Source: https://guthlabs.ai/docs/instruments/other-distributions-calculator-binomial-poisson-t-chi2/implementation/

instrument implementation / implementation-contract

# Other Distributions Calculator (binomial/Poisson/t/chi²) implementation

A source-bound implementation contract for Other Distributions Calculator (binomial/Poisson/t/chi²); 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**: t6-133

**Effect**: Computation or source lookup only

## Input and validation requirements

The degrees-of-freedom input ν=0 produces multiple undefined operations in the Student's t density. The calculator must reject it rather than return a numeric PDF; accepting it without validation would be a failure. The discrete CDF convention also materially changes the result unless explicitly specified.

## 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": {
    "distribution": "binomial",
    "n": 4,
    "p": 0.5,
    "k": 2,
    "plot_sample_k": [
      0,
      2,
      4
    ]
  },
  "expected_outputs": {
    "pmf": 0.375,
    "cdf": 0.6875,
    "mean": 2,
    "variance": 1,
    "plot_sample_points": [
      {
        "k": 0,
        "pmf": 0.0625
      },
      {
        "k": 2,
        "pmf": 0.375
      },
      {
        "k": 4,
        "pmf": 0.0625
      }
    ],
    "key_curve_features": {
      "support": "k in {0,1,2,3,4}; PMF is zero outside this support",
      "mode": "k=2",
      "symmetry": "PMF is symmetric about k=2"
    }
  },
  "working": "PMF at k=2: C(4,2) * 0.5^2 * (1-0.5)^(4-2) = 6 * 0.25 * 0.25 = 0.375. CDF through k=2: P(0)+P(1)+P(2) = [1*0.5^4] + [4*0.5^3*0.5] + [6*0.5^2*0.5^2] = 0.0625 + 0.25 + 0.375 = 0.6875. Mean = n*p = 4*0.5 = 2. Variance = n*p*(1-p) = 4*0.5*0.5 = 1. Plot samples: P(0)=C(4,0)*0.5^4=0.0625; P(2)=0.375; P(4)=C(4,4)*0.5^4=0.0625."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/other-distributions-calculator-binomial-poisson-t-chi2/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/other-distributions-calculator-binomial-poisson-t-chi2/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/other-distributions-calculator-binomial-poisson-t-chi2/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`