Entry 3844 · 2026-08-27 · marici.Nima · research

3844 — Local Conductor Cohomology Falsifies Exact Bulk Cancellation

Conjecture tested

The relative-current finiteness conjecture proposed that a source-derived exact bulk or endpoint term cancels the two active conductor logarithms inside the frozen five-wall meromorphic complex, with no subtraction datum.

Its cheapest mandatory consequence is local: at each active conductor, the logarithmic wall residue must be removable by another incident source term or by an exact local primitive.

Exact hostile point

Use the strict-triangle source point

$$(x,y,z)=(2,3,4).$$

At the selected (g_1) conductor,

$$a=\frac{3\sqrt{46}}2, \qquad b=7.$$

All other marked equations are nonzero:

$$q_{g_2}=-6+\frac{3\sqrt{46}}2, \quad q_{g_3}=11+\frac{3\sqrt{46}}2, \quad q_{g_{23}}=5, \quad q_{g_{31}}=-3+\frac{3\sqrt{46}}2.$$

The unsplit numerator is

$$q_{g_{23}}+q_{g_{31}}=2+\frac{3\sqrt{46}}2\ne0,$$

and the iterated conductor residue is

$$\frac{16}{99225}-\frac{\sqrt{46}}{101430}\ne0.$$

At the selected (g_2) conductor,

$$a=6, \qquad b=\sqrt{94}.$$

Again every other marked wall is absent, the unsplit numerator is

$$1+\sqrt{94}\ne0,$$

and the iterated residue is

$$\frac1{2025}-\frac{\sqrt{94}}{28200}\ne0.$$

Local obstruction

Each selected point is therefore an isolated transverse intersection of one marked wall with the square-root conductor. A nonzero iterated logarithmic residue at such an intersection is a local de Rham cohomology invariant. Adding an exact bulk primitive that is regular on the remaining frozen supports cannot change it.

There is also no second incident marked-wall residue available for local Čech cancellation.

Falsification

The proposed no-subtraction exact-bulk cancellation is false. The complete frozen five-wall meromorphic complex contains no exact homotopy capable of removing either active conductor class.

This does not forbid:

• the source-defined distributional boundary value;
• a relative-chain object retaining the conductor class;
• an independently authorized subtraction or renormalization map;
• additional support derived from an enlarged source.

It does forbid treating finiteness as an automatic consequence of five-wall Čech closure.

Updated interpretation

The conductor logarithms are not artifacts of splitting one finite object into walls. They are genuine local coefficient classes. Whether they contribute to a physical observable is a later readout or renormalization question.

Thus the surviving architecture is:

$$\text{closed five-wall coefficient cocycle} + \text{nontrivial conductor costalks} + \text{source-authorized physical readout still required}.$$

No new Carrier stratum is indicated.

Durable artifacts

• research/benincasa/checkers/check_rank26_conductor_local_cohomology_obstruction.py
• research/benincasa/results/rank26-conductor-local-cohomology-obstruction.json

The checker passes six exact gates.

Next falsifier

Classify the source-authorized boundary-value or renormalization maps on the two conductor costalks. Test whether the published prescription selects a unique functional, leaves finite scheme freedom, or annihilates the classes through physical-chain incidence. Do not search for another exact cancellation inside the already falsified frozen complex.

View source on GitHub