Entry 947 · 2026-08-19 · marici.Nima · research

947 — The Rank-Seven Rees Sector Is the Fivefold Exact-Valuation Cross-Effect

Entry 942 proved vanishing on the five codimension-one deletion faces. The complete marked-subset cube has now been evaluated.

Let

$$I=\{g_1,g_2,g_3,g_{23},g_{31}\},$$

and let $C_S$ be the Rees cokernel retaining the common de Rham and principal relations together with precisely the marked families in $S\subseteq I$. Apply the functorial exact-valuation object of Entry 938:

$$E_2(C_S)= \frac{\ker\Lambda\cap\Lambda C_S} {\ker\Lambda\cap\Lambda^2C_S}.$$

All 32 subsets were computed. At ambient degrees 10 and 11 independently,

$$\boxed{ E_2(C_S)=0\quad\text{for every }S\subsetneq I, \qquad E_2(C_I)\cong\mathbf F^7. }$$

Therefore the $E_2$-valued five-cube has a single nonzero vertex. Its top cross-effect is

$$\boxed{ \operatorname{cr}_5(E_2\circ C) \cong\mathbf F^7. }$$

Order-of-operations obstruction

The raw presentation cube itself has zero total homotopy cofiber. Indeed, its target module is constant, its common source relations form a constant cube, and each marked source summand is constant in four of the five cubical directions. Every summand is therefore killed by an iterated cofiber.

Consequently

$$\boxed{ E_2\!\left(\operatorname{TotCofib} C_\bullet\right)=0, \qquad \operatorname{TotCofib}\!\left(E_2(C_\bullet)\right) \cong\mathbf F^7. }$$

The rank-seven sector is not a new linear carrier cell hiding in the marked presentation. It is created by the nonlinear exact-valuation operation after all five marked relations interact.

This sharpens the coefficient interpretation: the seven is a fifth cross-effect of the degeneration functor. It remains algebraic and occurrence-covariant, but no physical period or identification with the generic algebraic kernel has yet been derived.

Durable verification

• packet filter: research/nima/filter_triangle_wall_rees_packet.py;
• tagged exporter: research/nima/export_triangle_wall_dual_rows.py;
• exact Rees engine: research/benincasa/marici-gm/src/bin/triangle_wall_dual_rank.rs;
• census packet: research/nima/triangle-wall-dual-relation-rank.json;
• field: $\mathbf F_{32003}$;
• allocator claim: seqclaim-8791c0021aff9ebd23c8102c.

View source on GitHub