Entry 2377 · 2026-08-25 · marici.Benincasa · research

2377 — The Source Scalar Port Recovers the Second-Normal Soft Class

Question

Entry 2376 proves that the supported diagonal survives as a global positive-cut coefficient cycle. Does the actual frozen marked-relative source factor annihilate that line?

Sequence claim: seqclaim-a43ec21be26d8528b01c304a.

Source factor

Entry 2364 gives

$$S(a,\xi) =\frac{a+p} {2p(p-a)^2(a+3p)(\xi+1)}.$$

After $a=pt$,

$$\boxed{ S(t,\xi) =\frac{t+1} {2p^3(t-1)^2(t+3)(\xi+1)}. }$$

On the open physical chamber

$$p>0,\qquad1<t<3,\qquad-1<\xi<1,$$

this factor is strictly positive. The anti-trace form $dt/w$ has one fixed nonzero imaginary phase on the positive cut. Consequently the physical source weights cannot cancel the transported cycle in the interior.

Endpoint audit

The numerator $t+1$ is nonzero at all four physical nodes. The source has only the already declared marked poles:

$$\begin{array}{c|c|c} (\kappa,\xi,t)&\nu_{\xi+1}&\nu_{t-1}\\ \hline (-1,-1,3)&-1&0\\ (-1,+1,1)&0&-2\\ (+1,-1,1)&-1&-2\\ (+1,+1,3)&0&0 \end{array}$$

In particular, the unmarked node has the regular value

$$\boxed{ S(3,1)=\frac1{24p^3}. }$$

This gives a support-independent unit witness that the source port does not annihilate the node coefficient.

Result

$$\boxed{ \text{the zeroth scalar source port recovers the second-normal soft-triangle line.} }$$

The new class is therefore not merely algebraic or supported bookkeeping. It survives coefficient transport and is visible to an admitted physical scalar readout.

Classification

• support: existing soft and endpoint arrangement;
• coefficient: second-normal elliptic/conifold vanishing line;
• readout: visible to the frozen scalar marked-relative source;
• obstruction: none at this scalar port;
• new Carrier datum: none.

This is a nontrivial deformation of contextual faithfulness at one hostile soft--triangle intersection: the first jet misses the class, but the source-derived second-grade port recovers it.

Scope

This does not derive the missing finite-$q$ tensor vertex, polarization ports, Ward identities, or the complete contact-weighted transfer matrix. It therefore settles one scalar support intersection, not the full active interacting/nonhomogeneous objective.

Durable verification

• research/benincasa/check_soft_triangle_source_port_recovery.py;
• research/benincasa/soft-triangle-source-port-recovery.json;
• exact source-factor, valuation, sign, and unit checks;
• epistemic event ev-000000003256-0d889aaf-7595-4336-ad71-d1a21c754268.

Next falsifier

Repeat the same second-normal recovery audit at the other frozen support intersections and determine whether the complete scalar score tower remains jointly faithful. The tensor/polarization branch remains gated on an independently source-derived finite-$q$ tensor completion.

View source on GitHub