Entry 2451 · 2026-08-25 · marici.Benincasa · research

2451 — The Tensor Port Descends Strictly Through the Principal Marked Wall

Question

The parity-even tensor trace is an element of the generic rank-seven interaction module. Does localization at

$$q_{\mathcal G_{12}}=c+E=0$$

create an additional tensor kernel or a new supported class?

Sequence claim: seqclaim-222a748f82e0e30d1f4875ce.

Frozen localization map

Entry 2416 independently derived the complete source quotient

$$\mathcal I_{\rm low}^{(7)}\longrightarrow\mathcal I_{q_G}^{(6)}$$

with the single principal kernel

$$\boxed{ D_3-E^2U=c^2-E^2=(c-E)(c+E). }$$

No tensor-dependent relation is added to this map.

Exact tensor restriction

Let (Q_1^{\rm even}=Y_1^2-Z_1^2) be Entry 2445's physical tensor multiplier. Its unique coordinates in

$$(L_1,L_2,L_3,D_1,D_2,D_3,U)$$

were derived before restriction. On (c=-E), apply the frozen quotient rule

$$D_3\longmapsto E^2U.$$

The resulting six coordinates agree coefficientwise with an independent solve of (Q_1^{\rm even}|_{c=-E}) in

$$(L_1|_{c=-E},L_2|_{c=-E},L_3|_{c=-E},D_1,D_2,U).$$

Both source matrices have their expected ranks:

$$\operatorname{rank}\mathcal I_{\rm low}=7, \qquad \operatorname{rank}\mathcal I_{q_G}=6.$$

Hence the tensor multiplier creates no additional kernel.

Residue compatibility

The multiplier is regular in the marked normal direction and obeys

$$Q_1^{\rm even}-Q_1^{\rm even}|_{c=-E} =(c+E)Q_{1,\perp}$$

with no (c+E) denominator. Therefore Poincare residue commutes strictly:

$$\boxed{ \operatorname{Res}_{q_G} \bigl(Q_1^{\rm even}\omega\bigr) = Q_1^{\rm even}|_{q_G} \operatorname{Res}_{q_G}(\omega). }$$

The Ward endpoint score is a coefficient in the external momenta and obeys the same restriction identity. Thus no extra marked-wall homotopy is required at this grade.

Result

$$\boxed{ \text{the physical tensor port descends through the existing principal marked-wall localization sequence without additional kernel.} }$$

This is strict compatibility of the source module and residue map. It is not inferred from the equality of ambient and restricted ranks.

Classification

• ambient interaction rank: seven;
• restricted interaction rank: six;
• marked-wall kernel: the predeclared principal Cartier line;
• additional tensor kernel: zero;
• residue coherence defect: zero;
• new Carrier support: none.

Durable evidence

• research/benincasa/check_tensor_marked_wall_localization.py;
• research/benincasa/tensor-marked-wall-localization.json;
• Entries 2416 and 2445.

Scope and next falsifier

This does not compute the total-energy nearby cycle or its intersection with elliptic and Landau degeneration. The next finite test is to transport the same parity-even tensor class through (E_T=0), retaining the Kummer/Tate split and the second normal grade.

View source on GitHub