What it shows
The record states the result this way:
The published record says, word for word (an excerpt)
The same family carries a certified floor as well as a ceiling, plus a proven ordering showing that moving two via pairs closer together increases many-body screening.
In plain words: across every layout in the family, the screening factor stays at or above the proved floor above, and at or below the proved ceiling. The proof processed 276103 boxes of the family’s parameters, certified 138052 of them, and found 0 failure regions.
Why it matters
A bound from one side says how bad a shortcut can be. A bound from both sides says, in the simplified model, how far the screening can range across the whole family without sampling layouts, and the ordering says which of two spacings screens more.
What is ours, and what is not
Interval branch-and-bound is a known method (see the prior art below). What is ours is this family, its closure model, and the certificates.
Who should care
- Package designers deciding how close to place via pairs.
- Reviewers. The bounds hold in a simplified model, and the gap to our full solver is stated, not proved.
The limits, in the record’s words
The published record says, word for word (an excerpt)
Monopole-closure statements with an additive, disclosed closure-vs-BEM gap. The design direction is a RIGOROUS ENDPOINT ORDERING between sep_mult 2.5 and 4.5, not a full pointwise monotonicity proof; full monotonicity is a disclosed empirical finding.
The published record says, word for word (an excerpt)
With entry 2 (`forall-impossibility-pairwise`)'s tightened ceiling the envelope is k ∈ [0.830, 0.9052453688833432]; it was [0.830, 10/11] before 2026-08-18.
The published record says, word for word (an excerpt)
The N=3 symmetric second family certifies k ∈ [0.370, 0.944], a far more dramatic floor: one optimally-placed guard via screens a pair to 37% of isolated coupling.
In plain words: the bounds and the ordering hold in the simplified closure model, with a disclosed gap to our full solver on top. The ordering is proved between two spacings, not at every spacing in between. The proof’s soundness also assumes the interval core rounds outward correctly, which is tested, not formally proved.
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.