Considering Counting Triangles to Unveiling Temporal Waves

By: John Gavel

For years, my work in Temporal Flow Physics (TFP) has pursued a radical idea: what if spacetime itself—with all its gravitational curves and quantum fluctuations—isn't fundamental at all? What if it emerges from a deeper reality: a network of one-dimensional temporal flows, weaving the universe together moment by moment?

It’s bold, yes—but I believe this view holds the key to a truly unified theory of physics, one that roots both quantum mechanics and gravity in the same temporal fabric.

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From Counting Triangles to Counting Time

My earliest simulations: I counted triangles.

More specifically, I measured how triangular motifs in temporal flow networks dissipated under coarse-graining. The decay rate of these patterns—captured by a parameter I called A₃—served as a stand-in for emergent gravitational effects. If motifs faded predictably with scale, it suggested that macroscopic structure (like spacetime curvature) could arise from microscopic flows.

These "motif-counting" simulations were my proof of concept. They showed that scale-dependent behavior—the essence of renormalization and curvature—naturally emerges in TFP from the structure of flow itself.

But even then, I knew triangles weren’t the heart of it.

TFP isn’t just about static geometry. It’s about dynamic interference between temporal flows. Gravity, in this picture, isn’t a force or a curvature imposed from above—it’s a rhythm, a mismatch, a wave in the unfolding of time itself.

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Unveiling Gravity’s True Mechanism: Temporal Flow Oscillations

At the core of TFP lies a simple but powerful concept: every point in the universe is a bundle of temporal flows, interacting, interfering, and evolving.

Each node in the network represents a temporal flow multiplet—a set of synchronized, one-dimensional flows with:

• Flow amplitude $F_i$: how strong the flow is.

• Phase $\theta_i$: where it is in its oscillation cycle.

• Natural frequency $\omega_i$: its intrinsic rhythm.

• Coupling strength $\lambda_{\text{coupling}}$: how strongly it interacts with its neighbors.

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Gravity from Mismatched Flows

Here's the insight: when these flows are slightly out of sync—in amplitude or phase—they create temporal interference patterns. These mismatches delay neighboring flows, creating ripples in causality itself. These ripples are what we perceive as spacetime curvature.

The effective metric in TFP, denoted $G_{\mu\nu}$, captures this idea:

$$G_{\mu\nu} = \ell_P^2 \left\langle \partial_\mu \delta F \cdot \partial_\nu \delta F \right\rangle$$

Where:

• $\ell_P$ is the Planck length.

• $\delta F = F_i - F_{\text{baseline}}$, with $F_{\text{baseline}} = 1.0$, represents deviations from uniform temporal flow.

• $\partial_\mu \delta F$ is the directional gradient of this fluctuation, estimated from differences between neighboring flows.

This formula lets me compute curvature directly from flow data—no abstract manifold required.

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CPT Violation: A Built-in Asymmetry

TFP doesn't just replicate known physics—it makes bold, testable predictions.

One of them concerns CPT symmetry—the idea that the laws of physics should remain invariant if we flip Charge, Parity, and Time simultaneously. TFP suggests this symmetry is not exact.

The CPT-violating term in my phase evolution equations is:

$$\frac{d\theta_i}{dt} = \omega_i + \lambda_{\text{coupling}} \sum_j \sin(\theta_j - \theta_i) + \delta_{\text{sign}} \cdot \text{sign}(t) \cdot F_i F_j \cos(\theta_j - \theta_i)$$

The $\delta_{\text{sign}}$ parameter introduces a persistent temporal asymmetry, a directional bias in how flow phases evolve. This asymmetry has profound implications—it directly alters the emergent curvature of spacetime.

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New Simulations: Spacetime Emerges From Flow

In my latest simulations, I went beyond counting motifs—I directly computed curvature from dynamic flow behavior. The results were striking:

Topology Shapes Curvature

I tested three network types:

• Lattice Networks (Ordered):

  • Highest oscillation amplitude

  • RMS curvature: 0.003228

• Random Networks:

  • Lowest amplitude and frequency

  • RMS curvature: 0.002117

• Small-World Networks:

  • Intermediate amplitude

  • Highest frequency

  • RMS curvature: 0.002484

Insight: Regularity leads to more structured curvature. Disorder smooths it out. Efficiency of information flow (as in small-world networks) creates complex, subtle geometry.

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CPT Violation Regulates Curvature

On a 2D lattice, I varied $\delta_{\text{sign}}$:

• No CPT violation ($\delta_{\text{sign}} = 0$) → RMS curvature: 0.005185

• Mild CPT violation ($\delta_{\text{sign}} = 0.01$) → 0.003552

• Stronger violation ($\delta_{\text{sign}} = 0.1$) → 0.003328

Insight: CPT violation doesn’t increase curvature—it dampens it. This is counter-intuitive and novel. It suggests that temporal asymmetry may act as a regulator, reducing geometric intensity and smoothing spacetime.

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Amplitude Predicts Curvature

The average oscillation amplitude of flows tightly correlated with RMS curvature. This reveals a deep, quantitative link between the strength of temporal fluctuations and the intensity of gravity itself.

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What Comes Next?

These results mark a major leap for Temporal Flow Physics. They affirm that spacetime curvature and gravity aren't fundamental forces but emergent behaviors of deeper temporal flows. Most excitingly, they suggest that CPT violation—normally considered a fringe possibility—could be a central player in shaping the universe's geometry.

Next steps for me:

• Extend the simulations to include nonlinear topologies, black hole-like regions, and expansion dynamics.

• Explore how these temporal flows interact with quantum field coherence, entanglement, and gauge forces.

• Refine the theory’s observable predictions, especially around CPT asymmetry, and explore experimental routes to test them.

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Conclusion:

From counting triangles to decoding the rhythm of time, my journey in TFP is driven by one belief: that the universe is not built from space and particles, but from time itself—flowing, interacting, and weaving the cosmos from within.

And if that's true, then we’re not just observers of spacetime.
We’re participants in its unfolding wave.