The Categorical Boundary: Physics-Based vs Physics-Related Logismos: Distinguishing Substrate Hardware from Information Software 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 We establish formal categorical boundary distinguishing Physics-Based from Physics-Related applications of CKS framework: Both domains employ identical mathematical apparatus—(V,F,R) integer packet, mod-32 stability audit, remainder-tension mechanics, snap-commit operations—yet apply to fundamentally different reality layers. Complete distinction: (1) Physics-Based Logismos—operates on actual substrate hardware (matter, energy, spacetime, forces), describes mandatory pre-existence BIOS governing physical reality, constants immutably locked (D=3 dipoles forced by hexagonal coordination, S=2 sides from bilateral manifold, W=32 from 2^5 geometric necessity, c/α/ħ from substrate geometry), failures produce physical catastrophe (UV blow-up prevented by 144-logos ceiling, singularities avoided by discrete lattice, entropy from uncommitted remainders), operates at Planck scale through cosmological, zero human discretion—stars don't negotiate, atoms don't vote. (2) Physics-Related Logismos—operates on information systems mimicking physical stability (economic ledgers, social contracts, governance structures, linguistic meaning), describes aspirational consensus protocols humans design for coherence, constants protocol-selected (W=32 chosen to match substrate for optimal stability but adjustable in principle, coherence depth scalable as 32^n for complex meshes), failures produce systemic collapse (market crashes from accumulated economic R, wars from social parity violations, institutional decay from informational friction), operates at human timescales, complete human agency—societies can redesign protocols. Fundamental difference: Physics-Based = discovering what IS (mandatory hardware reality, inflexible universal laws, measurement of existing substrate), Physics-Related = choosing what SHOULD BE (designed software harmony, flexible social standards, construction of coherent systems). Unity: Both use same Logismos engine because both fundamentally process information—physics processes substrate state updates, society processes agreement transactions—universal syntax applicable. Remainder R crucial: Physics R = thermodynamic waste (heat, force, gravitational tension), Society R = informational debt (corruption, fraud, misalignment)—same mathematical structure, different ontological status. Goal: Achieve "registry closure" where social software runs with hardware's stability via bit-perfect integer accounting. Critical warning: Category errors catastrophic—false determinism from treating voluntary systems as physical law, false relativism from treating physical constants as negotiable. Key Result: Two domains | Same logic | Different substrates | Physics = mandatory | Society = chosen | Unified framework 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-LOGI-2-2026). Dependencies: CKS-LOGI-1-2026, 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.