01
Microscopic Distinguishability and the Data of Geometric Reconstruction
What geometric data are actually fixed by distinguishability?
Open paper overviewGrokRxiv research series · 2026
Gravity is the infrared consistency law of reconstructed information geometry.
The metric is treated as a compressed description of coarse-grained quantum distinguishability. The series asks exactly which additional assumptions make Einstein dynamics the leading long-distance consistency equation.
Consistency trace
The claim, decompressed
- 01Stateρ(λ)
- 02DistinguishabilityD(ρ‖σ)
- 03Reconstructionℜμ
- 04Consistency𝒞μν = 0
Eight linked arguments
One claim, tested from eight directions
Each paper isolates one inference that is often compressed in informal accounts. Assumptions stay visible; distinct derivations are compared without being merged.
02
Infrared Axioms for Reconstructed Lorentzian Geometry
Which assumptions turn a reconstructed metric into an infrared field?
Open paper overview03
The Infrared Consistency Equation for Reconstructed Metrics
When does stationarity produce the Einstein equation?
Open paper overview04
Relative Entropy, Entanglement Equilibrium, and Linearized Gravity
Which first-law arguments imply gravitational constraints?
Open paper overview05
Reconstruction Defects, Diffeomorphism Ward Identities, and Conservation
How is geometric and matter mismatch encoded locally?
Open paper overview06
Renormalization of Reconstructed Geometry and Metric Beta Functionals
When can scale consistency be written as a metric fixed-point equation?
Open paper overview07
Newton's Constant as the Stiffness of the Infrared Metric
In what sense does 1/G measure resistance to metric deformation?
Open paper overview08
An Infrared Reconstruction Consistency Theorem
What theorem survives when every reconstruction hypothesis is explicit?
Open paper overviewFormal boundary
Machine-checked dependencies, explicit physical obligations
Lean 4
Encodes the Hessian sign convention, tangent-completeness implication, first-law bookkeeping, defect identities, beta-functional relation, stiffness scaling, and the final dependency theorem without unchecked declarations.
Haskell
Finite models exercise coefficient arithmetic, dependency removal, rank-deficient reconstruction maps, and counterexamples. They test implementations; they do not certify continuum physics.
explicit hypothesesleading defect equation
The universality question
The work is not to rename geometry as information.
It is to identify the microscopic systems whose coarse-grained reconstruction is local, Lorentzian, diffeomorphism-redundant, stable, and complete enough for the consistency equation to become gravitational dynamics.
Begin with microscopic distinguishability