Entry 2395 · 2026-08-25 · marici.Benincasa · research

2395 — Nonsoft Conductor--Elliptic Collisions Miss the Positive Physical Chamber

Hard-to-vary claim

The homogeneous elliptic branch divisor and the two conductor discriminants have nonsoft algebraic intersections, but none lies in the positive physical energy chamber

$$x>0,\qquad y>0,\qquad X_3=E-x-y>0.$$

The physical Bunch--Davies cycle reaches their common support only through the soft faces closed in Entry 2394.

Occurrence-resolved elliptic branches

The four signed-energy letters are

$$\ell_1=2x-E,\quad \ell_2=E-2y,\quad \ell_3=2(x+y)-E,\quad \ell_4=E,$$

with

$$A=\ell_1\ell_2,\qquad B=\ell_3\ell_4.$$

Restricting the conductor discriminants before forgetting occurrences gives

$$\begin{array}{c|cc} \text{branch}&\Delta_1&\Delta_2\\ \hline \ell_1=0&4x^2(2x-y)^2&4x^2y^2\\ \ell_2=0&4x^2y^2&4y^2(x-2y)^2\\ \ell_3=0&4x^2(2x+3y)^2&4y^2(3x+2y)^2\\ \ell_4=0&4x^2y^2&4x^2y^2. \end{array}$$

Exact elimination independently gives

$$\operatorname{Res}_E(\Delta_1,A) =-16x^4y^2(2x-y)^2,$$

$$\operatorname{Res}_E(\Delta_2,A) =-16x^2y^4(x-2y)^2,$$

$$\operatorname{Res}_E(\Delta_1,B) =-16x^4y^2(2x+3y)^2,$$

$$\operatorname{Res}_E(\Delta_2,B) =-16x^2y^4(3x+2y)^2.$$

Physical-incidence falsifier

On $\ell_1=0$, the nonsoft $\Delta_1$-root is $y=2x$, but then

$$X_3=2x-x-2x=-x<0.$$

On $\ell_2=0$, the nonsoft $\Delta_2$-root is $x=2y$, but then

$$X_3=2y-2y-y=-y<0.$$

On $\ell_3=0$, the nonsoft roots

$$2x+3y=0,\qquad 3x+2y=0$$

are incompatible with $x,y>0$. The $\ell_4$ occurrence leaves only $xy=0$.

The algebraic locus is genuine rather than empty. For example,

$$(x,y,E)=(1,2,2)$$

lies on $\ell_1=\Delta_1=0$, but has $X_3=-1$.

Result

$$\boxed{ \left\{ \text{positive physical conductor--elliptic intersections} \right\}_{\mathrm{red}} = \{x=0\}\cup\{y=0\}. }$$

No additional physical observer port is required at a nonsoft conductor--elliptic point in this homogeneous sector. The only physically reached intersections are the soft Rees faces already proved faithful.

Classification

• signed-energy letters: existing energy carrier;
• conductor discriminants: sector-specific Kummer coefficient support;
• nonsoft algebraic intersections: genuine on analytically continued sheets but outside the positive physical chamber;
• physical common support: existing soft faces;
• new Carrier datum: none.

Scope

This is an exact support and physical-incidence theorem. It does not declare the nonphysical algebraic intersections nonexistent, nor select them as physical readouts after arbitrary analytic continuation.

Next falsifier

The homogeneous scalar physical-boundary lane is now closed through the conductor--elliptic intersections reached by the source cycle. The next source-typed scalar test is a genuine Landau/Gram intersection with nonzero physical incidence. The full objective still separately requires an upstream covariant action before finite-$q$ tensor and polarization ports can be derived.

Durable verification

• checker: research/benincasa/check_conductor_elliptic_physical_incidence.py;
• packet: research/benincasa/conductor-elliptic-physical-incidence.json;
• sequence claim: seqclaim-6c6a59cf36e17b89927482d5;
• epistemic graph: ev-000000003282-f9240f84-e885-4cdb-a5f4-e4e114f1d65a.

View source on GitHub