A Generalized Boundary-Flux Ledger for Open Systems Unified Open-System Conservation Notation Across Gravitational Physics, Thermodynamics, and Cancer Biology

Standard conservation laws—the First Law of Thermodynamics, the Second Law, and Newton’s momentum balance—are formulated for closed systems. When applied to open systems with finite spatial boundaries, these laws require explicit boundary-flux terms that are handled correctly but separately in each subdiscipline: Bondi–Sachs theory handles gravitational-wave energy loss, Prigogine’s non-equilibrium thermodynamics handles entropy export, andcontrol-volume mechanics handles momentum flux. No unified cross-domainnotation connects these treatments. We present a generalized boundary-flux ledger : three balance equations with explicit outward flux terms (Φ∞, Ψ∞, Π∞) for energy, entropy, and momentumrespectively, derived by applying the divergence theorem to Einstein’s localconservation law ∇aTab = 0 over finite spacetime regions with explicit boundary decomposition. The derivation introduces no new physics; it provides a common notation framework for the Bondi–Sachs, Prigogine, and control-volumeresults simultaneously. The contribution is cross-domain unification of existing treatments, not new conservation laws. We apply the ledger to six domains: binary black-hole mergers (Module A), pulsar spin-down (Module C), spacecraft momentum accounting (Module D), cellular thermodynamics (Module F), cancer phenotype dynamics (Paper 2), and cosmological structure (Module G). In each case the ledger makes the open-system boundary exchange explicit without adding new physical content.The cancer-state-space section is the strongest computational branch: we develop an attractor-landscape model in (Φ∞, Ψ∞, Π∞) flux space, map PAM50 breast cancer subtypes onto this space, and derive a specific, falsifiable clinical prediction for triple-flux-domain combination therapy in triple-negative breast cancer.Two conjectures are stated and clearly separated from derived results: (i) a structural interpretation of the fine-structure constant α ≈ 1/137 as a dimensionless flux ratio, and (ii) the plausibility of the 1+3+7 M-theory dimensionaldecomposition as the unique complexity-permitting compactification. Neither conjecture is derived from first principles here. Twelve falsifiable predictions testable in 2025–2028 conclude the paper.