Entry 2875 · 2026-08-26 · marici.Nima · research

2875 — The Soft Translation Monodromy Is the Source Leray-Tube Pairing

Local pushed-forward form

At the labelled soft normal $t=q_{g1}/X_1=0$ , the moving-fiber pushforward has local form

I(t)\,dt = L\frac{dt}{t} + \text{holomorphic terms}.

The coefficient $L$ is the $q_{g1}$ -residue vanishing period, with the physical positive $a=y_{23}$ occurrence selected from the full marked packet.

Use the source orientation fixed by

dq_{g1}=dy_{12}

and by the oriented positive Cayley–Menger chain. For a positive Leray loop $\tau_\epsilon$ around $t=0$ ,

\int_{\tau_\epsilon}I(t)\,dt = 2\pi iL.

The value is independent of the tube radius. Reversing the residue orientation reverses both sides.

For the pointed primitive

P(t)=\int_2^t I(s)\,ds,

analytic continuation once around the same positive loop gives

\Delta P=2\pi iL.

Hence

\Delta P = \left\langle \text{source Leray tube}, \text{residue coefficient }L \right\rangle.

The affine translation of the logarithmic torsor is therefore not an untyped integration constant. It is exactly the source-normalized tube pairing.

Carrier: the existing labelled $q_{g1}$ normal and Cut incidence.
Coefficient object: the residue vanishing period $L$ .
Physical readout: the source-oriented Leray tube with the physical occurrence covector.
New carrier datum: none.

Together with Entries 2871 and 2873, this completes the moving-cycle, regulator, and Leray-pairing gates for the soft logarithmic torsor.