Two-Branch versus Three-Channel Closure Splitting in ECSM: A Minimal Test of Triadic Matter Branching

This paper presents a minimal notebook-backed response-functional test of triadic matter branching in the Emergent Condensate Superfluid Medium (ECSM) framework. A preceding ECSM paper proposed that once ultraviolet or high-frequency response saturation forces coherent propagation to fail, energy may localise into a stable non-propagating response packet. It further argued that such a localised excitation cannot remain a featureless scalar lump if it is to support persistent matter-like structure. A two-branch split can provide polarity, handedness, or mirror imbalance, but stable persistence requires an additional neutral closure channel. The present paper tests that proposal by comparing two possible split channels of a saturated parent excitation: a two-branch mirror split, P → A + B, and a three-channel closure split, P → A + B + C0, where C0 is neutral under the charge-like projection but may carry closure, phase, helicity, or response-load bookkeeping. Using a schematic response functional containing parent load, split cost, closure demand, helicity demand, and branch capacity terms, the scan produces three ordered regimes. At low load the parent remains stable. At intermediate load the two-branch split is favoured. At high load the neutral closure branch becomes energetically selected. The transition points in the reference scan occur at approximately L1 ≃ 1.32 and L2 ≃ 3.56. The result supports the structural ECSM hypothesis that two branches provide polarity, while three branches provide polarity plus closure. The paper does not claim to derive neutrinos, electrons, or Standard Model interactions. It establishes a narrower result: in a finite-response matter-genesis model, a neutral closure channel can become dynamically necessary at high saturation load. The numerical scan is reproducible from the accompanying Jupyter notebook hosted in the ECSM framework repository.