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Abstract
The Gravity Hill Theorem is presented as a geometric-dynamical node of the author's physical and mathematical program: a local gravitational potential, packet curvature and Reper foundation may produce a regime in which an effective potential hill gives a sign inversion of the observed acceleration, local retention of trajectories and quasi-periodic domains of motion without direct appeal to an external hidden mass. The restored version is stated cautiously as a working formal formulation inside the KLT/RBD doctrine, pending numerical and observational refinement.
Keywords
gravity hill; packet physics; Reper; KLT; V*P; local potential; packet curvature; effective mass; CGI; PN.2
1. Problem setting
In ordinary mechanics a test body moves in a potential field: acceleration is determined by the gradient of the potential. In Kurpishev Logic this description is not rejected, but treated as a reduction of a more general packet layer. The moving object is represented as event@state C@C, and the field receives a Reper closure Rep=(R,I,U;D), where D fixes the sufficient foundation of the chosen model.
2. Intuition of the hill
A gravity hill appears when the local geometry of the potential and packet curvature produce a domain in which a body does not simply fall toward a minimum, but passes through an inversion of the effective direction of acceleration. This can be read as a local extremum where the metric reduction no longer coincides with the full packet connectivity.
3. Packet model
Let W_phys be a physical reduction of FOS, and let c=(e,s) be a test event@state. The field is encoded by the pair PIX@PEAKS: PIX fixes the event distribution, while PEAKS fixes the state of amplitudes and extrema. The effective potential is written as Phi_eff = Phi_0 + Phi_pkg + Phi_rep, where Phi_0 is the classical part, Phi_pkg is the packet curvature correction, and Phi_rep is the Reper foundation of the observed regime.
4. Theorem statement
Theorem. Let a domain Omega carry an admissible field Reper Rep_g=(R_g,I_g,U_g;D_g), and let the effective potential Phi_eff have a local packet extremum q0. If Dom(Omega), D_g, cr(U_g,I_g;R_g,D_g)=-1 and CGI(Omega)<1 hold, then there exists a neighbourhood U(q0) in which the observed acceleration admits sign inversion relative to the classical reduction a0=-grad Phi_0. Such a neighbourhood is called Kurpishev gravity hill.
5. Proof scheme
The proof proceeds in four steps. First, the domain Omega and the sufficient foundation D_g are fixed. Second, the classical potential is lifted to the packet object Phi_eff. Third, the harmonic Reper closure of the field is checked. Fourth, the sign of the effective acceleration is compared with the classical reduction. If CGI<1, the gap does not destroy the Reper, but is retained as a locally admissible packet deformation.
6. Consequences
First, not every anomalous trajectory requires an external hidden mass; some anomalies may result from reducing packet connectivity to a single metric too early. Second, stable quasi-periodic zones may arise as local retention domains around a Reper extremum. Third, the gravity hill is a test case for KLT/RBD auditing of physical hypotheses.
7. Boundary of claims
This version does not claim to replace general relativity or standard cosmology. It fixes the author's working theorem within Kurpishev packet physics and sets strict conditions for further testing: domain, sufficient foundation, Reper closure, CGI control and numerical modelling.