What this proves — and what it does not

Every artifact in this portfolio has a "Scope, honestly" section. This is the same argument in one place, because the distinction matters more than any individual tool and it is the thing most likely to be misread from a green result.

Necessary, not sufficient

The five laws, the screening ceiling, the certified bound — all of them are necessary conditions. A physically realizable network must satisfy them. It does not follow that satisfying them makes a network realizable, or correct, or a good model of the thing you built.

A perfectly passive, perfectly reciprocal, perfectly causal model of entirely the wrong structure passes every check in this portfolio.

So the honest reading of a green result is: nothing was caught. That is genuinely worth having — it rules out a class of failure that is otherwise invisible and that simulators propagate silently — and it is not validation.

Admissibility is not accuracy

This is the same point in the vocabulary the tools use.

• Admissible: could exist. The laws test this.
• Accurate: matches the thing you fabricated. Nothing here tests this.

The only way to establish accuracy is comparison against measurement or against a converged field solve. No tool in this portfolio does either, and none claims to.

Computational, not measured

Nothing here has touched a probe. Every number in every artifact is computed. The corpus is synthesised from closed-form models, the coupling reference models are thin-wire forms in a homogeneous medium, and the certified bound is a theorem about a model.

Where a number came from something that is not in the release, the artifact says so at the number rather than in a footnote. Three such figures exist across the portfolio and each is labelled where it appears.

A theorem about a model is not a theorem about Maxwell

screening-ceiling publishes a genuine machine-certified result: for every layout in a four-parameter family, k ≤ 0.909090909091. Interval branch-and-bound, 237,490 certified leaves, zero failure regions.

That is a theorem about a monopole-closure model — a zero-parameter analytic multiple-scattering approximation. It matches a boundary-element reference to 0.081% in the exact two-cylinder limit, and the closure-versus-solver gap is an additive, disclosed, unresolved term that is never absorbed into the bound.

That 0.081% is the one figure on this site you cannot re-derive from published code: it came from the boundary-element solver used to develop the closure, which is not part of any release here. It is quoted because it bounds how much trust the closure has earned, and a reader is entitled to know which numbers are checkable and which are taken on our word. Everything else on these pages is reproducible with the commands beside it.

The distinction is not pedantry. A reader who takes it as a statement about Maxwell's equations has been misled, and the dataset's own scope line travels with the data in theorem.json precisely so that cannot happen quietly.

Sampling cannot prove; it can refute

The browser demo lets you move four sliders and hunt for a layout that breaks the certified bound. You will not find one — but the reason matters. Sampling a continuum establishes nothing about the points you did not sample. What sampling can do is refute, and handing a skeptical reader a cheap way to try to catch us being wrong is the point of shipping it.

The same applies to interval-core's self-check: it samples, so it can find a broken enclosure and cannot certify a correct one. It is evidence, not proof.

Where a law firing is not a defect

The clearest case in the portfolio, and the one that most often surprises people:

A ferrite isolator is real, buyable hardware, and it fails reciprocity.

Its medium is non-reciprocal, so S ≠ Sᵀ is the device working correctly. The check firing there is a true positive for the law and a false alarm for the device.

sparam-conformance keeps such a case in its corpus deliberately, because any honest tool has to handle it. A checker that treats every law failure as a defect will reject legitimate hardware; one that suppresses reciprocity to quiet the noise goes blind to the transposed-reshape bug the law exists to catch. The right answer is neither — it is to record that non-reciprocity is expected for that file.

Similar situations exist for maxwell-lint (a conversion that is genuinely singular) and abstain-bench (a model that abstains correctly and is therefore "wrong" on OOD cases by construction).

What the tools refuse to guess

Throughout the portfolio, when there is no answer the tools refuse rather than producing one. That is a deliberate stance and it costs convenience:

• a file containing NaN is refused, not parsed, because a verdict computed on NaN is not a verdict;
• a singular S→Y conversion is refused with the frequency named, not returned as a large finite number that looks actionable;
• a coupling ceiling with no reference matrix is refused, because k is a ratio and there is no verdict without a denominator;
• a checker that never reported a law is INCOMPLETE, not CONFORMING — an unreported law was not checked, and a corpus cannot certify what it never saw;
• SARIF results carry no line region, because a physics failure happens at a frequency and inventing a line would misreport where the problem is.

Each of those has an "easier" alternative that produces a confident-looking answer. That is exactly why they are refusals.

What would change these limits

Honest answers, not roadmap items:

Limit	What would lift it
Admissibility, not accuracy	Comparison against measurement or a converged field solve
Computational, not measured	A VNA on real hardware
A model, not Maxwell	Bounding the closure-versus-solver gap, not just disclosing it
One family, not all layouts	More families through the same prover
Synthetic corpus	Labelled measured data with its artefacts

None of these is close. Saying so is more useful than a roadmap that implies otherwise.