What question did this study set out to answer?

To provide a manual for deriving all known physical, biological, and cosmological constants using Logismos in a framework with no transcendentals.

March 7, 2026Open Access

The Complete Derivation Manual: How to Derive Everything from N=7 Using Logismos in Base-Partigen

Key Points

To provide a manual for deriving all known physical, biological, and cosmological constants using Logismos in a framework with no transcendentals.
Constituent derivation using the CKS framework.
Utilization of nested VFR tuples and rational arithmetic.
Exact calculations of constants with integer ratios and closed rational operations.
Verification of predictions through forensic analysis of empirical data.
Demonstrated derivation of physical constants without using π or e.
Exact representation of constants using integer ratios and nested VFR tuples.
Calculated specific biological constants like C. elegans cell counts exactly.
Verified that derived predictions align with empirical data through integer multiple ratios.

Abstract

The Complete Derivation Manual: How to Derive Everything from N=7 Using Logismos in Base-Partigen 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 present the complete operational manual for deriving all physical, biological, and cosmological constants from N=7 using Logismos VFR notation in base-Partigen (℘=32^ (-1) ). This is pure rational arithmetic—no transcendentals, no limits, no approximations until final display. Every derivation uses nested VFR tuples operating exclusively in ℚ. We demonstrate: (1) how to bootstrap from N=7 to generate W=32 and ℘=32^ (-1) using only integer ratios, (2) how nested VFR tuples V₁, [V₂, F₂, R₂, R₁] allow exact representation of all constants, (3) how to derive αEM^ (-1) =137+36, 1000, 0/1000 as pure ℚ without invoking π or e, (4) how to calculate C. elegans cell counts 959=1024×[4, 7, 0, 1, 0] exactly, (5) how temporal constants like τ=15+19, 100, 0/100 emerge from ℚ-only operations, and (6) how to verify every step maintains ℚ-closure. This is mathematics, not physics approximation. Every operation is a ratio of integers. Every result is exact. The universe computes in ℚ using VFR; we show you how. Key Innovation: Nested VFR allows exact ℚ-representation of all substrate constants without transcendentals. 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-11-2026). Dependencies: CKS-LOGI-10-2026, 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.

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