Gravity from Information Geometry: A Lean 4 Formalization of Emergent Spacetime
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Re: Gravity from Information Geometry: A Lean 4 Formalization of Emergent Spacetime
#2We 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.
The code is available at: https://github.com/ktynski/ParsimoniousFlow
Re: Gravity from Information Geometry: A Lean 4 Formalization of Emergent Spacetime
#3We 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…
I'd be curious to hear what you think of: New Framework Proposes Spacetime as an Emergent Irreversible Information Process https://news.ycombinator.com/item?id=46674020
Re: Gravity from Information Geometry: A Lean 4 Formalization of Emergent Spacetime
#4Paywall. Unfortunately, in this day-and-age, the question arises: how much of this was generated by AI agents?
Re: Gravity from Information Geometry: A Lean 4 Formalization of Emergent Spacetime
#5Paywall. Unfortunately, in this day-and-age, the question arises: how much of this was generated by AI agents? https://news.ycombinator.com/item?id=44907440#44907441
For me, at least with desktop Firefox with uBlockOrigin, I can scroll through the full 17 pages to the bottom. Without having to 'login' with/via whomever.
Re: Gravity from Information Geometry: A Lean 4 Formalization of Emergent Spacetime
#6You should compare notes with this guy, who derived everything with pi instead of the golden ratio: