DPF Series - High Gain as a Threshold Product in DPF Terrain: Why sulfur-linked buffering and structured hydration govern volatility vs integration, Lantern of Sulfur, Concept B2, v2026.12

This preprint defines high gain in Directional Pressure Failure (DPF) terrain as threshold proximity within a constrained distributed-load biological system. Building on the Vertical Terrain Axis framework of Lantern of Sulfur (LoS), Concept B2 formalizes a material compliance gate: X = E × Iᵥ × Iₜ × B Where execution direction (concentration vs redistribution) is determined not by input magnitude but by the product of: E — Exit availability / permission Iᵥ — Vascular interface integrity (glycocalyx) Iₜ — Tissue transmission integrity (ECM / interstitium) B — Buffering medium capacity (sulfur-linked buffering / redox / charge–water behavior) When X falls below a state-dependent threshold T(s), identical inputs execute as upward pressure concentration (DPF). When X meets or exceeds T(s), execution proceeds as downward redistribution (coherence). This module clarifies sulfur-linked buffering and structured hydration not as supplement strategies but as material properties governing interface compliance and load transmission. The Acid Window is formalized as a timing-dependent execution surface in which exit permission and buffering margin align to permit redistribution without increasing force. No treatments, dosing strategies, or clinical protocols are proposed. This paper defines portable operators used by subsequent DPF / LoS modules. This work is part of the Lantern of Sulfur (LoS) framework, a systems-level model of electrolyte balance, RAAS signaling, and physiological coordination. For the complete Lantern of Sulfur framework, reading order, and updated convergence dynamics materials, see the Lantern of Sulfur Master Index (Concept DOI): https://doi.org/10.5281/zenodo.17915492