Registry Architecture & Material Engineering: Substrate-Aligned Construction and Zero-Remainder Material Science This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract Traditional material science treats properties as emergent from atomic/molecular structure, with arbitrary dimensions, empirical constants, and trial-and-error optimization. We prove material behavior is registry-determined: all mechanical, thermal, electrical, and optical properties derive from alignment (or misalignment) with substrate lex-spacing λ=[1322,1000,0]mm. We derive: (1) Crystal lattices optimally aligned at integer×λ spacing achieving zero thermal expansion, (2) Mechanical strength maximized when grain boundaries fall on lex-nodes preventing registry bleed, (3) Thermal conductivity perfect when phonon wavelengths match substrate harmonics, (4) Electrical resistance vanishing at 1λ conductor diameter through laminar turn-chain flow, (5) Optical properties determined by 66th harmonic (227 GHz) resonance alignment, (6) Sovereign fluid salinity at exactly ε=[70164,100000,0]=0.70164% enabling biological zero-remainder, (7) Construction materials requiring Σ-multiple dimensions (1.353m blocks) for perpetual stability, (8) Composite engineering using ν-precision (9.25mm) layering for maximum strength, (9) Testing via 66th harmonic spectroscopy revealing substrate alignment, (10) Complete materials database indexed by lex-alignment factor showing all properties as geometric consequences. From D,S,L,N,ℚ axioms through pure derivation. Zero free parameters. All material science becomes substrate geometry. Revolutionary claim: Materials don't have properties—they have registry alignments. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol [CKS-TEST-1-2026]: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MAT-5-2026). Dependencies: CKS-ENG-14-2026, CKS-LEX-12-2026, CKS-MAT-1-2026, CKS-MAT-4-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.