PAPER-FBT08D: Asymptotic Null-Shear Readout of the QGT Propagation Layer

Abstract

This paper develops an asymptotic boundary representation of the QGT propagation layer introduced in FBT08C. The main text of FBT08C defines a local pre-spacetime velocity ratio νQ(u, v) =|Ωread(u, v)| / √︁gread(u, u)√︁gread(v, v), which satisfies 0 ≤ νQ ≤ 1 on a K¨ahler-compatible QGT readout chart. After finite vacuum calibration, this gives veff = c∗νQ ≤ c∗. The present paper asks how this causal-readout layer may appear when the downstream Lorentzian readout admits a suitable future null boundary. The answer is conditional. FBT08D does not introduce null shear as a new primitive object of the FBT framework. Rather, it records a possible asymptotic boundary representation: (︁Mread4 ,Qread, c∗)︁---(︁PshearI+ ,ΩshearI+)︁, where the right-hand side is a boundary field space of null-cut and null-shear data. In this representation, a null-cut function Z(xa, ζ, ¯ζ) encodes cuts of future null infinity, while its angular second derivative σ = ð2Z records the shear deformation of the cut. The paper clarifies three structural interfaces. First, the balanced tension shell of FBT01D, CT + S2Morse = 0, is read as a local quadratic seed for a null-characteristic structure. After square-rooting and homogeneous null lifting, it gives a local null-cone generator rather than a shear field directly. The shear appears only as the angular deformation of the associated null-cut data. Second, the infinite relative thimble-depth limit is identified as the natural null-like boundary interface of the massive thimble sector: ΔD → ∞ =⇒ e−ΔD → 0, M0e−ΔD → 0. This is a zero-rest-mass boundary branch, not an absence of physical energy. The null-shear readout is then interpreted as the trace-free boundary deformation of this null-like interface. Third, the paper explains why possible nontrivial shear residue should not come from purely local Darboux data. Locally, Darboux coordinates make the symplectic structure standard. Nontrivial shear-type information can only arise from global organisation: holonomy, monodromy, Chern data, Darboux–Floer gluing, or thimble continuation. Thus the possible boundary shear is read as an asymptotic imprint of global dual-phase twisting after a stable four-dimensional carrier and Lorentzian causal readout have been selected. The updated version (v0.3) incorporates two upstream geometric bridges. FBT0E provides the Grassmannian embedding of the coherent-state carrier, anchoring the stable fourdimensional carrier and its null boundary in the Pl¨ucker/Schubert stratification of Gr(3, 6). FBT0D supplies the singular-fibre language in which the Darboux–Floer twisting that generates non-trivial shear can be understood as monodromy around degenerate fibres of the dual-phase torus. The resulting architecture places FBT08D between FBT08C, FBT15A, FBT22B, FBT23, FBT0C, and now FBT0E/FBT0D. It supplies a conditional null-boundary representation of finite QGT causal readout, clarifies the infinite-depth null interface, and organises the boundary shear layer as a downstream readout rather than a new primitive degree of freedom. The non-central SU(2) tension algebra supplies the local spherical screen SU(2)/U(1) ∼=S2 on which null directions and spin-weighted shear data may be represented. Exact SU(2) symmetry gives the zero-shear reference cut, while nontrivial shear arises only from global Darboux–Floer or thimble-induced deformations of the null-cut data.