The direct answer
Establish the full count manifest, operand bounds and exact accumulator range before admitting a fixed-width integer sum. NumPy documents modular integer arithmetic without an overflow error, so successful return alone cannot establish an exact total. Preserve the selected representation through capture and handoff; correct arithmetic remains separate from complete usage evidence, current rights and budget authority.
A plausible total can miss the arithmetic contract
A fictional AI usage report totals four permitted event counts. Each individual count passes its input check, and a later screen displays a nonnegative integer. The team still needs evidence that the chosen accumulator could represent the complete sum. A believable display is not that evidence.
This proposed profile concerns a read-only report in invented demo usage units. It neither settles provider billing nor reserves funds. Select exactly four complete, independently admitted counts on one record axis, all in the same unit. No import, array, scalar, dtype, sum or overflow fixture was constructed or executed; the teaching cases are PROPOSED_UNRUN.
Make the accumulator choice explicit
The inspected NumPy v2.5 sum reference assigns dtype to both the result and its accumulator. Its default generally follows the input dtype, with promotion rules for narrower integers relative to the platform integer. The same page states that integer arithmetic is modular and overflow raises no error.
For this application, the reviewed plan must name its accumulator instead of inheriting an unexplained input or platform choice. That is an admission policy, not a claim that every default is narrow or that every integer operation overflows. The actual adapter must establish the selected type through the entire operation.
The reference also permits a separate output destination whose values may be cast. Our profile excludes that destination and any later narrowing conversion. A wider intermediate calculation would not justify publishing a differently represented total without its own supported handoff contract.
Prove the complete nonnegative envelope on paper
The NumPy v2.5 iinfo reference describes integer machine limits, including the type’s minimum and maximum. Its int32 example gives a maximum of 2147483647. These are documentation facts, not values retrieved from an installed runtime.
For a concrete teaching plan, propose that fixed signed-integer representation and four counts, each between zero and 1000 demo units. The worst-case mathematical sum is 4 × 1000 = 4000, below the stated maximum. Starting at zero, every partial sum of these nonnegative operands is also between zero and 4000. This is elementary paper reasoning, not a NumPy output.
| Application choice | Required relationship |
|---|---|
| Complete admitted count N | Exactly four expected events, each included once. |
| Per-event bound B | Every admitted value is an integer from zero through 1000. |
| Accumulator maximum M | The actual selected representation supports the reviewed range. |
| Whole-operation envelope | N × B is no greater than M; no negative adjustments or changed initialization. |
The numerical choices are a small teaching example, not production capacity recommendations. A fifth event, a larger bound, another unit or a negative correction changes the proof. Hold the changed proposal before aggregation rather than trusting a previously approved worksheet.
Check before a narrowing handoff can lose the evidence
Require independently supported extraction of the original bounded integers before any fixed-width conversion. If an earlier component may already have changed a value, checking only its later representation cannot establish the original count. This worksheet supplies no importer or conversion algorithm.
Element validity and total representability are different gates. For a general nonnegative envelope, each value may fit while N × B exceeds the chosen maximum. That conservative envelope then fails this plan even if some particular batch might be smaller. A different, tighter admission proof would require a separately reviewed design; do not silently compute first and call its output the proof.
Keep the existing shape and identity contract separate. A correct arithmetic range cannot identify missing, duplicated or masked events. Conversely, four correctly associated events do not establish the accumulator range.
Carry one arithmetic receipt into the report
Invent manifest M-A, count contract C-A, accumulator plan D-A and report R-A. These paper references bind the proposed evidence. They describe no provider identifiers or computed objects. The ordinary positive makes only this bounded read-only total plan eligible when every required association is independently supported.
| Receipt field | Evidence required before release |
|---|---|
| Manifest | All four permitted event identities, revisions and exactly-once inclusion. |
| Operands | Original integer kind, nonnegative bounds, complete input and common unit. |
| Representation | Actual explicit accumulator type, range and unchanged result handoff. |
| Operation | Whole record axis, reviewed initialization and no masking or extra destination. |
| Proof and capture | Supported envelope plus complete result association, errors and unknowns. |
| Use | Current reporting rights and separate usage-accounting policy. |
The collection guide still governs correspondence and completeness. The budget guide still governs reservations and uncertain charges. An arithmetic receipt replaces neither.
Walk eight inert admission cards
| Condition | Proposed disposition |
|---|---|
| 1. Four admitted bounded counts and every receipt cell hold | Conditionally admit only the declared total plan. |
| 2. Each value fits, but the whole envelope exceeds M | Reject this accumulation plan before the operation. |
| 3. A result is plausible or no error was reported | Do not substitute that observation for the missing range proof. |
| 4. Actual accumulator or result representation differs | Hold the changed numeric handoff. |
| 5. Values may have narrowed before admission | Original operand validity remains unknown. |
| 6. Axis, mask, initialization, count or bound changes | Outside the reviewed complete-batch operation. |
| 7. Total seems right but an event is missing, duplicated or differently denominated | Reject the independent manifest or unit contract. |
| 8. Exact arithmetic fits but reporting rights or usage completeness fails | Withhold the affected claim or disclosure. |
Name the evidence that remains unavailable
Actual runtime, original input extraction, dtype support, complete adapter, initialization, output handoff, resource bounds and current rights are unknown here. Each missing prerequisite blocks a real positive. No overflow result numeral, benchmark, provider total or successful report is claimed.
Boundary is prelaunch. This proposed worksheet is not a shipped numerical verifier or spend controller. It supplies no cast recipe, overflow handler, automatic wider-type fallback or alternative library. The existing synthetic policy evidence covers different behavior.
Primary sources
Official references supporting the guidance. Examples in this guide are synthetic and are not reports of a production incident.