Differential Folding Topological Constraint Framework: A Minimal Phenomenological Model for Discrete Folded States, Capacity Constraints, and Residual Stability

This work introduces the Differential Folding Topological Constraint Framework(DFTCF), a minimal phenomenological mathematical model for describing discretefolded states under capacity limitations and residual stability conditions. The framework defines a discrete configuration space, a non-negative foldingcost functional, and a global capacity constraint expressed as σ + ε ≤ Z, where σ represents the ordered folding contribution, ε represents residualavailable capacity, and Z represents the total capacity of the underlyingmathematical substrate. Discrete stable configurations are characterized through a residual function R(N*) = 0, where the stability residual maps discrete folding indices into a real-valuedstability condition. The existence of such solutions is treated as amathematical assumption requiring further analytical investigation. A candidate discrete mode with N = 58 is introduced as an external candidateparameter rather than a derived physical constant. The framework furtherproposes an antisymmetric observable mapping based on orientation-dependentresponse differences, providing a possible future falsification pathway. DFTCF is not intended as a replacement for established physical theories.Instead, it provides a phenomenological mathematical architecture for studyingcapacity-constrained discrete states, emergent structures, and possibleconnections between topology, information constraints, and observablesymmetry-related responses.