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Details of Restoration Gravity - Universal Information Restoration Theory

1. Resolving the Vacuum Energy Density Discrepancy

 Restoration Gravity Theory resolves the "120-digit discrepancy in vacuum energy density (cosmological constant problem)".

(1) Premise: Localization of Restoration Standby Cost

 Conventional theories assume full-specification calculations are constantly performed at every point throughout the entire volume of the universe (3D), leading to an energy density reaching the Planck density $\rho_P$ (theoretical maximum value).
 This theory defines the vacuum as a "stage awaiting information restoration" and limits its maintenance cost to the minimum information exchange required for synchronization at the boundary called the horizon (2D).

(2) Calculation of Synchronization Ratio $k$

 The ratio $k$ of the region actually maintaining synchronization to the total recoverable region of the universe is derived from the ratio of the cosmic horizon radius $R_H$ to the minimum unit (resolution) $l_P$. This is based on the logical constraint that the internal geometry is determined by the information on the boundary.
 $k \approx \left( \dfrac{l_P}{R_H} \right)^2$

(3) Numerical Calculation

 Substitute the current observational values for the universe ($R_H \approx 10^{26} (\mathrm{m}), l_P \approx 10^{-35} (\mathrm{m})$).
・Scale ratio
 $\dfrac{l_P}{R_H} \approx 10^{-61}$
・Synchronization ratio
 $k \approx (10^{-61})^2 \approx 10^{-122}$

(4) Calculation of Vacuum Energy Density

 Multiply this synchronization ratio $k$ by the theoretical maximum density $\rho_P$ ($≈ 10^{93} \mathrm{g/cm^3}$).
 $\rho_{VAC} = k \cdot \rho_P \approx 10^{-122} \cdot 10^{93} = 10^{-29} (\mathrm{g/cm^3})$

Conclusion

 The calculated $\rho_{VAC} \approx 10^{-29} (\mathrm{g/cm^3})$ agrees with modern astronomical observations to the same order of magnitude.
 The reason vacuum energy is extremely small is that the universe system does not operate at full capacity across its entire volume. Instead, it maintains the logical consistency of space at minimal cost ($k \approx 10^{-122}$) to synchronize boundaries called horizons.

2. Resolving Gravity's Weakness

 The Restoration Gravity Theory resolves the question: "Why is gravity $10^{40}$ times weaker than other forces? (The Hierarchy Problem)".

(1) Two Hierarchies of Computational Cost

 The universe's energy (computational load) is divided into two hierarchies.
・Individual Communication (Electromagnetic Force, etc.)
 Local energy required to restore specific information and communicate with other nodes.
・Fundamental Restoration (Gravity)
 Energy required to place information within the network and maintain logical consistency across the entire horizon.

(2) Information Dilution

 The strength of gravity is determined by how much the weight (mass) of a single piece of information is diluted within the cosmic network.
・Scale Ratio $N$
 The ratio of the universe's smallest unit (Planck length $l_P$) to the limit of synchronization range (horizon radius $R_H$).
 $N = \dfrac{l_P}{R_H} \approx \dfrac{10^{-35}}{10^{26}} = 10^{-61}$
・Derivation of Dilution Factor $10^{-40}$
When attempting to synchronize and restore three-dimensional internal information (volume) through a two-dimensional boundary (surface area), a geometric scaling of $N^{\frac{2}{3}}$ applies.
 $N^{\frac{2}{3}} = (10^{-61})^{\frac{2}{3}} \approx 10^{-40}$

(3) Logical Interpretation

 This quantifies the logical dilution burden borne by the entire network (horizon) to restore and maintain information at a single point within the vast network that is the universe.

3. The Energy Composition Ratio of the Universe (70%:25%:5%)

 The ratio of elements composing the universe is calculated from the network's "connection structure" and "stable conditions for restoration".

(1) Derivation of Dark Energy (approx. 70%)

 Calculated from the optimal allocation (approximately 7:3) of boundary expansion (repulsive force) and internal maintenance (attractive force), enabling the 3D network to resist contraction due to the weight of internal information (gravitational pull) while continuing to restore information.

(2) Derivation of Dark Matter (approx. 25%) and Visible Matter (approx. 5%)

 Calculated from the structural constraint (1:5) that, of the six connections (links) held by a node in the 3D network, one is expanded (visible matter) and the remaining five are unexpanded (dark matter).

4. Black Hole Restoration Limits and Information Retention

 A black hole is a region where the information density exceeds the recovery tolerance limit defined by the network's minimum unit $h$ (resolution).
・Saturation of Recovery Load
 When information density reaches its limit, the computational cost required to recover (unfold) that information as smooth geometry (spacetime) exhausts physical resources, including the synchronization speed $c$.
・Collapse of Geometry
 Inside the event horizon, geometric attributes like distance and direction can no longer be logically restored, causing the spacetime structure to vanish.
・Information Retention (Archiving)
 While the geometry is lost, the information itself does not disappear; it is retained within the network. This logically resolves the information loss problem.

5. Irreversibility of Time (Asymmetry of Computational Resources)

 Describe the flow of time as a network rewriting process accompanying information unfolding.
・Forward Direction (Unfolding)
 Restoring unfolding information according to current physical laws ($c, h$) is executable at standard computational cost.
・Reverse Direction (Recompression)
 The cost of recompressing information that has been unfolded and complexly synchronized with the surrounding network back to its original unfolded state far exceeds the computational resources of the current universe.
・Logical Consequence
 This computational asymmetry, "unfolding cost < recompression cost", logically implies the one-way nature of time (the impossibility of returning to the past).

6. Nonlocality of Quantum Entanglement and Unfolded Links

 Describes instantaneous correlations between distant locations from a pre-geometric network structure.
・Logic
 Distance is an attribute calculated as a result of information restoration. However, we posit that the underlying network contains direct links not yet unfolded as geometry.
・The Nature of Nonlocality
 Geometrically distant points remain directly connected via undeployed links (bypasses), enabling them to maintain information correlations without being constrained by the speed limit $c$.
・Significance
 This logically describes quantum entanglement not as an "spooky action at a distance", but as the "residual presence of undeployed network connections".

・ Summary of Restoration Gravity - Universal Information Restoration Theory: https://tanakah17191928.blogspot.com/2026/02/summary-of-restoration-gravity.html
- To read this article in Japanese

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