A physics engine, and a verification tool enforced on top of it. PhysWall inverts a closed, published, non-linear physical law at a single measurement point — and refuses when the inverse is not unique. Seven laws, one engine, and the same refusal in all of them.
Nobody measures how steady a shooter's hand is, or the roughness of copper sealed inside a circuit board. But a law connects each of them to something you can measure, and run backwards it gives you the figure nobody took — and when the measurement cannot support one, the gate closes and nothing is returned.
The field calls this an inverse problem: a closed form run backwards from what was measured. Hadamard’s test for one is whether a solution exists, is unique, and is stable — and a problem failing any of the three is ill-posed. Every refusal here is one of those three, named.
Every number on this site reproduces from a source that is named. Five of the main claims are listed with the exact check that would break each one, and none of those checks needs anything from us.
Two of the five are claims this site got wrong. They are still printed, next to what replaced them — a site that shows only what survived gives you nothing to compare the survivors against.
Every field knows an inverse can have more than one answer. What everyone does about it is try to get past it — these are quotes from the literature:
neural networks, to escape local minima generative models, that produce a field anyway "merging iterative and probabilistic approaches to overcome the non-uniqueness"
All reasonable, if a single answer is what you need. This engine returns the ambiguity instead: when two inputs reproduce the same measurement, the verdict is NOT UNIQUE and both are printed.
Two distinct states, one observable, the same value. Physics has had the word for a century.
Malus at 1 deg and at 179 deg
-> the same transmitted intensity
two Q values on a matching network
-> the same return loss
a biased result, or an honest one with
an underestimated uncertainty
-> the same En
⚠ It is not superposition. Superposition means a combination of two solutions is itself a solution. Here it is not: cos² gives the same intensity at 1° and 179°, and 90° — halfway between — gives something else entirely. An engineer would correct that in one line, and be right.
You lift a degeneracy by adding an independent observation. So the engine returns both values and the observation that would separate them:
a second round against a different reference, for a failed En a measurement at a second frequency, for a matching network a contributor with its own declared source, for an uncertainty budget
A refusal that names its own remedy is a result. One that does not is an apology.
The same rule found a search ceiling being reported as a measurement, a fixture that returned the same number for every input, a claim of "measured" where the paper said "expected", and a published range that the file it cited contradicted. Four of those were our own. A tool that only ever catches other people's mistakes has not been pointed at itself.
A computational claim splits three ways, and the split is the honest description of where this stands:
verification is the arithmetic right validation does it match the real world UQ how wide is the answer
These tools are UQ. Every one of them answers how much a measurement allows you to conclude, and refuses when the answer is not unique. None of them is validated against measurements of our own — there are none — and only one domain has been moved by an outside measurement at all.
And what is unusual is not the band. Metrology software gives you a band. So does every RF engineer with a sensitivity calculation. What is unusual is that one engine asks the same question in seven fields and refuses in the same way in all of them:
two roots, and it will not choose one source entered twice the law does not hold here
Antenna matching, thermal ceilings, conductor loss, bit erasure, river discharge, wave dispersion, anapole scattering. A specialist in any one of them has never had reason to see it as the same problem — and it is the same problem.
When a measured number does not match what a law predicts, the difference sits in one of four places:
the machine what the measurement itself could not resolve the formula what the law leaves out the object what this particular sample did the definition which version of the quantity was meant
The first three are what any textbook on measurement error covers. The fourth is barely mentioned anywhere. It is the one where two people can both measure correctly and still disagree, because they were measuring quantities that share a name and not a definition.
In 1999 one team worked in pound-force-seconds and another in newton-seconds. Both numbers were right. The spacecraft burned up.
A calculator returns a number. Always. Even when the measurement cannot support one.
It separates that gap into the four parts above.
And when the quantity has no single definition at all, it returns no verdict rather than a large error.
Describe what you measured and what you want to know, in your own words, and it will point you at the right one — or say plainly that there isn't one here.
It routes. It does not answer — every number on this site comes from a tool that shows its working.
Or go straight to one: basketball · which explanation survives · the seven bounds · speed climbing · light time · a stream gauge, read twice · where shallow water ends
Energy integrity is finished enough to ship, and it is held back. The reason is written down in full →
Not a field. A moment.
Anyone who has been handed a number and did not know whether to believe it. That happens in a lab, in a spreadsheet, in a post-mortem, and it happens every time a model returns something confident about a question it could not actually answer.
There are two different disappointments here and only one of them is ours. "Nobody knows" is frustrating, and people accept it. An answer that was confident and wrong is something else. The calculator returned a number. The spreadsheet returned a number. Neither said "I do not know", because neither can.
That is the gap this closes, and it is the only claim on this page that is about us rather than about physics.
Not that the arithmetic is more precise: it is IEEE 754, and every calculator on earth has the same sixteen digits. Not that the mathematics is new — we checked fifteen times, and bias separation in Kalman filtering, Type A against Type B in the GUM, and BIPM key comparisons all got there first.
What we claim is narrow: every uncertainty tool available to the public propagates a budget forwards, and none of them takes an observed discrepancy and says how much of it is yours.
If you know one that does, tell us. It is the only claim we have, and we would rather hear it from you than keep saying it.
One engine, shown nine times. Each of these is a question somebody is paid to answer, and each one is answered on this site today, against public data, in a way you can check in a browser.
Which loss term is binding on this board?
Conductor loss goes as √f and dielectric loss as f. They cross, and
which one binds depends on where you are.
→ the doubling problem
Is my instrument drifting, or is the world?
A gauge drops 2.50 ft overnight. A second route says whether that was
the sensor or the channel.
→ a stream gauge, read twice
Where does the approximation I am using stop being true?
Shallow-water theory holds below kh = π/10. Outside it the
formula still returns a number.
→ where shallow water ends
How much of this gap is my instrument?
A measurement disagrees with a calculation. Four axes, and the split is
derived rather than assumed.
→ error propagation
Can this be matched at all?
Bode-Fano gives a floor no passive network beats. Knowing before two weeks
of tuning is the whole value.
→ the seven bounds
Which explanation survives the evidence?
Thirty aviation reports, coded from the reports alone, agreeing on the
cause in twenty-six.
→ which explanation survives
Is this streak real, or is it sixty shots?
A 35% shooter produces 15% and 55% by chance alone, and how often depends
only on how many attempts.
→ sixty shots is not a percentage
What can this measurement not decide?
A distance is one number on a line. It does not say where on the line,
which way, or when.
→ light time
Can I hand it a law it has never seen?
Declare a closed law and a measurement. It inverts, or it refuses.
→ bring your own law
Each tool states its own maturity — validated, beta, filter or held — and what it has not been checked against. Which is which.
PhysWall was developed and architected by Gadi Zion.
Built on PhysWall — the same engine reads antenna bandwidth, conductor loss, bit erasure and heat limits. It answers what the measurement implies, and refuses when the measurement cannot say.⚠ Check this instead of believing it. Every number here reproduces from a source that is named, and the claims that turned out wrong are still printed next to what replaced them. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. How to check each one →
Four-dimensional gap decomposition. A closed physical law, run backwards: measure one side and the other falls out. The gap between the measurement and the law splits into four — the machine, the formula, the object, and which definition you chose. And when the quantity has no single definition, the gate closes and nothing is returned.