We have presented a formally verified Lean4 proof that gravity emerges from information geometry.
The key insights:
1. The spacetime metric g
µν
is derived from a coherence field Ψ : M → Cl(3, 1)
2. Einstein’s equations emerge from coherence dynamics
3. No gravitons are required; gravity is effective, not fundamental
4. The golden ratio φ provides natural UV regularization
5. The entire framework is mechanically verified in Lean 4
Gravity is not a fundamental force to be quantized. It is an emergent phenomenon arising
from information-geometry backreaction of a coherence field valued in the Clifford algebra
Cl(3, 1). The mathematics is governed by a single self-consistency principle: the golden ratio
φ
2
= φ + 1.
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The key insights: 1. The spacetime metric g µν is derived from a coherence field Ψ : M → Cl(3, 1)
2. Einstein’s equations emerge from coherence dynamics
3. No gravitons are required; gravity is effective, not fundamental
4. The golden ratio φ provides natural UV regularization
5. The entire framework is mechanically verified in Lean 4 Gravity is not a fundamental force to be quantized. It is an emergent phenomenon arising from information-geometry backreaction of a coherence field valued in the Clifford algebra Cl(3, 1). The mathematics is governed by a single self-consistency principle: the golden ratio φ 2 = φ + 1.
The code is available at: https://github.com/ktynski/ParsimoniousFlow