A subset is not another conservation term¶
GA-SYN-011 · Edition 2026.10.7 · Synthetic technical investigation
Proposition and operational question¶
If burned resources are already included in spent resources, adding burned again violates the stated conservation equation.
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 resource unit is indivisible and all balances are nonnegative integers. Issued equals available plus reserved plus spent. Burned is a descriptive subset of spent and must be no larger than spent. The counterparty cannot issue new resources during the observation. This is a single balance-sheet state, not an economic model.
Worked synthetic trace¶
The executable starts with eleven available units, reserves four, spends three of the reserved units, and marks two of those spent units as burned. It prints the accounted total after every transition; the total stays eleven when burned units remain a subset.
Issued is eleven, available seven, reserved one and spent three. Seven plus one plus three equals eleven. Two of the three spent units are classified as burned. That classification changes no total: burned is two and ordinary spent excluding burned is one. Both classifications sum back to the already recorded spent three.
Negative control¶
The mutant adds the burned subset as a fourth independent term: seven plus one plus three plus two equals thirteen. The discrepancy is detected. A label for irreversible loss can be useful, but treating it as a new balance would double count. The original declaration of which sets overlap is therefore part of the invariant.
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 | Author execution of the independent public teaching case budget, 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. An internal author run does not count as independent review.
Limitations and open obligations¶
The one-state calculation does not establish every transition preserves conservation, prevent overflow, price resources, or prove incentives. Issuance, reservation release, crashes and concurrent transfers need additional transition tests. The wider RCFS amendment and split/merge constructions remain separate obligations; this teaching arithmetic cannot close them.
Prior art and contribution limit¶
Explicit provenance and typed accounting help distinguish classifications from transfers. Conservation is elementary accounting rather than a novel theorem. The value of the example is that its negative case makes an easy-to-hide overlap assumption testable. 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 budget
python examples/investigations/check.py --case budget --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-011, edition 2026.10.7, 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.