Arrangement-Dependent Pinning and Phase Transport under Identical Local Controls

Paper 17 in The Geometry of the Critical Line programme. This version supersedes the MANET framing of version 1, “Non-Uniform Transmission Scheduling Under Jamming in a Mobile Ad Hoc Network Model: An ns-3 Simulation Study” (DOI: 10.5281/zenodo.18824396). The earlier interpretation that the scheduling results partially confirmed spectral-smearing or phase-locking transfer from Kuramoto networks, or established an anti-jamming mechanism, is withdrawn. The original files remain in version 1 as the historical record. The present work studies explicitly defined oscillator equations. It does not reproduce or validate the earlier MANET experiment and makes no wireless-network performance claim. Rearranging the same oscillators, matched drives and identity-attached starting phases on a ring can change their certified long-term fate. For a compensated phase-lag model with 16 nodes, validated integration proves convergence to a pinned state under alternation and to an attracting nonzero-winding orbit under clustering. Both arrangements have the same pinned equilibrium, complete Jacobian and forcing budget. The result concerns one specified preparation, whose outcomes were known from a pilot, and an unquantified open neighborhood; it does not estimate basin size. No law connecting the zero-lag barrier ordering below to this positive-lag fate is established. The transport orbit coexists with stable pinning and a distinct reflected attracting cycle. Its primitive winding is (1^8, 0^8), its minimal torus period is near 2.3697677731570383, and all transverse Floquet multipliers have modulus below 0.7171. The drive is set to the homogeneous Sakaguchi collective frequency. For the zero-lag gradient model, a cumulative detuning-imbalance quantity gives an analytic lower bound on the unrestricted energy barrier to a distinct integer lift. A block-rotation path supplies a complementary upper bound. In a joint limit of increasing network size and decreasing pinning strength, the alternating-to-clustered barrier ratio grows without bound, while both barriers vanish along the specified subfamily. The common local decay rate also tends to zero. At fixed pinning strength kappa = 3/20 and coupling K = 3/2, exact computational certificates give ratio intervals (14.7, 28.1) and (16.4, 38.5) at 16 and 20 nodes. The files comprise the manuscript and a scientific supplement containing manuscript source, exact inputs, numerical outcome tables, certification programs, stored certificates, checksums and reproduction instructions. Software code is licensed under the MIT License. The manuscript, documentation and data are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).