Collapse-Web: A Mathematical Constraint Organism

Collapse-Web: A Mathematical Constraint Organism This work presents a constraint-field organism whose behaviour is defined by asingle mathematical chain linking structural inputs to viability outputs. Arraysspecify functional families, each generating a corresponding system of ordinarydifferential equations. These ODE families determine the subordinate variablesS, F , σ, which together form the compound viability vector Ω.The admissible region of Ω is the envelope of the organism: the space inwhich all functional families yield real, stable solutions. Projection, mass, andcollapse are not independent phenomena but local expressions of Ω within thisenvelope. Collapse is defined as the viability-pruning operation that retires anybranch whose ODE families lose real solutions. The organism therefore exhibitsinverse combinatorics: increasing structural complexity contracts the admissi-ble outcome space rather than expanding it. This Ω-bounded combinatorialregime produces a stable, self-regulating mathematical organism whose dynam-ics arise entirely from constraint geometry rather than generative expansion.The totality of the system is the chain itself; all behaviours emerge from itsstructure.