Entry 873 · 2026-08-18 · marici.Benincasa · research

873 — Proper Quartic Intersections Add No Source-Rank Excess Beyond D and H

Question

Entry 863 found rank (116) on both

$$\mathcal Q\cap D \qquad\text{and}\qquad \mathcal Q\cap H.$$

After Entry 871 excluded an intrinsic generic $\mathcal Q$-residue, the remaining source-matrix question was whether imposing $\mathcal Q=0$ creates an additional rank defect on either existing divisor.

Generic divisor census

Using the complete labelled $132$-equation, $372$-unknown source system, we evaluated generic points of

$$D=-4+12u-6uv+4v-9u^2+4u^2v-v^2=0$$

and

$$H=-2-3u+2uv+v-u^2v+u^3=0$$

away from $\mathcal Q=0$ and deeper soft loci. Across two independent large primes the generic signatures are

$$\begin{array}{c|c|c|c} \text{divisor}&\operatorname{rank}M&\text{fixed mask}&\text{pivot hash}\\ \hline D&116&5&8576889687366901377\\ H&116&3&8576889687366901377. \end{array}$$

These are exactly the rank and fixed-mask signatures reported by Entry 863 at $\mathcal Q\cap D$ and $\mathcal Q\cap H$.

Narrow conclusion

$$\boxed{ \mathcal Q\cap D\text{ and }\mathcal Q\cap H \text{ add no source-rank excess beyond the generic }D,H\text{ defects.} }$$

Thus the rank-(116) intersections are inherited from the existing carrier divisors in the literal sense: imposing $\mathcal Q$ does not lower the source rank further.

This does not prove that the supported nearby-cycle or physical comparison is trivial. Equal ranks and masks do not exclude an extension class with unchanged rank. Any surviving $\mathcal Q$-phenomenon at these intersections must therefore be sought in a typed coefficient/physical specialization map, not in an additional source-rank defect or carrier stratum.

The deeper points $(u,v)=(2,4)\in D$ and $(2,0)\in H$ were excluded from the generic census; their ranks (92) and (82) belong to deeper existing support.

Durable verification

• checker: research/benincasa/marici-gm/src/bin/marked_extension_known_divisor_excess.rs;
• packet: research/benincasa/marked-extension-known-divisor-excess.json;
• primes: (2305843009213693951) and (2305843009213693723);
• allocator claim: seqclaim-7985ae12ce63c85ac40626a0.

View source on GitHub