What it shows
A shortcut that is wrong is not useless if you know where it is wrong and in which direction. An error that overstates coupling is safe for a margin check; one that understates it is not. A map of both, over the range of dimensions a design uses, tells a designer when the shortcut can be trusted.
The record states the result this way:
The published record says, word for word (an excerpt)
Three of the nine named industry shortcuts — pairwise_superposition, thin_wire_point_charge and per_unit_length_2d — carry a two-sided invalidity map over the declared parameter box stating where the shortcut is conservative and where it is dangerous; the other six are named UNMAPPED and each states why it was not run. The maps are SAMPLED empirical frontiers, re-derived live from their published samples rather than read from the certificate, not certified complete partitions — and they exonerate the one that holds: thin_wire_point_charge, worst error −5.1%, with 0.578% of the box falsifying it.
In plain words: three shortcuts are mapped: adding up the coupling of each pair of vias, treating a via as a thin wire, and the flat cross-section model of a line. Six more are named and not mapped, each with its reason. The thin-wire shortcut holds up: its worst error is the figure quoted above, and only 0.578% of the mapped range contradicts it in the record’s test. The maps come from samples, recomputed from the published samples, so they show where the shortcut was seen to fail, not a proof that it fails nowhere else.
Why it matters
Shortcuts like these are used because full solves are slow. Knowing that, at every sampled point of the mapped range, a shortcut erred on the safe side in one reading and on the unsafe side in another changes how its answers should be used.
What is ours, and what is not
That adding up pairs misses many-body effects is known, and per-unit-length line models are textbook (see the prior art below). What is ours is the two-sided maps over this range, against our reference solves, and the reasons given for the shortcuts left unmapped.
Who should care
- Signal-integrity and package engineers who use these shortcuts in early checks.
- Reviewers. The record states that the maps are sampled, and that the reference is our own solver.
The limits, in the record’s words
The published record says, word for word (an excerpt)
A map over the declared parameter box against owned reference solves; it is a statement about model error inside that box, not about any vendor's product.
The published record says, word for word (an excerpt)
pairwise_superposition is 100% conservative and 0% dangerous read as aggressor coupling, and 0% conservative and 100% dangerous read as return coupling — the same signed error, two readings. Its 5% accuracy frontier sits 3.28 orders past the mapped box maximum. per_unit_length_2d under-predicts by 10.2%–46.4%. The honest counterpart is what sells it: thin_wire_point_charge is GOOD, worst error −5.1%, with only 0.578% of the box falsifying it. It is NOT in the counted suite.
In plain words: at every sampled point of the range, the adding-up-pairs shortcut erred the same way, so whether it was on the safe side depends on how its number is used: on the safe side read as the coupling an aggressor causes, and on the unsafe side read as the coupling through the return path. It reaches the record’s accuracy threshold only far beyond the largest dimensions mapped. The flat cross-section model under-predicts by between 10.2% and 46.4%. All of this is against our own reference solves, inside the stated range, and says nothing about any vendor’s tool.
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.