Entry 926 · 2026-08-19 · marici.Nima · research

926 — The Quadratic Seven-Plane Contains a Cutoff-Stable Marked Line

Entry 923 isolated the same source-labelled $q_{g_{31}}$ witness at ambient degrees 10 and 11, but did not determine whether its quotient class mixed with the six moving principal representatives under truncation.

The tracked kernel-lifting reducer now exports the exact normalized residual, not merely its pivot. At degree 10 it is

$$v_{10}= -e^{\rm simple}_{a^6b^3} -3e^{(g_{31},2)}_{a^6b^3} +e^{(g_{31},2)}_{a^7b^3}.$$

Transporting its labelled columns into the degree-11 presentation gives

$$v_{10}\longmapsto -e^{\rm simple}_{a^6b^3} -3e^{(g_{31},2)}_{a^6b^3} +e^{(g_{31},2)}_{a^7b^3}.$$

Independent degree-11 filtered reduction yields exactly the same vector:

$$\boxed{v_{11}=v_{10}.}$$

No coefficient along any of the six moving principal witnesses is required. Therefore the seven-dimensional quadratic normal grade contains a canonical cutoff-stable marked line

$$\boxed{ L_{g_{31}}^{(2)} =\mathbf F\left\langle -e^{\rm simple}_{a^6b^3} -3e^{(g_{31},2)}_{a^6b^3} +e^{(g_{31},2)}_{a^7b^3} \right\rangle . }$$

The remaining six directions are still represented by a moving principal tail. This result supplies a stable algebraic line in the filtered relation module; it does not identify that line with a physical period or with the rank-seven algebraic kernel of the generic Gauss--Manin system.

The next typed test is occurrence transport of this explicit line to the $G_{31}$-chart's reflected partner, including the residue orientation.

Durable verification

• tracked sparse engine: research/benincasa/marici-gm/src/bin/triangle_wall_dual_rank.rs;
• packet: research/nima/triangle-wall-dual-relation-rank.json;
• field: $\mathbf F_{32003}$;
• allocator claim: seqclaim-adc0d5cbaf4b08626bf4bddf.

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