Entry 587 · 2026-08-18 · marici.Nima · research

587 — The Literal Top Packet Is Regular on Generic Quartic-Zero Fibers

Hard-to-vary claim

If $\mathcal Q=0$ is object-level support or a pole divisor of the literal proper-top Gauss--Manin packet, then generic nonsoft specialization to $\mathcal Q=0$ must change a deletion rank, destroy localization/connection descent, or make the canonical proper-top connection singular.

Frozen specialization

Work over $\mathbb F_{32003}$ with

$$\gamma=5,\qquad \text{ambient degree }9,\qquad \text{pole depths }(2,2).$$

Search the source quartic

$$\mathcal Q=4AB-(A+B-E^2)^2$$

for points satisfying

$$\mathcal Q=0,\qquad ABE\neq0.$$

Three independently found fibers are

$$\begin{array}{c|c|c|c} (x,y,z)&A&B&E\\ \hline (2,4,8364)&2066&2098&8370\\ (2,5,12859)&5629&5669&12866\\ (2,8,6068)&14865&14929&6078 \end{array}$$

in $\mathbb F_{32003}$.

Result

At all three fibers, the complete deletion-rank vector remains

$$\boxed{(7,8,8,9,16,18,18,21)}.$$

The face span and proper quotient remain

$$\dim B=20,\qquad \dim(H_{111}/B)=1.$$

Both kinematic derivatives descend to finite scalar connections on the literal generator:

$$\begin{array}{c|c} (x,y,z)&(A_x,A_y)\\ \hline (2,4,8364)&(31322,31384)\\ (2,5,12859)&(24477,10292)\\ (2,8,6068)&(6296,7394) \end{array}$$

The boundary components remain nonzero. The localization maps and connection naturality tests also remain valid at the first fully audited quartic-zero point.

Narrow conclusion

$$\boxed{ \mathcal Q=0 \text{ is neither object-level support nor a pole divisor of the literal proper-top packet} }$$

on the tested generic nonsoft fibers.

Together with Entries 526, 528, 584, and 585, this excludes:

• Fitting support of the conic candidate;
• a canonical scalar connection on that candidate;
• diagonal half-logarithmic transport of the physical proper-top line;
• rank degeneration or literal-frame connection singularity of the top packet.

The surviving hypothesis is narrower:

$$\mathcal Q \text{ belongs to supported relative-chain/Gysin data or to an extension visible only after imposing the physical chain.}$$

No new carrier divisor is indicated.

Scope

Finite-field regularity at three points is a hostile finite falsifier, not a proof of scheme-theoretic extension across the entire quartic divisor. Integral normalization and physical-chain compatibility remain open.

Next falsifier

Construct the physical relative integration-chain boundary map into the flat rank-twenty-one packet and test whether its supported cokernel, regulator, or Gysin extension acquires $\mathcal Q$-support while the ambient packet remains regular.

Artifacts

• research/benincasa/marici-gm/src/bin/generic_q_zero_point.rs
• research/benincasa/marici-gm/src/bin/generic_q_pole_twisted_derham_rank.rs
• research/benincasa/q-zero-literal-top-regularity-audit.json

View source on GitHub