PAPER-FBT08E: From Stable Internal Configurations to Effective Particle Worldlines

The Fracture–Berry–Tension framework now organises its regular six-dimensional geometry through the principal relative-phase bundle T2rel ↪→ X(6)regπ −→ B(4)reg. FBT0A supplies the local fracture and symplectic-reduction model, whereas FBT0B supplies the global torus-fibration architecture. A connection on this bundle gives the local organisation TX(6)reg = HA ⊕ V, and FBT01A describes the associated carrier curvature, phase curvature, and mixed horizontal–vertical readout. The four-dimensional base is therefore not obtained by discarding two internal coordinates. The relative phases remain genuine fibre data, while collective placement is read on the base. The present paper formulates the bridge from this bundle-supported internal geometry to an effective particle worldline. An effective particle is not identified with an individual binary state, one slot, the relative-phase torus, a single Lefschetz thimble, or a curve in the six-dimensional total space. It is represented by a persistent stable internal type carried by an internally reduced configuration with finite readout support, admissible branch and thimble data, balanced tension closure, and covariantly transported internal identity. The finite internal readout input is the twelve-dimensional complex slot carrier inherited from FBT22 and DCQ7A, QCslot = ECh ⊗C VV , dimC ECh = 3, VV = Λ3C4, dimC QC slot = 12. This is a Chern-labelled readout multiplicity. It is not identified with the twelvereal-dimensional Cartan deformation reservoir of FBT22, nor with the twelve-complexdimensional ambient mixed Plücker sector of FBT0E. Only the readout-slot count is required by the worldline construction. The central new step is a positional localisation construction on the four-dimensional readout base. FBT06B–D provide, over each admissible base point b, a convergent fibrewise Lefschetz thimble together with a normalised quantum measure νb and partition function Zb. FBT01A supplies the horizontal–vertical mixed readout data required to make this fibrewise quantum structure sensitive to collective placement on the base. These ingredients define an effective positional localisation functional Φpos[Cst; b]. Its minimiser set Loc(Cst) = arg minb∈B(4)admΦpos[Cst; b] determines the positional status of the stable configuration. On the point-localised branch, Loc(Cst) = {X}, the positional readout is derived as Rpos(Cst) = X. Thus particle position is not identified with an internal phase coordinate, a point of the Lefschetz thimble, or a primitive six-dimensional carrier coordinate. It is the unique collective minimum selected on the four-dimensional base by the combined fibrewise quantum weight and horizontal–vertical readout geometry. For a sufficiently slow stable evolution, Cst = Cst(τ ), persistence of the non-degenerate localisation minimum gives a smooth history X(τ ) = Rpos(︁Cst(τ ))︁. When this history is causal with respect to the Lorentzian structure supplied by FBT01E and FBT08A, its image defines the effective particle worldline. The main theorem is conditional and representation-independent: for a fixed admissible positional-readout structure, every sufficiently slow persistent stable history determines X : I −→ B(4)adm, X(τ ) = Rpos(︁qint(Cst(τ )))︁. If this history is causal with respect to the Lorentzian readout metric, its image is an effective particle worldline. Internal-equivalent representatives produce the same base curve. This is representative independence, not a claim that all mathematically possible positional readout maps are uniquely determined. Finally, the paper preserves a corrected QGT-compatibility diagnostic. The defect εQGT measures whether an effective positive metric–phase pair remains close to a scaled compatible almost-Hermitian structure after truncation or coarse-graining. Small defect indicates approximate QGT coherence; it is not imposed as a necessary condition for the existence of a worldline. Positional readout is also kept distinct from physical observation: the latter requires a further observable map of the type developed in FBT32.