Geometric-Time Locking, Sector-Plane Field Equations, and the Kinematic Omniverse: Internal Hyper-Propagator Damping in O--QFT

This article develops the field-equation and scattering interface by which geometric-time locking (GTL) produces internal hyper-propagator damping in O--QFT. The construction begins from an ambient geometric-time support space \ (R^K, 3 ₆ₓ\), with \ (K=-3\), and uses a selected unit carrier \ (G\) to define a locked Lorentzian four-volume with local signature \ ( (1, 3) \). The resulting four-dimensional readout is \ (R^1, 3 ₆ₓ\), not ordinary \ (R^1, 3 ₌₈₍₊₎ₖₒ₊₈\): the coordinate written \ (x₀\), equivalently \ (G₀\) or \ (x₀, \), is first a selected geometric-time support coordinate rather than a primitive Minkowski clock-time coordinate. This readout distinction is what motivates the sector-plane bookkeeping used throughout the article. In \ (R^1, 3 ₆ₓ\), point-particle supports may be compared at the same ordinary clock time while occupying different affine positions along the selected GT support coordinate. The retained post-GTL label \ (= (s, bₛ) \), with \ (s\N, A\\), records this support information. Fields, sources, creation and annihilation operators, and Wick contractions are therefore labelled by \ (\). For each fixed sector plane, the plane-local canonical algebra carries the usual bosonic CCR or fermionic CAR. Fields with different sector-plane labels contractions are therefore labelled by \ (\). For each fixed sector plane, the plane-local canonical algebra carries the usual bosonic CCR or fermionic CAR belong to independent free algebras unless the action contains an explicit support-changing kernel. Equivalently, the equal-locked GT canonical relations are plane diagonal. At \ (X₀, =Y₀, '\), the scalar relation has the schematic form\ [ _ (X₀, , x), ' (Y₀, ', y) = i\, '³ (x- y), \]while the fermion relation has the schematic form\ \ _{ (X₀, , x), '^ (Y₀, ', y) \} = '³ (x- y) 1 ₒ₏₈₍. \ ('\) is the sector-plane label-identity factor: it enforces equality of both the sector orientation and the affine GT placement carried by \ (= (s, bₛ) \). Thus the sector-plane subscript is a selection rule in the free canonical algebra, not merely a decorative label. The sector entry \ (s\) is the reduced \ (Z₂\) -valued antipodal orientation bit of the selected carrier line, with \ (N=+1\), \ (A=-1\), and \ (G^ orₛ=ₛ G\). The affine entry \ (bₛ\) records support placement along that selected carrier line. Thus \ (\) labels the plane-local fields, sources, and contraction channels; it does not replace the carrier itself. The carrier remains the selected direction \ (G\), or the unoriented line \ (G^K-1\), and is not turned into a sector-plane-labelled carrier. In particular, \ (Q䂺 ₆=Q ₆\), so the transverse GT projector depends on the selected carrier line, while \ (= (s, bₛ) \) specifies which sector-plane source block and canonical contraction channel are being used over that carrier. The article then implements GTL at the action/source level, derives the projected Euler rule, Noether currents, sector-signed geo-momentum charges, and scalar, fermion, and photon free equations with residual GT phase data. Source normalized LSZ keeps external states and physical cuts ordinary, while uncut internal Wick covariances retain the residual endpoint quotient generated by the GTL-projected field equations. In spacelike transfer, that quotient is represented by a completely monotone Laplace--Stieltjes branch kernel attached only to uncut internal covariances. The hyper-propagator factor is therefore an internal-covariance remnant of the GTL-projected source structure, not an external regulator appended to a completed QED amplitude.