ESSC v25: Triadic Branch Gates and Branch-Dependent Projection Rotation in the ESSC Map

ESSC v25 reports a triadic reformulation of the ESSC map. The main result is that the system is best organized not first by a single compressed coordinate or by the v24 observable backbone alone, but by a layered branch architecture built from center, periphery, and signed radial connection. In this reading, the ESSC map is most naturally resolved into three observational branches: low-side, high-core, and high-pair-residual. The paper shows that branch switching is governed by a simple two-stage geometric gate written in terms of center and periphery. First, sufficiently counter-directed center commitment separates the low-side branch. Among the remaining systems, a center-leading amount relative to periphery separates the persistent high-pair-residual sector from the realized high-core branch. Signed radius is not required for the top-level branch cut. Instead, once branch identity is fixed, signed radius acts as a branch-dependent internal projection rotator, most coherently on the high-core branch. A further result is that the previously used compressed high-side quantity and the v24 observable size-velocity backbone are both retained but reassigned to lower descriptive layers. In this architecture, the triadic branch gate comes first, branch-internal signed-radius response comes second, and compressed or observable frozen high-side forms come third as subordinate summary layers. The paper emphasizes that this is an observational and structural result within the current tested setting, not yet a first-principles derivation or a claim of final universal closure.