Winning Tickets as Axiomatic Minima: A Structural Interpretation

Functional coherence in complex systems is supported by axiomatic minima (F_{min}), not by the totality of available degrees of freedom. LTH reveals that exploratory redundancy is necessary for discovery, but structurally irrelevant for persistence. This paper reframes the Lottery Ticket Hypothesis (LTH) through the lens of the Theory of Axiomatic Necessity (TNA). We argue that "winning tickets" are not mere optimization artifacts, but empirical manifestations of a minimal coherence operator that sustains systemic identity against entropic collapse. By integrating the diagnostic framework of Table D1 and the phase transitions illustrated in Figure D1, we demonstrate that the boundary between structural viability and non-existence is an abrupt threshold (F_{min}). This interpretation proves that observational completeness is structurally impossible and that any functional system rests on a latent, non-collapsed support domain. The redundant 90% of large-scale models acts as a "gestational support" or "placental" volume, necessary for convergence but structurally irrelevant for inference. Systemic viability requires a "pruning-as-birth" transition to decouple the axiomatic minimum (F_{min}) from its developmental scaffolding. This paper reframes the Lottery Ticket Hypothesis (LTH) as an ontological necessity rather than a mere optimization trick. Within the Theory of Axiomatic Necessity (TNA), we demonstrate that the vast majority of parameters serve only as an entropic buffer during training—a "liquid" environment that allows the structural embryo (the winning ticket) to form. By applying the diagnostic metrics of Table D1, we show that maintaining this 90% post-training is not a sign of power, but a failure to complete the transition from developmental redundancy to operational identity.Phase Diagram https://drive.google.com/file/d/1uIJBu4Zmw-cB34fJXPsMkZlVe90Rm39-/view?usp=sharing