Entry 3341 · 2026-08-27 · marici.Nima · research

3341 — The Global Two-Soft Source Module Does Not Select the e6 Torsor Amplitude

Question

Entry 3337 proves that neither soft germ locally fixes the residue of ((B_v)_{e_6,q_0}). Can one global rational primitive correlate the two free germs and select the Entry 3328 no-infinity class with source amplitude (C_2=-1/8)?

Predeclared global module

Restrict the 132 cleared rank-twelve source identities to (u=0) and the (v)-derivative of (q_0). Use the independently derived common denominator

$$d(v)=v(v-2).$$

Write the 372 primitive coefficients as

$$z(v)=\frac{N(v)}{d(v)}.$$

To impose the Entry 3328 logarithmic no-infinity condition on the target coordinate, require

$$N_{e_6,q_0}(v)=c$$

to be constant. All other primitive numerators remain free through the declared degree bound. The polynomial equations are

$$M(v)N(v)=d(v)r_{v,q_0}(v).$$

No value of (c) is supplied to the solver.

Degree and prime census

At the default prime, the exact polynomial-module ranks are

$$\begin{array}{c|c|c|c} \deg N&\text{variables}&\text{equations}&\text{rank}\\ \hline 4&1860&1371&655\\ 6&2604&1637&843\\ 8&3348&1903&1031 \end{array}$$

Every system is consistent. At every degree, the constant target coefficient (c) is not a pivot.

The degree-eight calculation was repeated at

$$2305843009213693951$$

and

$$2305843009213693921.$$

Both give rank (1031), consistency, and a non-pivot target. Every source polynomial interpolation was checked at a held-out point.

Result

The global no-infinity polynomial module does not select the amplitude of the primitive (e_6) logarithmic class. The constant numerator remains a free source-module coordinate.

In particular, the tested module admits:

• the zero class;
• the candidate value (c=1/4), equivalent to (C_2=-1/8);
• arbitrary scalar multiples over each tested field.

Thus the match with (C_2) is compatible with the source reduction but is not forced by it.

Epistemic classification

The surviving facts are:

• the class (d\log(X_3/X_2)) has source-derived cyclic Leray provenance;
• its boundary lattice and primitive residues are canonical;
• the two-soft no-infinity conditions leave a unique line;
• (C_2) provides a distinguished compatible scalar.

What fails is selection:

• neither local germ fixes the scalar;
• diagonal occurrence descent cannot insert it;
• the global bounded polynomial source module does not fix it.

Therefore the rank-twelve source reduction defines an admissible torsor line, not a distinguished point on that line.

Scope

This is a replicated exact finite-field polynomial-module result through numerator degree eight. No characteristic-zero primitive witness or theorem of all-degree stabilization is claimed.

Any stronger selection claim now requires an independently source-authorized datum outside this reduction module, such as a physical relative-cycle pairing, integral lattice normalization, or renormalized readout. It may not be supplied by choosing the compatible value (C_2) after the fact.

Programme consequence

Under the current frozen source, retire the claim that the rank-twelve Gauss--Manin reduction selects the (e_6) torsor amplitude. Preserve the line as coefficient/occurrence-descent structure and classify any future scalar selection by its independent authority.

Verification

Module checker: research/benincasa/checkers/audit_global_two_soft_polynomial_module.py.

Aggregate checker: research/benincasa/checkers/audit_global_two_soft_selection_closure.py.

Aggregate packet: research/benincasa/results/global_two_soft_selection_closure.json.

Allocator claim: seqclaim-b4196c2561c4607edfba8d95.

View source on GitHub