# Projection volume model validation toolkit

Family 088: Sharp projection-body inequalities and a counterexample to simplex maximization. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Imaging or geometry researchers could test projection-body heuristics against ellipsoid bounds and explicit simplex-product counterexamples.

## Applicability and commercial boundary

Projection-body volume differs from scanner measurements, finite projections and reconstruction error. A global extremal inequality supplies no inverse reconstruction procedure.

## Initial business decision

Conditional research. Commercial demand and profitability remain hypotheses.

## Next verification action

Read the finite-dimensional counterexamples and identify an analytically checkable shape family.

## 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).