Resonance‑Based Subspace Dynamics (RBS‑D) — Publication No. 26 The S₈ Field Body: Geometric Realization of a Planetary Operator (Framework 2)

Resonance‑Based Subspace Dynamics (RBS‑D) — Publication No. 26 is part of Framework 2 of the RBS‑D research program. While Framework 1 (Masterpaper 00 and Publications 1–24) established the mathematical, computational and experimental foundations of RBS‑D, Framework 2 focuses on the structural interpretation and classification of physical state forms. Publication No. 26 introduces the S₈ Field Body, a geometric and functional operator that represents the horizontal field architecture of a planetary system. The S₈ Field Body integrates: a 5‑layer vertical vector (U1, U2, r, φ, τ), an S₈ surface matrix of eight resonant field surfaces, an S₆ axis order (orthogonal and diagonal axes), a 13‑mode resonance manifold, a cosmic coupling shell τ, and a multi‑component stability operator. The publication demonstrates how planetary field structures, resonance envelopes, directional axes and cosmic interaction layers can be expressed through a unified operator algebra. It establishes the S₈ Field Body as a complete planetary analogue, fully compatible with ATM‑15, ATM‑31, and ATM‑63, and integrates it into the broader structural logic of Framework 2. Publication No. 26 continues the development of a universal structural language for mathematics, physics and complex systems, connecting geometry, topology, nonlinear dynamics, resonance theory, operator theory and planetary field science.