Linear Density as the Primary Gravitational Constraint

Title: Linear Density as the Primary Gravitational Constraint: A Structural Audit of the Gravitational Constant

Description:

This paper provides a forensic audit of gravitational geometry, establishing that the Schwarzschild relation implies a constant linear density ($\lambda$) which serves as the primary ontological constraint of the manifold. By defining the relationship between mass, length, and time as a commensurate triadic identity ($\iota c\lambda=1$), the framework reveals the gravitational constant G to be a secondary scaling artifact rather than a fundamental constant of nature.

Using the same Triple Product logic found in classical thermodynamics, the paper demonstrates that the Newtonian gravitational potential is recovered exactly as the isotropic readout of a one-dimensional linear ledger. A central discovery of this audit is the identification of the Isometric Hinge at 35.26°—the geometric coordinate where linear and volumetric measures reach parity. At this alignment, the framework yields a 0.000000% variance from established orbital data for major Solar System bodies (Moon, Earth, Jupiter, Sun), confirming the mechanical precision of the triadic ledger.

Key Highlights:

• Mechanical Redundancy of G: Deconstruction of the gravitational constant into a composite of the Mass Torque ($1/c$) and the linear invariant ($\lambda$).

• Forensic Parity: Absolute zero-variance reconciliation with classical orbital baselines via the Isometric Hinge.

• Inverse Equivalence Gauge: A simple graph that plots the inverse equivalence of lambda, c, and gravitational potential as a universal invariant. 

• Thermodynamic Symmetry: Alignment of the gravitational manifold with the equilibrium logic of closed triadic systems.