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.
A physical-logic engine that decomposes a measurement gap along four axes — the machine, the law, the object, and which definition — and runs every domain through one structure.
RF matching, PCB loss, orbital conversion, photonic scattering, stream gauges, ocean waves, basketball. Same engine, same refusal: when the measurement cannot carry a conclusion, it says so instead of answering.
If my measurement is accurate to 1%, how accurate is the answer?
The same shape turns up wherever a number is derived rather than read, including when the reading is a sample rather than a count.
One table. The source column is the one no other tool asks for, and it is what makes all three questions answerable.
A power law is the easy case, because one exponent carries the whole answer. When the law is a closed bound rather than an exponent, the same question needs a different tool.
Loaded with a real published budget: EA-4/02 example S4, the 50 mm gauge-block calibration, seven contributions in nanometres. Its five comparator readings are -100, -90, -80, -90, -100 and the published document states their mean as -94 nm (STATED_MEAN = -94). Press the third question.
⚠ Source is not bookkeeping. Two contributors from one certificate are one contributor entered twice — the sum double counts and no arithmetic check can see it. JCGM 100:2008 clause 4.3.10 warns against exactly this, and it binds every laboratory accredited by an ILAC signatory.
For a power law there is an exact answer, it is the same at every point, and it is almost never 1%.
Take any closed law that is a power law in the quantity you are deriving:
y = k · xⁿ
Invert it. A 1% error in y gives exactly |1/n| percent in x. At every point on the curve, independent of k, independent of where you are measuring.
law form n error × Wien displacement T = b/λ −1 1.000 Stefan-Boltzmann T = (P/σ)^¼ 4 0.250 Beer-Lambert c = A/ε 1 1.000 pendulum length L = g(T/2π)² 0.5 2.000
Stefan-Boltzmann calms errors. One percent in radiated flux gives a quarter of a percent in temperature, because the fourth root flattens everything. A pendulum doubles them, because you are squaring a period.
Most people carry an assumption that inversion preserves error — that 1% in gives roughly 1% out. It does not. It multiplies by 1/n, and n can be anything.
Which means the same instrument, feeding two different laws, gives answers of very different quality. That is not a property of the instrument. It is a property of the exponent.
x = (y/k)^(1/n) dx/dy · y/x = 1/n
The logarithmic derivative is constant. k cancels. Position on the curve cancels. There is nothing left to depend on.
Only for power laws. The moment a law has a saturation, an asymptote or a sum of terms, the amplification varies with position — and near the law's own limit it can go to infinity.
Michaelis-Menten v = V·S/(K+S) blows up as v → Vmax Carnot η = 1 − Tc/Th blows up as η → 1 radioactive decay f = ½^(t/T) amplification is 8266/t
The last one is worth a moment: carbon dating amplifies error by 8266/t years. It crosses 1.000 at 8,267 years and keeps falling. The inversion gets better with age, not worse — what degrades on an old sample is the detector counting a vanishing signal, which is a different limit entirely.
Seven closed bounds, each reporting the band on its answer rather than a bare number.
An accredited lab's uncertainty budget can fail two opposite ways, and A2LA — the accreditation body — names both in its published list of common deficiencies, where uncertainty ranks #2 of 10.
too little required contributors left out
too much "combining all contributors on an
equal basis may lead to an
overestimation"
Three documented cases, all of the same shape:
the reference standard's resolution,
listed separately from its certificate
-> the certificate already contains it
Stability and Drift, both listed
-> evaluate one, not both
hysteresis on a transducer used in
one direction only
-> it does not apply
The GUM says so directly — JCGM 100:2008, clause 4.3.10 warns against double counting, and that clause binds every one of the 11,000+ calibration laboratories accredited by ILAC signatories.
⚠ Because none of it can be seen in the numbers. Four uncertainty values on a page look independent whatever they are. Telling them apart needs the source of each one — came from a certificate, or was measured here — and no calculator asks.
The free template from A2LA lists Resolution and Reference Standard Uncertainty as two separate rows and asks you to fill both. It computes correctly on whatever you give it. Correct arithmetic on the same source entered twice is still the wrong answer.
⚠ Nothing on this page was measured by us. The deficiency ranking is A2LA's, the clause is ILAC's, En is defined in ISO 13528:2022, and the GUM warning against double counting is JCGM's. Every figure comes from a body with no stake in this working.
EA-4/02's own worked example S4 — the gauge-block calibration that commercial uncertainty software validates against — states an arithmetic mean of −94 nm from five readings that average −92 nm. Everything below that line is correct: seven contributions, RSS 36.4 nm, U = 73 nm, reproducing exactly.
⚠ So a summary must follow from the data it summarises, and this engine now checks that too. Give it the raw values and the stated figure and it recomputes rather than carrying the figure forward. Nobody recomputes a number they were handed, which is how one survived twenty-six years inside the example an industry calibrates against.
This engine refuses to run a quantity without a declared source, and refuses when two inputs declare the same origin — the certificate cannot appear twice. That was an internal rule about honesty long before it was anything else, and it turned out to be the thing nobody else asks for.
A calibration laboratory that reports an uncertainty smaller than its accredited CMC is in breach: ILAC P14 clause 5.5 forbids it outright, and A2LA lists it as the second most common finding on calibration certificates.
Proficiency testing measures it with En, from ISO 13528:2022, and unlike a z-score it contains the uncertainties:
En = |x_lab − x_ref| / √(U_lab² + U_ref²) |En| ≤ 1.0 satisfactory
⚠ |En| > 1 means either the result is wrong or the uncertainty was underestimated — and one round does not separate them. That is not a limitation of the lab. It is a property of the measurement: the same En comes out either way.
result off by 0.45, U honest En = 1.59 result off by 0.20, U too small En = 1.29 both a little En = 1.29
A failed En costs a documented nonconformity, a root cause investigation, objective evidence to the accreditation body, and usually a repeat PT round. A lab that knows which of the two it is repeats once. A lab that guesses repeats twice.
This engine returns NOT UNIQUE for exactly this shape: a measurement that two different causes reproduce equally well. It will not pick one, and picking one is what costs the second round.
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 →