Scientific measurements

aner.science provides native measurement uncertainty through EvidenceTensor: nominal values, physical units and retained error source identity travel together through supported affine operations. The module supports explicitly exact values, unknown uncertainty and a declared source aware measurement model. It runs on frozen CPU Float64 values and needs no external service or data package.

Start with the complete small example below, then use the EvidenceTensor API reference for constructor details, overloads, diagnostics and resource costs. Shared calibration sensor fusion develops the same model into a longer application with a frozen physical relationship and intentional failure. These pages are references and applications within aner.science; they do not require importing a deeper module name.

Choose the value contract

Import aner.tensor alongside aner.science when creating numerical literals or SemanticTensor values. Ordinary Tensor operations and neural losses consume numerical values; they do not infer or propagate measurement uncertainty. A variance alone does not define a Gaussian distribution, confidence interval or prediction probability.

Measurement workflow

1. Declare nominal values and physical units. Use science.calibrated for independent reading noise plus one common calibration source, or science.measurements to specify independent base sources and their coefficients explicitly.
2. Select observations with gather_rows. Selection retains the original source identities, including repeated observations.
3. Combine compatible observations through add, subtract or the two operand mean; convert units or apply a frozen physical affine relationship.
4. Read the nominal value, variance, standard uncertainty or covariance. Use summary/explain and source map accessors to inspect the declared model.
5. At a values only interoperability boundary, call export_values(reason) and retain its report. The numerical consumer then receives nominal values without the evidence contracts.

Two separate constructor calls create separate source registries. Reusing the same names or numeric settings does not prove independence or a known correlation between them. Declare related readings together, then gather them from that one value. Unknown uncertainty is not zero: covariance, variance and supported propagation refuse an unknown model.

Run a complete example

After installing Aner, save the following program as science_basics.aner, or use the bundled source. With the bundle's examples directory in the current folder, run:

aner check examples/science_basics.aner
aner run examples/science_basics.aner

The complete fixture is in source. No CSV file, database, GPU or network is required; the default CPU Float64 configuration is sufficient.

// CPU Float64 measurements with independent reading noise and shared calibration.
import aner.tensor
import aner.science

let readings = science.calibrated([[20.0], [22.0]], "degC", 0.2, 0.3)
let first = readings.gather_rows(List(0))
let second = readings.gather_rows(List(1))
let fused = science.mean(first, second)
let difference = first.subtract(second)

print("Fused temperature")
print(fused.item())
print(fused.unit())
print("Fused variance is 0.11 within tolerance")
print(fused.variance() > 0.109999999999 && fused.variance() < 0.110000000001)
print("Shared covariance is 0.09 within tolerance")
let shared = science.covariance(readings, 0, 0, readings, 1, 0)
print(shared > 0.089999999999 && shared < 0.090000000001)
print("Difference temperature")
print(difference.item())
print(difference.unit())
print("Difference variance is 0.08 within tolerance")
print(difference.variance() > 0.079999999999 && difference.variance() < 0.080000000001)
print("A reading minus itself has zero variance")
print(first.subtract(first).variance())
print("Kelvin conversion retains the source model")
let kelvin = fused.convert("K")
print(kelvin.item() > 294.149999999 && kelvin.item() < 294.150000001)
print(kelvin.variance() > 0.109999999999 && kelvin.variance() < 0.110000000001)

Expected output:

Fused temperature
21.0
degC
Fused variance is 0.11 within tolerance
true
Shared covariance is 0.09 within tolerance
true
Difference temperature
-2.0
delta_degC
Difference variance is 0.08 within tolerance
true
A reading minus itself has zero variance
0.0
Kelvin conversion retains the source model
true
true

Each observation has variance 0.2² + 0.3² = 0.13 degC². Their covariance is the shared calibration variance 0.09 degC². The mean has variance 0.11 degC²; the difference has variance 0.08 delta_degC². Converting an absolute temperature to Kelvin changes the nominal offset, while retaining the same physical variance. Tolerance checks keep the example reproducible across harmless Float64 formatting differences.

If you save the source outside the bundle, use aner check science_basics.aner and aner run science_basics.aner instead. Explicit source coefficients provides a second complete program covering measurements, exact, unknown and acknowledged numerical export; its expected output and assumptions are in the EvidenceTensor reference.

API map

All functions below are native and require import aner.science. EvidenceTensor receivers also support the corresponding method spelling, such as value.variance() or value.convert("K"). The full typed signatures appear in the EvidenceTensor reference.

Errors and current limits

Wrong Aner argument types or missing imports fail aner check. Scientific runtime failures are source located R3503 diagnostics with a semantic code such as E_UNIT_INCOMPATIBLE, E_CORRELATION_UNKNOWN, E_AXIS_ALIGNMENT, E_EVIDENCE_UNSUPPORTED, E_BACKEND_UNSUPPORTED, E_NUMERIC or E_RESOURCE_BUDGET. An error stops the operation; uncertainty is never silently replaced with zero or discarded by propagation.

Evidence construction requires frozen CPU Float64 values, at most 65,536 scalar cells and at most 262,144 active source coefficients. The explicit measurements constructor admits at most 4,096 base sources; each source name is a unique nonempty UTF-8 String of at most 128 bytes without control characters. Fitted contextual transformations retain at most 64 registered operation records. Nonzero errors that underflow or overflow the supported Float64 representation fail explicitly.

The current model covers declared affine source relationships. General nonlinear uncertainty propagation, GPU evidence kernels, source map persistence, arbitrary covariance matrices, Monte Carlo distributions and uncertainty aware neural training remain future functionality. See the EvidenceTensor reference for precise time/space costs and the SemanticTensor unit registry for accepted unit names.