Algorithm Runtime Estimator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json