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We announce a structure theory for measures on Rⁿ equipped with the parabolic distance. Our results include a parabolic rectifiable Reifenberg theorem for arbitrary Radon measures, qualitative and quantitative characterizations of regular parabolic rectifiability by Jones square functions, and sharp results for Lᵖ beta numbers. The results hold in every parabolic dimension and extend the theories of Edelen--Naber--Valtorta, Azzam--Tolsa and David--Semmes to space-time. The stated theorems and corollaries, together with their proofs, are formalized in Lean~4 with Mathlib.
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Robert Koirala (2026) studied this question.
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