Source: https://guthlabs.ai/docs/instruments/algorithm-runtime-estimator/

instrument / verified-clean

# Algorithm Runtime Estimator

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](<https://guthlabs.ai/docs/instruments/algorithm-runtime-estimator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/algorithm-runtime-estimator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/algorithm-runtime-estimator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/algorithm-runtime-estimator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Computing & Information

**Tranche**: tranche-4

**Evidence ID**: t4-172

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The arithmetic model is valid under explicit exact-operation-count and positive-rate assumptions. The instrument remains NEEDS_REVIEW until it defines the complexity-class-to-f(n) mapping, logarithm base, custom-formula grammar and validation, valid input domains, and human-scale formatting conventions. The honest label appropriately limits the claim to a rough order-of-magnitude estimate.

### Formula and scope findings

- The division formula time = ops/rate is standard only when ops is an exact operation count and rate is measured in operations per second.

- A Big-O complexity class such as O(n) or O(n²) does not determine an exact operation count because constants, lower-order terms, and implementation details are unspecified; the instrument needs an explicit f(n) mapping or a declared convention such as f(n)=n².

- The supported complexity classes, logarithm base, and custom-formula syntax are not defined. Different log bases change the estimated operation count by a constant factor.

- Human-scale formatting and rounding rules are unspecified, so the exact displayed value for ms, s, hr, days, and years is ambiguous.

### Unit assumptions

- n is a dimensionless nonnegative input size; integer n is assumed for these examples.

- rate is strictly positive and measured in operations per second.

- ops is measured in the same operation unit represented by rate.

- Runtime seconds are computed as ops ÷ rate; 1 second = 1000 milliseconds.

- For the logarithmic test, log2 is explicitly assumed.

- For any day or year formatting, 1 day = 86400 seconds; the definition of a year must be specified, such as 365 days or 365.25 days.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A zero operations-per-second rate makes the runtime denominator vanish, requiring rejection or producing Infinity in plain JavaScript. The O(n log n) convention is also under-specified because the logarithm base changes the estimate.

## 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": {
    "n": 7500000,
    "complexity_class": "O(n)",
    "rate_ops_per_sec": 2500000
  },
  "expected_outputs": {
    "ops": 7500000,
    "runtime_seconds": 3,
    "human_runtime": "3 s"
  },
  "working": "f(n)=n=7,500,000 ops. time=ops/rate=7,500,000 ÷ 2,500,000=3 seconds. 3 seconds=3 s."
}
````

## 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`