# Infinity-harmonic interpolation regularity reference

Family 377: Interior $`C^{1,\alpha}`$ regularity for infinity-harmonic functions. First source-informed review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Interpolation and PDE researchers can track the claimed interior differentiability of bounded infinity-harmonic functions in dimensions at least three.

## Applicability and commercial boundary

The Hölder exponent and constants are dimension-dependent and not explicit. No endpoint or boundary regularity is asserted. A numerical interpolator is not automatically infinity-harmonic or accompanied by a usable mesh-error rate.

## Initial business decision

Conditional research. Commercial demand and profitability remain hypotheses. Research usefulness is not evidence of a buyer budget.

## Next verification action

Inspect effective estimates and identify an independently verified solver convergence result before promising a quantitative interpolation certificate.

## Evidence scope

The catalog statement and main-paper abstract or introductory theorem passages were individually reviewed. Available family-level scope documents were inspected, with attention to version differences and exclusions. This is a first application triage, not a full proof audit or independent Lean verification. Family 376 has nine paper abstracts inspected; selected scopes are not assumed to cover all nine papers in full. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Pinned sources

- [Uniform Interior $`C^{1,\alpha}`$ Estimates for Infinity-Harmonic Functions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026/interior-c1-infinity-harmonic.pdf)