Cost and Admissibility: A Structural Constraint in the Triaxial Existential Field

Abstract This paper makes explicit a constraint implicit across the Triaxial Existential Field (TEF) programme: admissible persistence is never free. “Cost” is defined structurally as the unavoidable asymmetry that any persistence-capable configuration must incur under Intention‑to‑Exist (ItoE), not as energy, suffering, entropy, or value. We show that TEF entails that nothing admissible persists without cost, because coherence, reflexivity, and participation jointly require the non‑refundability of operational distinction. Cost is thereby identified as the operational signature of admissibility, and existential/operative modality is fixed as persistence under that constraint. The argument resolves the null‑equivalence objection at the constraint and structure registers without revising TEF’s primitive set. Descriptive interfaces with identity, entropy, cosmic expansion, consciousness, and ethics are then provided with explicit scope limits and failure conditions. No new primitives are introduced; ontology remains locked. This paper is defensive and consolidative; it introduces no new explanatory resources.