Fundamental Dynamic Structures II: Topological Matter and Prototype Interaction Channels

Within the Fundamental Dynamic Structures (FDS) program, we develop a two-dimensional topological-matter sector in a logarithmic Schrödinger medium. Defects are occupation zeros carrying wrapped plaquette winding inherited from the FDS network core (Paper A). In the autonomous focusing-droplet sector, the tested m = 1 and m = 2 vortex branches are dynamically unstable and can lose winding through the zero-density exterior; this is contrasted with externally trapped zero-background vortices (spectrally stable in cubic GP: Kollár; Kollár & Pego) and with vortices embedded in the untrapped repulsive medium. A structure-preserving finite-volume Bogoliubov–de Gennes analysis of embedded vortices — parameter-free after scaling in the *infinite-domain* equation, a specialty of the logarithm — finds no complex or negative-Krein core-localized modes for m = 1 in the tested channels; for m = 2, a core negative-Krein mode whose interaction with discretized phonon levels produces **alternating real and complex finite-volume resonance windows** (complex throughout R = 18–48 and at every scanned radius R = 108–160; real at R = 88–104 at fixed spacing h = 0.02, where the core mode and a phonon mode are separately visible); and four strongly localized negative-Krein core modes for m = 3, with an observed finite-box resonance window in the ℓ = 2 channel. These results define a **finite-volume charge-selection hierarchy favoring primitive unit winding — unit winding is distinguished by the absence of detected negative-energy core structure, while higher winding develops such structure with increasing multiplicity**; the infinite-domain (radiative vs. discrete-eigenvalue) status of both m = 2 and m = 3 remains open. Real-time simulations qualitatively reproduce cluster-resolved m = 2 → 1+1 splitting, while disassembly of a nonstationary imprinted m = 3 state is retained as a protocol observation rather than a stability result. Vortex–antivortex dipoles approach the point-vortex limit (v·d → 1.010), and local pair-energy slopes move toward 2π. A separate focusing-gausson prototype produces similar conservative early accelerations for three probes spanning an 8:1 inertial-mass range; mass independence after verified phase locking remains a specified conjectural test. Maxwell theory and gravity are not derived. In three dimensions the present scalar sector supports S¹ vortex lines; a Hopf/Vakulenko–Kapitanskii sector would require an enriched S²/ℂP¹ order parameter and a Skyrme-type stabilizing term.