# Inverse boundary measurement evidence workbench

Family 365: Joint metric and connection recovery from one boundary patch. First source-informed review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Tomography research teams can distinguish smooth joint metric/connection identifiability on a single open patch from rough scalar-conductivity counterexamples and gauge ambiguity.

## Applicability and commercial boundary

The latest statement uses an ideal zero-frequency boundary operator, smooth data, dimension at least three and a trivial rank-two Hermitian bundle, with recovery only up to boundary-fixing diffeomorphism and unitary gauge. It supplies no finite noisy reconstruction guarantee. The formal scope covers only the older bounded measurable scalar nonuniqueness result.

## Initial business decision

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

## Next verification action

Implement versioned theorem contracts and a measurement-versus-assumption gap report; do not label a finite electrode reconstruction as formally unique.

## 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

- [Determination of a metric and a unitary connection from one boundary patch](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Determination-of-a-metric-and-a-unitary-connection-from-one-boundary-patch-October-5-2026/paper.pdf)
- [Smooth anisotropic uniqueness in the Calderón problem from one boundary patch](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Smooth-Anisotropic-Uniqueness-in-the-Calderon-Problem-from-One-Boundary-Patch-September-24-2026/paper.pdf)
- [Nonuniqueness for bounded measurable scalar conductivities in three dimensions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonuniqueness-for-Bounded-Measurable-Scalar-Conductivities-in-Three-Dimensions-September-23-2026/paper.pdf)
- [Selected formal scope](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/365.md)