Preserving a number can still change its meaning¶
GA-SYN-009 · Edition 2026.10.9 · Synthetic technical investigation
Proposition and operational question¶
A projection check over both quantity and unit rejects a changed unit even when the numeric quantity is preserved.
This matters when a continuing task reuses an earlier decision or representation. A final success label can conceal a different failure earlier in the trace. The proposition therefore identifies the exact observation that would refute it.
Definitions, trust and failure model¶
The desired observation is four items. A proposed projection supplies a quantity and a unit. Equality of both fields defines preservation for this teaching case. The producer may produce any of three candidates; the validator is trusted to compare both observables. There is no conversion between boxes and items in the declared model.
Worked synthetic trace¶
The candidates are four items, four boxes and five items. The first is accepted. The second preserves the numeral but changes the unit, so it is rejected. The third preserves the unit but changes the numeral, and is rejected. This makes the observable contract explicit before checking the generated result. A different valid unit conversion would require an additional declared relation and evidence.
Negative control¶
The mutant compares quantities alone. It accepts four boxes. A schema ensuring that quantity is an integer would not detect that error either. The failed check therefore concerns interpretation preservation, not merely structural validity. The example is deliberately smaller than any compiler intermediate representation.
Three evidence records and separate axes¶
| Record | Method and evidence | Scope and status |
|---|---|---|
| Research | Authored finite argument and explicit counterexample, 12 October 2026 | Analytical; limited to the definitions above |
| Reference | My execution, with AI assistance, of the independently designed public teaching case projection, 12 October 2026 |
Fault-tested; externally reproducible with the commands below; no independent reproduction claimed |
| Production | None for this proposition | No product conformance inferred |
Engineering maturity: reference_implemented, referring only to the disclosed teaching case. Assurance: analytical, fault_tested, externally_reproducible, each restricted to its evidence record. These labels are independent dimensions, not a score or a global verification flag. The exact machine-readable record is in the public evidence catalog. My own runs do not count as independent review.
Limitations and open obligations¶
The unit model does not prove complete dependency discovery, semantic understanding, arbitrary compiler correctness, accessibility equivalence or safe application repair. Observation can omit important behavior. Drift detection does not grant authority to correct a user-owned resource. IC/POAR and Semantic OS proposals retain specification-to-runtime and refinement obligations beyond this finite test.
Prior art and contribution limit¶
Semantic representations and identifiers are established foundations. They help state what is meant but do not automatically preserve meaning through transformation. The possible contribution of the wider work lies in maintaining explicit obligations across changes; this dossier tests only one tiny preservation relation. See the primary reference and the comparison guide. No priority or superiority claim follows from this example.
Reproduction and falsification¶
From the successor public source package, use CPython 3.12.14 and no external packages:
python examples/investigations/check.py --case projection
python examples/investigations/check.py --case projection --mutant
The first command must exit zero, with no positive violations and at least one negative violation. The second intentionally exits one and prints an actual violated case. It is a deliberate fault result, not an installation failure. Source and reproduction contract identify the exact population and scope.
Submit a counterexample, a missing assumption or a prior-art correction through the review guide. Include GA-SYN-009, edition 2026.10.9, the command, input and output, and whether the objection concerns the model, implementation or proposed product relationship. Do not send credentials or confidential customer material.