What it shows
A computer adds and multiplies with a fixed number of digits, so almost every step rounds a little. That matters when the goal is to prove that a quantity stays above a floor for every design in a range, because a rounding error could hide a case that breaks it.
Interval arithmetic carries a lower and an upper bound for every number and rounds the lower one down and the upper one up. A search then splits the range of designs into boxes until every box is proved, so no design in the range is skipped.
In the record’s words, a small trusted core turns an ordinary computer search into ranges that come with a proof:
The published record says, word for word (an excerpt)
One small trusted numerical kernel turns floating-point search into proof-carrying enclosures
Why it matters
This is what turns a sampled search into a statement about a whole family. The floor under the add-up-the-pairs error is proved with it, and so is every other family-wide statement on this site.
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. New carriers bring new families of layouts, and a statement about a whole family needs arithmetic that cannot round a failing case away.
Who should care
- Signoff and verification software makers that want bounds over a range of designs rather than samples. It is shown on one family of via layouts only.
- Reviewers of our results. The family-wide statements are only as sound as this core and its assumptions.
The limits, in the record’s words
The published record says, word for word (an excerpt)
Soundness is under the IEEE-754 fp64 model, not exact real arithmetic.
The record also states a limit on speed. A more general way of tightening the ranges, which we built and checked, improved on the plain ranges by only about 1.1 times, no better than the hand-written formulas it was meant to replace.
The guarantee also assumes the computer’s log and exp functions are as accurate as stated, which is checked on samples, not proven. It bounds our simplified model, and says nothing about real silicon.
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.