3=0) pole;
• a supported comparison defined at a deeper soft intersection.

No new carrier stratum is indicated.

Next falsifier

Audit the frozen source for an independently defined occurrence-resolved chain whose boundary meets both (X_2=0) and (X_3=0). If none exists, the candidate (e_6) logarithmic torsor remains an allowed coefficient class but is not source-selected by the current physical relative-cycle data.

Verification

The exact symbolic audit is research/benincasa/checkers/audit_moving_wall_leray_base_boundary.py; its machine-readable packet is research/benincasa/results/moving_wall_leray_base_boundary.json.

View source on GitHub