What it shows
The lab’s own entry states the result this way:
The published record says, word for word (an excerpt)
The frozen 31-panel solver's discretization error against a panel-free spectral continuum truth is median-of-max 3.0e-4 / worst 6.9e-4 over 15 layouts
The published record says, word for word (an excerpt)
the exact bipolar closed form to 6.2e-15 and a 100-digit mpmath anchor to 50 digits
In plain words: against a continuum solution of the same model, our frozen solver’s worst error per layout has a median of 0.00030071701513187805 across 15 layouts, and the worst case is 0.0006883956817843971, as fractions of the answer.
Why it matters
A comparison against a solver is only as good as the solver. Stating the solver’s own error, measured against exact references, tells a reader how much of any later difference could be the solver’s.
What is ours, and what is not
Measuring a method against exact references and its own refinements is standard practice (see the prior art below). What is ours is this ladder for our solver and its published numbers.
Who should care
- Reviewers of our solver comparisons, who need the solver’s own error first.
- Field-solver developers comparing discretisation error on the same model.
The limits, in the record’s words
The published record says, word for word (an excerpt)
Continuum truth of the 2-D quasi-static MODEL, not measured silicon. The N=10,000 residual is subsampled (5% rows plus all excited-via panel rows) and is never called exact-everywhere.
The published record says, word for word (an excerpt)
An honest finding inside: order-1 panel convergence with a 31↔63-panel sign flip — the canonical 31-panel point is a pre-asymptotic sweet spot.
In plain words: this measures the model’s discretisation, not how a built package behaves. The largest case’s residual is checked on a sample of rows, and the solver’s standard setting sits at a point where its error happens to be small, not where it has settled.
Outside comparison
Compared with: mpmath, an open-source Python library for arbitrary-precision arithmetic. Retrieved 2026-10-05. mpmath, its public page · the retrieval record
Open source for this step
Tools and datasets we publish for the package step of building a multi-chip package. They are the checkers around this work, not a copy of the result itself.
- physics-lint: One command that checks a folder of physics models against a fixed set of named physical rules, with findings straight into CI.
- maxwell-lint: Flags a coupling extractor whose answers no passive set of conductors could produce.
- sparam-lint: Is your signal-response model physically possible? Five physical laws checked from the command line.
- interval-core: The interval arithmetic core behind our proofs over whole families of layouts.
- touchstone-tools: Read, write and convert Touchstone files, the standard text files that record how signals pass through a package's connections, and refuse to write one that cannot be read back.
- physics-lint-mcp: The physics checks, callable by an AI agent.
- physics-lint-action: A GitHub Action that fails the build when a model breaks one of a fixed set of named physical rules.
- Signal-response validity corpus: A labelled corpus of physically invalid signal-response networks, and a scorer that grades any checker against it.
- screening-ceiling: The screening-ceiling family as an open dataset.