Sci - Pre-Geometric Calculus: Master Equations of the Dimensionless Mathematics Framework

Sci - Pre-Geometric Calculus: Master Equations of the Dimensionless Mathematics Framework Armstrong Knight — intent-tensor-theory. com — 2026 This paper is the canonical mathematical reference for the Dimensionless Mathematics framework and the Intent Tensor Theory (ITT) research program. It collects, organizes, and stabilizes the complete equation set across all published ITT papers into a single citable source with frozen notation throughout. The framework is organized into four formally separated layers: admissibility (boundary closure conditions: 𝔦 (W) =0, Dₑff→0), bloom (local structure emergence: Q = Aₜot/ (Θ·Sfree) > 1), persistence (stability through time: Sₛel = R/ (Ṙ·tᵣef) ≥ 1), and bleed (the observable containment factor: β = e^-S*, ρₒbs = β·ρₛubstrate). The pre-geometric free energy analogue 𝒢 = Aₜot − Θ·Sfree is introduced as the central variational object. The complete pipeline (H, ∇H, K, ω) → (𝔦, dₑff, Sₛel) → 𝒢 → S* → β → ρₒbs is presented with full derivations. Cosmological specialization to flat ΛCDM yields Scos = 1/ (3Ω_Λ) = 0. 487 today, the 283 horizon-information identity, the corrected w (z) formula, and the zₐcc ≈ 0. 63 prediction. Six open derivation problems are precisely stated. The paper serves as the mathematical foundation for T4-18 (cosmological constant), T4-19 (dimensional plane error), and T4-20 (Yang-Mills mass gap).