Ronen Weinberg

Machine-Checked Simplicial Chain Complexes over F_2 and Metric Filtration Invariants for Relational Resolution Theory in Lean 4

We present a self-contained, machine-checked formalization in the Lean 4 theorem prover (Mathlib4) of the core algebraic-topological invariants underlying discrete metric filtrations in Relational Resolution Theory (TRR 3.0). Specifically, we formalize: (1) the monotonicity and d...

Methodological Audit of Large-Scale Signals in Cosmicflows-4: Shuffle-Null Persistent Homology and the Bulk Flow by Distance Indicator

We audit two large-scale signals in the Cosmicflows-4 (CF4) compilation: (i) an excess of H1 persistent-entropy ordering relative to an angularly shuffled null, and (ii) the cosmic bulk flow at 90–130 Mpc. (i) In nested spheres the contrast reaches z_shuf ≈ 8σ, and a core-excised...