# Inverse boundary measurement evidence workbench Initial decision: **Prototype evidence workflow**. First dossier, 9 October 2026 Australia/Brisbane. Buyer demand, commercial novelty and profitability are unvalidated. ## Research finding The latest family 365 paper claims that ideal zero-frequency measurements, with inputs and observations on one arbitrary nonempty open boundary patch, determine a smooth metric and smooth unitary connection on a trivial rank-two Hermitian bundle in dimension at least three. Determination is up to a diffeomorphism and unitary gauge fixing the observed patch. An older paper in the same family gives two distinct uniformly positive bounded measurable scalar conductivities with identical full boundary data. The family formal document covers only that older nonuniqueness result. Regularity and version are therefore part of the product contract. ## Problem and buyer An industrial impedance-tomography R&D team or an academic imaging software group needs to explain what an inverse experiment can identify. A reconstruction may fit its measured channels while depending strongly on mesh, regularization, model class or selected electrodes. The initial buyer is the team commissioning an experimental model review, rather than a clinical end user. ## What the finding could enable A versioned inverse-problem contract framework can connect reconstruction reports to exact identifiability assumptions. New research directions include same-patch experimental studies, joint metric/connection toy models and explicit gauge-equivalence reporting. The immediate software value is detecting unsupported inference from an ideal continuum uniqueness theorem to a finite noisy experiment. These are applications proposed from the findings; the papers do not supply an operational imaging device. ## Technical and commercial limits The full boundary operator contains infinitely many ideal tests. Finite electrodes, bounded frequencies, uncertain boundary shape, discontinuous material coefficients and measurement noise introduce separate inverse problems. Gauge-equivalent representatives cannot truthfully be sold as uniquely recovered physical coordinates. The newer recovery claims need expert proof review and are outside the inspected formal scope. A regularity assertion in an input manifest is unverified unless accompanied by appropriate evidence. ## Minimal architecture Model manifest -> source/version resolver -> statement and scope mapping -> assumptions and gauge record -> electrode/patch measurement manifest -> reconstruction-run import -> sensitivity and held-out evaluation -> gap report. Each obligation records supported, contradicted or unknown status and a human-readable evidence reference. The report distinguishes a published statement, a selected formal statement, a static audit and an observed numerical experiment. A connector can begin with EIDORS exports, without executing imported proof code. ## Existing alternatives and differentiation EIDORS already supplies forward and inverse impedance/diffuse-optical modeling software. Its own tutorial demonstrates how modeling and reconstruction choices can bias an inverse result. A new forward solver alone would enter an established ecosystem. The proposed distinction is source-linked identifiability and measurement-coverage review integrated with an existing solver, with an explicit comparison to that team's manual review process. [EIDORS](https://eidors3d.sourceforge.net/), [EIDORS bias tutorial](https://eidors3d.sourceforge.net/tutorial/cheating_EIDORS/tutorial210-cheating.shtml). ## Monetization hypothesis Test an AUD 8,000–20,000 scoped model review for an R&D group and an AUD 500–1,500 monthly team plan only if repeated reports save specialist time. These are proposed prices, not customer evidence. At an illustrative AUD 12,000 review price, 40 expert hours costed at AUD 180/hour consume AUD 7,200 before support, software maintenance, sales and overhead. Contribution before those other costs is AUD 4,800; exceeding roughly 67 such expert hours consumes the full fee. An expert-service bottleneck must be reduced or priced honestly. ## Validation experiment Create three model contracts: a smooth same-patch ideal operator, a finite-electrode approximation and a rough scalar conductivity case. The tool must preserve gauge ambiguity, flag missing finite-noise stability evidence and prevent the newer recovery statement from inheriting the older formal badge. Compare review time and missed scope gaps against a manual checklist on three existing public model examples. No customer outreach is performed under this research task. ## Conditions to reject or defer Reject if buyers need only established numerical inversion and do not pay for evidence review, if review costs exceed the fee, or if a repeatable scope report cannot improve on their current process. Defer clinical claims, high-stakes certification, new physical hardware and new uniqueness assertions until independent expertise and appropriate validation exist. ## Next concrete action Build the source-and-obligation contract linter with adversarial version and finite-measurement fixtures. Extract the exact latest theorem and its gauge action before designing a numerical reconstruction experiment. ## Pinned research sources - Family 365: [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). - Family 365: [selected formal scope](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/365.md); not independently checked here. The repository statements are treated as source claims. No full proof review, buyer interview or clinical/engineering certification has been completed.