The instrument fleet
LIVETwelve generators, six of them outside medicine, each carrying the physics of one instrument. 10 of them prove that physics against an analytic invariant — a closed form, a conservation law, or an exponent — that a model without it cannot satisfy. Measured per modality, on real corpora.
1. 10 instruments, 10 proofs
A generator that adds noise to an image can be tuned to look like anything and can be checked against nothing. A generator that simulates the instrument has to obey the instrument’s physics, and physics is falsifiable. Each lane below declared a law before it ran, derived the value that law requires, and measured what its own forward model produced.
The right-hand column is the control, measured on the same corpus, and it comes in two kinds. On some rows it is a model without the physics — an additive Gaussian field where there should be photon counting, a linear RGB gain where there should be Beer-Lambert. On others it is the knob that must not preserve the invariant: a common gain has to break the force balance, or a calibration error would be invisible. Both make the same point. An invariant is only evidence if something could fail it, so each row carries the thing that does.
| Instrument | The invariant | Required | Measured | The control |
|---|---|---|---|---|
Ultrasound L1 · medicine | speckle SNR on a uniform phantom the model counts the interference of scatterers inside a resolution cell | 1.91306 | 1.91173 | a gain-and-noise model moves this number whenever the gain moves |
Radiography L2 · medicine | log-log slope of SNR against dose, over 7 exposures the model counts photons, one at a time, through Beer-Lambert attenuation | 0.5 | 0.499901 | 1.00007 a fixed-amplitude Gaussian noise model, on the same images |
Haematology microscopy L3 · medicine | spread of the OD ratio across density bins at 1.4x concentration the model counts dye concentration in optical density, not brightness | 0 | 0.0040222 | 0.408511 the best linear RGB gain leaves this fraction of the change unexplained |
Fundus photography L4 · medicine | added local variance, brightest bin over darkest the model counts photons at the sensor, so noise scales with the signal | must exceed 1 and rise with luminance | 4.69363 | 0.817527 an additive Gaussian field of matched sigma, on the same frames |
IMU, device change L5 · wearables | knobs whose largest effect lands in their declared group the model counts the mounting frame, the anti-alias filter and the clock | one group per knob, declared before the run | 13 of 13 | a single noise knob has one signature, not thirteen |
IMU, placement change L6 · wearables | log-log slope of the centripetal term against rotation rate the model counts rigid-body kinematics between two points on one body | 2 | 2 exact to float64 | the companion exponent in the lever arm is 1.0, measured to 6.7e-16 -- the pair is the evidence, not either one alone |
PPG, optical L7 · wearables | knobs moving their designated feature in the declared direction the model counts light through perfused tissue, and the analogue front end | all of them, declared in advance | all correct | sign agreement is free to get wrong and cannot be tuned into existence |
Gait, force plates L8 · biomechanics | worst relative change in each foot's total vertical force, over 8 placements the model counts load transfer between sensors under one foot | 0 | 3.33e-16 exact to float64 | 0.5 a common gain of 0.5 -- a calibration error -- moves the total by exactly half, which is why calibration is observable at all |
Environmental sensors L9 · environment | worst relative error recovering tau by the step route the model counts the first-order thermal lag of a housed sensor | 0 | 1.00e-12 exact to float64 | a smoothing filter has no tau to recover |
Multispectral / earth L10 · earth | largest NDVI change over the whole solar-elevation sweep the model counts band-resolved radiance, solar geometry and path radiance | 0 | 3.33e-16 exact to float64 | -0.10283 additive path radiance at 25 DN in the red band, which moves NDVI on every window |
Each lane chose its own law, and the choices disagree with each other on purpose. A radiograph’s bright regions are the fewest photons and a microscope’s are the most, so the two lanes’ noise polarities run opposite ways. A fundus frame has its own field stop, so it treats its border the opposite way a blood smear does. A fleet in which every lane made the same choice would be a fleet copying itself rather than modelling instruments — and a lane that had copied its sibling’s sign would have been confidently wrong.
Careers (L11) is Family B and carries no invariant of this kind. Family B generates a population, not a measurement of one, so there is no instrument whose physics could be conserved. Its analogue of an invariant is the held/failed ledger over published marginals: 35 HELD, 14 FAILED, published as a ceiling rather than a score.
2. What that buys, that a noise model cannot deliver
The clearest single demonstration came out of the radiography lane, and it is a statement about the whole field’s methodology rather than about our code.
tube voltage (kVp) vs display window width, and they are the same image
A display window whose lower edge sits at zero attenuation and whose width is 1/µ is a tube-voltage change, pixel for pixel. At 90 kVp against an equivalent window width of 1.494965, the two images differ by 0 grey levels, with 0.0% of pixels differing by more than one level.
So “this image has more contrast” is not evidence of an acquisition change at all — and a contrast perturbation is precisely what the field publishes as a domain shift.
Two things do separate them, and both exist only because the model counts photons rather than adding a noise field:
Noise per unit contrast
noise_flat_sd / contrast_struct_sd
the tube's output rises as the square of the voltage, so a kVp change moves the number of quanta per unit contrast and a display window cannot.
Beam-hardening curvature
hard_att_skew
a standardised third moment is invariant to any affine map, so neither a kVp change nor a display window can move it and a pointwise NON-LINEAR map can.
Both discriminators exist only because the model counts photons. A corruption-style model that adds noise and adjusts contrast cannot tell a machine change from a monitor setting -- and a contrast perturbation is precisely what the field publishes as a domain shift.
3. How we know: the controls nobody else runs
The fleet answers “does the generator carry real physics?” and the answer is yes, measurably. It does not answer “can that generator be fitted to a real difference between two sites and recover the instrument?” — a separate question, and one we tested rather than assumed.
That is the honest shape of the claim, and it is a narrower one than it is a weaker one. We build synthetic data from the physics of the instrument, and we can prove the physics is right. We are also the only people who have tested whether fitting that physics to a real site difference recovers the instrument — which is why we know it does not yet. A generator that works and a calibration claim that is still open is a more defensible position than a calibration claim nobody has audited, including our own of six months ago.
The generator is the product. The calibration claim is an open research problem with six measurements attached, and the measurements are ours.