Bounded answer
Verify an implementation of Automatic differentiation against independent fixtures, boundary cases, invariants, and a reference result with declared tolerance. Version the implementation and preserve a receipt for every fixture.
This guide defines a verification boundary. It contains no new theorem proof, astronomical observation, calibration result, or measured uncertainty.
Input contract
What must be fixed first
Named definition, observable, or target quantity
Units, domain, coordinate frame, and assumptions
Versioned reference, algorithm, or instrument method
Tolerance, uncertainty, and boundary cases
Procedure
Work the decision in order
- 1
State whether Automatic differentiation is a definition, derivation, computation, observation, or inference.
- 2
Fix symbols, units, frames, assumptions, and excluded cases.
- 3
Expose the derivation, measurement chain, or algorithm as ordered steps.
- 4
Check independent fixtures, controls, or calibration references.
- 5
Propagate uncertainty and test boundary conditions.
- 6
Emit a result with provenance and a clear inference limit.
Expected outputs
- Definition or measurement contract
- Reproducible derivation, fixture, or observation chain
- Uncertainty and inference-boundary statement
Refuse when
- The source, formula, observable, units, or frame is ambiguous.
- A numerical output cannot be recomputed from stated inputs.
- An inferred physical quantity is described as directly observed.
Subject-specific decision record
What a complete answer would require
- Minimum evidence
- Named definition, observable, or target quantity; Units, domain, coordinate frame, and assumptions; Versioned reference, algorithm, or instrument method; Tolerance, uncertainty, and boundary cases.
- Pass condition
- Return definition or measurement contract, reproducible derivation, fixture, or observation chain, uncertainty and inference-boundary statement only after every required input and ordered check is satisfied.
- Current result
- No subject-specific result has been produced by this method guide.
Questions this guide answers
How can an implementation be verified for automatic differentiation?
Verify an implementation of Automatic differentiation against independent fixtures, boundary cases, invariants, and a reference result with declared tolerance. Version the implementation and preserve a receipt for every fixture.
What inputs must be fixed for Automatic differentiation?
Named definition, observable, or target quantity; Units, domain, coordinate frame, and assumptions; Versioned reference, algorithm, or instrument method; Tolerance, uncertainty, and boundary cases.
What should a machine return for Automatic differentiation?
Definition or measurement contract; Reproducible derivation, fixture, or observation chain; Uncertainty and inference-boundary statement. Every output remains bound to the exact inputs and decision state.
When must a system refuse Automatic differentiation?
The source, formula, observable, units, or frame is ambiguous. A numerical output cannot be recomputed from stated inputs. An inferred physical quantity is described as directly observed.
What does this guide not establish about Automatic differentiation?
A worked example establishes one case, not universal performance. Formal validity does not establish empirical adequacy or implementation correctness. An observation supports only the inference licensed by its calibration and model assumptions.
Limits
- A worked example establishes one case, not universal performance.
- Formal validity does not establish empirical adequacy or implementation correctness.
- An observation supports only the inference licensed by its calibration and model assumptions.