Considering Counting Triangles to Unveiling Temporal Waves

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  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. 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 sp...
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Spacetime temporal symmetry breaking

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 matrix formulation to capture the relationship between time and space:


T = [

[t_11, t_12, t_13, ..., t_1n],

[t_21, t_22, t_23, ..., t_2n],

[t_31, t_32, t_33, ..., t_3n],

...

[t_m1, t_m2, t_m3, ..., t_mn]

]


Where the matrix T represents the temporal dynamics and rate interactions at different points in time and space.


And the transformation between time and space was expressed as:


[r_1(t), r_2(t), r_3(t)] = S × T


Where the matrix S contained the transformation coefficients that mapped the temporal dynamics (T) to the spatial coordinates (r_1, r_2, r_3).


Now, with the incorporation of temporal symmetry breaking, we can further refine this matrix-based representation:


T = [

[t_11 + δO_11, t_12 + δO_12, t_13 + δO_13, ..., t_1n + δO_1n],

[t_21 + δO_21, t_22 + δO_22, t_23 + δO_23, ..., t_2n + δO_2n],

[t_31 + δO_31, t_32 + δO_32, t_33 + δO_33, ..., t_3n + δO_3n],

...

[t_m1 + δO_m1, t_m2 + δO_m2, t_m3 + δO_m3, ..., t_mn + δO_mn]

]


In this matrix T, each element t_ij includes the corresponding temporal symmetry breaking term δO_ij, which represents the fluctuations or deviations from the average temporal dynamics at that particular point in time and space.


The transformation equation would then become:


[r_1(t), r_2(t), r_3(t)] = S × (T + ΔT)


Where ΔT is a matrix containing the temporal symmetry breaking terms δO_ij, capturing the influence of these temporal fluctuations on the emergence of spatial dimensions.


This matrix-based representation elegantly aligns with the concept of incorporating temporal symmetry breaking into the spatial emergence equation. So, it allows for a more comprehensive and integrated modeling of the interplay between time, temporal fluctuations, and the manifestation of spatial dimensions.


With temporal symmetry breaking terms directly into the matrix T, and then incorporating that modified temporal matrix into the transformation to spatial coordinates, the combination captures the coupling between the temporal fabric and the emergence of space.

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