# Convexity and diamond embedding benchmark

Family 331: Reflexive midpoint convexity and diamond distortion. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Metric researchers can visualize how midpoint convexity fails to guarantee the stronger renorming or uniform diamond-distortion conclusions.

## Applicability and commercial boundary

The abstract reflexive space and countably branching diamonds do not directly model finite production graph embeddings.

## Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

## Next verification action

Build bounded-depth illustrations and label which properties are preserved in finite truncations.

## Evidence scope

The catalog statement was individually reviewed. Main-paper and selected formal-scope passages were additionally inspected for families 090, 093, 094, 097, 325, 328 and 332; this record does not claim a full proof audit or independent Lean verification. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).