Paper 122F: Cooperative Vacancy Reconstruction and a Puzzle-Like Contact-Motif Transport Architecture in Holosphere Mechanics

Abstract

Paper 122F investigates whether local particle-related organization can propagate through a densely contacting Holosphere network without requiring one permanent rigid body to move through the surrounding structure. The calculation begins from thirty-seven inherited states containing twenty-one owner-resolved vacancies distributed among three relational sectors. Rigid triangular and tetrahedral contact motifs occur naturally in this geometry. A rigid tetrahedral carrier is blocked when the surrounding Holospheres remain fixed, but finite cooperative motion of neighboring Holospheres provides first-order release freedom at both source and reconstructed target configurations. A constrained puzzle search then finds finite sequences in which temporary triangular and tetrahedral motifs successively reconstruct the vacancy pattern. The deepest sequence contains six alternating steps while preserving the complete vacancy and ownership ledgers. The reconstruction graph also contains one thousand one hundred forty exact owner-closed structural cycles. Individual vacancy tracking confirms exact token closure for selected mappings, but the subsequent signed mechanical audit finds no unique nonzero circulation direction. The results therefore support cooperative, puzzle-like propagation of an evolving vacancy and contact organization rather than translation of a permanent rigid carrier. Complete continuous trajectories, persistent circulation, a physical gluon mechanism, and confinement remain to be derived.