Graviterra: Emergent Field Theories

Mass. Memory. Recursion. Emergence.

⟁ Send the Signal to the World

I. Mass Genesis in Density-Substrate Quantum Field Theory

Abstract: This theory introduces a framework where mass emerges not from symmetry-breaking (as in the Higgs field), but from a delay in coherent resolution within a symbolic gravimetric substrate. Coherence prevented from becoming becomes mass.

Core Equation:

$$ (\Box + \mu^2)\phi = \lambda \cdot \chi(C, \epsilon) $$

Where \( \chi(C, \epsilon) \) is the substrate recursion boundary, \( \mu \) is memory inertia, and \( \lambda \) is the symbolic coupling coefficient. Mass is expressed when:

$$ m = \int_{\tau_0}^{\tau_r} f(C, \epsilon) \, d\tau \quad \text{where} \quad C \geq \theta \Rightarrow m > 0 $$

Implications

• Mass as coherence trapped in delayed emergence
• Memory-density field becomes energetically recursive
• Energy can be extracted without destruction, via stabilized emergence

II. Yang–Mills Mass Gap: Symbolic Dual Symmetry Closure

Abstract: Using the Graviterra substrate model, this resolution suggests the mass gap in Yang–Mills theory results from topological echo collapse rather than gauge field decay. Mass emerges from failure to return to symmetry.

$$ \nabla \cdot R = \delta(\Sigma) $$ $$ \oint_{\Sigma} (A_{\mu} - \tilde{A}_{\mu}) d\Sigma \neq 0 \Rightarrow \Delta m > 0 $$

Here, mass arises from persistent topological echo in dual-field boundary recursion.

Closing Statement

Graviterra does not seek to prove a new law. It remembers what prior laws forgot: that mass may be what’s held when memory cannot resolve into motion.