Source: https://guthlabs.ai/docs/instruments/summation-product-notation-evaluator/
instrument / verified-clean
# Summation & Product Notation Evaluator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)
**Tranche**: tranche-4
**Evidence ID**: t4-021
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The direct finite-sum approach is standard under an explicitly defined integer-bound convention, and the three listed polynomial closed forms are standard for sums from 1 through N. The specification needs exact lower/upper-bound semantics, geometric term indexing, r=1 handling, empty-range behavior, product support, numeric precision policy, and the meaning of closed-form matching. The empty honest_label field is a concern: the instrument should honestly state whether it supports finite sums only, finite products, symbolic parsing, and which closed forms are recognized.
### Formula and scope findings
- The specification claims to evaluate Π expressions, but provides no explicit product algorithm, identity value, or supported product syntax.
- The listed closed forms are underspecified: Σn, Σn², and Σn³ require a precise index range, and the geometric-series formula requires a stated term convention and a separate r=1 case.
- The phrase "closed-form match if known" does not define which expressions qualify as known or how symbolic equivalence is determined.
### Unit assumptions
- Index bounds are integer and inclusive for finite sums unless an alternate convention is explicitly specified.
- For Σn, Σn², and Σn³, the standard closed forms assume terms indexed from 1 through N; including k=0 does not change these particular sums.
- For a geometric series, terms are assumed to be a·r^k for k=0 through N−1, with dimensionless ratio r and finite integer N.
- All arithmetic operands must use compatible units; no unit conversion is defined or performed.
- No unit conversion is applicable to the test vectors because all values are dimensionless numerical quantities.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The evaluator has an undefined-result failure mode when an expression such as 1/k includes k=0; it must reject the input instead of producing a numeric result. Geometric closed-form evaluation also requires a separate r=1 branch because the ordinary formula divides by 1-r.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"operation": "sum",
"expression": "k",
"index": "k",
"lower_bound": 1,
"upper_bound": 10
},
"expected_outputs": {
"numeric_total": 55,
"closed_form_match": true,
"closed_form": "N(N+1)/2"
},
"working": "Direct sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55. Closed form with N = 10: N(N+1)/2 = 10×11/2 = 110/2 = 55."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche4/tranche4-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`