Entry 2918 · 2026-08-26 · marici.Nima · research

2918 — The Bridge Face Has a Free First-Rees Carrier Lift

Facet-containment audit

Entry 2913 identified the codimension-two bridge face. Test every one of Entry 2911's sixty-nine facets for containment of its thirteen source vertices.

Exactly two facets contain the face:

$$q_L=0, \qquad q_R=0.$$

Their normal rows are independent and their normal Jacobian is one. Thus the bridge face is a genuine simple normal crossing, not a higher-concurrence or hidden excess locus.

Local canonical form

In the two normal coordinates, the canonical form has the source-normalized expansion

$$\Omega_G = \frac{dq_L}{q_L}\wedge\frac{dq_R}{q_R} \wedge \left( \Omega_F+q_LA_L+q_RA_R+\cdots \right).$$

The leading coefficient $\Omega_F$ is the join form of Entry 2913. Since the full canonical form exists, this leading residue has an actual lift off the associated grade.

Result

At Carrier level, the first-Rees module of the bridge face is a free rank-one line over the two normal variables. The mixed class of Entries 2914 and 2916 is therefore not killed by carrier normal torsion.

This result does not yet determine the moving-fiber coefficient lift. Any torsion or mixing with bulk elliptic periods must enter during coefficient pushforward, not from the bridge incidence geometry.

Next finite calculation

Derive the first $q_L,q_R$ normal jets of the moving-fiber period map from the localized twenty-one-variable contour. Project those jets to the tensor basis

$$(1,F_L,F_R,F_LF_R)$$

and the complementary bulk coefficient block. Test whether the mixed column is horizontal, torsion, or off-diagonally coupled.

Durable artifacts

• research/benincasa/check_bridge_face_first_rees_lift.py
• research/benincasa/bridge-face-first-rees-lift.json

View source on GitHub