What it shows
A signal model of package wiring says how much of a signal goes in which direction at each frequency. A physical piece of wiring cannot hand back more energy than it receives, and it behaves the same in both directions. A fitted or learned model can break both rules by accident.
The usual fix is to fit a model and then repair it. Our models are built in a form where breaking either rule is impossible: a short algebraic argument shows it for any values of the model’s parameters. The core algebra step is also checked by Lean, a proof checker.
The published record says, word for word (an excerpt)
Reciprocal, passive S-parameter structures are generated by construction: σ_max(S) ≤ 1 and S = Sᵀ hold exactly for any parameters, eliminating a class of non-physical output rather than repairing it.
Why it matters
A model that creates energy breaks the circuit simulations downstream of it, and the damage has to be caught and repaired after the fact. A form that cannot do it removes that class of error before it starts.
Why now: chip makers are moving to packages that hold several chiplets, and Intel has announced glass substrates for such packages, planned for the latter part of this decade. Each new carrier needs new signal models of its wiring.
Who should care
- Signal-integrity and packaging simulation software makers. Models that need no passivity repair step.
- Teams that train models of wiring from data. A structure that keeps a learned model passive and reciprocal, whatever it learns.
The limits, in the record’s words
The published record says, word for word (an excerpt)
PASSIVITY is structural and holds for any parameters. ACCURACY is not structural and is 0.44% median on ONE structure class only.
The guarantee says nothing about whether a model is accurate. The wide-frequency form can only describe responses that fade smoothly with frequency (in the field’s terms, only real poles), so it cannot yet represent resonances, the sharp peaks a real package shows at some frequencies.
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 for predictions that break basic physics, 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 N-port Touchstone files, and refuse to emit 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 predicts physics that cannot exist.
- 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.