Source: https://guthlabs.ai/docs/instruments/big-o-growth-comparison-plotter/implementation/

instrument implementation / implementation-contract

# Big-O Growth Comparison Plotter implementation

A source-bound implementation contract for Big-O Growth Comparison Plotter; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-010

**Effect**: Computation or source lookup only

## Input and validation requirements

The hazard probes expose two required failure modes if unguarded: n=0 produces undefined logarithmic values and nonpositive points that cannot be represented on a log-scale chart, while n=1024 overflows the JavaScript Number representation for O(2ⁿ) and O(n!). The implementation should reject, omit, or explicitly label these results. Numeric readouts also depend on the undocumented logarithm-base convention.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "n_values": [
      1
    ],
    "classes": [
      "O(1)",
      "O(log2 n)",
      "O(n)",
      "O(n log2 n)",
      "O(n^2)",
      "O(2^n)",
      "O(n!)"
    ],
    "constant_factors": {
      "O(1)": 1,
      "O(log2 n)": 1,
      "O(n)": 1,
      "O(n log2 n)": 1,
      "O(n^2)": 1,
      "O(2^n)": 1,
      "O(n!)": 1
    },
    "log_base": 2
  },
  "expected_outputs": {
    "samples": {
      "n=1": {
        "O(1)": 1,
        "O(log2 n)": 0,
        "O(n)": 1,
        "O(n log2 n)": 0,
        "O(n^2)": 1,
        "O(2^n)": 2,
        "O(n!)": 1
      }
    },
    "curve_features": {
      "O(log2 n) root": "n=1",
      "O(n log2 n) root": "n=1",
      "log_scale_rendering": "invalid for the two zero-valued curves at n=1"
    }
  },
  "working": "At n=1: O(1)=1. log2(1)=0, so O(log2 n)=0. O(n)=1. O(n log2 n)=1*0=0. O(n^2)=1^2=1. O(2^n)=2^1=2. O(n!)=1!=1. The zero values are mathematically correct but cannot be drawn on a strictly positive log y-axis."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/big-o-growth-comparison-plotter/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/big-o-growth-comparison-plotter/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/big-o-growth-comparison-plotter/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`