Proto-Spinor Closure and Worldsheet Encoding in Modal Triplet Theory

This paper develops a local shadow bridge between proto-spinorial triadic closure and the worldsheet encoding already derived in the Modal Triplet Theory string series. The upstream input is the proto-spinor triadic carrier Ξ = (Ψ, C, L, N), where Ψ is the proto-spinor closure object, C is the circle bookkeeping carrier, L is the lens redundancy-transport carrier, and N is the nil termination carrier. The downstream input is the bounded worldsheet projection from the coherent fixed-point sector to a two-dimensional string description. The central result is a slab-local shadow-bridge theorem: whenever an admissible slab supports both a Lorentzian spinorial or twistor encoding and the bounded worldsheet projection, the resulting Weyl, Dirac, and twistor variables and the resulting open and closed worldsheet sectors are overlapping downstream encodings of the same carrier. Closed sectors preserve the return-consistency role of circle bookkeeping, boundary-sensitive sectors preserve the transport and anchoring role of lens transport, and discrete admissible excitation survival preserves the selection role of nil termination. The paper also clarifies the status of two-dimensionality. It does not claim to derive from scratch that triadic closure uniquely forces a worldsheet. Instead, it shows that triadic closure can force a carrier-preserving extended chart beyond a purely pointwise encoding, and that the MTT string series already provides a controlled two-dimensional realization of such a chart through the bounded worldsheet projection. In this framework, strings are not primitive filaments but downstream shadows of proto-spinorial triadic closure. A second main result is a local bridge theorem near alignment. Under explicit regularity hypotheses, the quadratic admissibility burden on the worldsheet side matches the quadratic admissibility burden on the carrier side up to controlled cubic remainder. The paper then gives constructive normal-form models for the closed-sector circle block, the open-sector lens block, and the local nil-sector survivor block, and shows that these assemble into a combined local synthesis theorem. The publication-level claim is therefore not a global string/proto-spinor equivalence, but a blockwise constructive local equivalence of admissibility burdens on common admissible overlap slabs.