Source: https://guthlabs.ai/docs/instruments/shannon-entropy-information-content-calculator/mechanism/

instrument mechanism / verified-clean

# Shannon Entropy / Information Content Calculator mechanism

The inspectable method record for Shannon Entropy / Information Content Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core entropy and self-information formulas are correct, but the instrument cannot receive a PASS until the redundancy definition, text-symbol/preprocessing rules, probability validation constraints, and zero-probability behavior are specified. The honest_label field is empty; it should state that text results are empirical sample estimates and that redundancy uses the explicitly selected definition.

- The entropy formula H=-Σ pᵢlog2(pᵢ) and self-information formula I(x)=-log2(p(x)) are standard when probabilities are dimensionless, normalized, and the logarithm is base 2.

- The claimed output 'redundancy vs max entropy' has no specified formula. A conventional definition is absolute redundancy R=log2(M)-H, or normalized redundancy Rₙ=1-H/log2(M); the catalog must specify which one or both are intended.

- The entropy formula needs the convention 0·log2(0)=0, and the self-information formula needs an explicit result or constraint for p(x)=0.

## Units and conventions

- All pᵢ and p(x) values are dimensionless probabilities in [0,1] and must sum to 1 for an explicit distribution.

- Logarithms are base 2, so entropy and self-information are measured in bits; entropy is bits per symbol when computed from a symbol distribution.

- For text input, probabilities are assumed to be empirical character frequencies: count each character, divide by total character count, and do not apply normalization, case folding, or whitespace removal unless specified.

- Maximum entropy is assumed to be log2(M) bits per symbol for M possible or observed symbols.

- The test vectors below use absolute redundancy log2(M)-H and normalized redundancy 1-H/log2(M), with normalized redundancy also shown as a percentage.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mode": "probability_list",
    "symbols": [
      "H",
      "T"
    ],
    "probabilities": [
      0.5,
      0.5
    ]
  },
  "expected_outputs": {
    "entropy_bits_per_symbol": 1,
    "frequency_table": [
      {
        "symbol": "H",
        "probability": 0.5
      },
      {
        "symbol": "T",
        "probability": 0.5
      }
    ],
    "self_information_bits": {
      "H": 1,
      "T": 1
    },
    "maximum_entropy_bits_per_symbol": 1,
    "redundancy_bits_per_symbol": 0,
    "normalized_redundancy_percent": 0
  },
  "working": "H=-(0.5×log2(0.5)+0.5×log2(0.5))=-(0.5×(-1)+0.5×(-1))=1 bit/symbol. I(H)=-log2(0.5)=1 bit and I(T)=-log2(0.5)=1 bit. M=2, so Hmax=log2(2)=1. Absolute redundancy=1-1=0 bits/symbol. Normalized redundancy=1-(1/1)=0=0%."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not define validation behavior for negative or out-of-range probabilities, zero-probability self-information, the normalized redundancy 0/0 case, or text conventions such as case sensitivity. These can produce rejection requirements, infinities, undefined values, or materially different entropy results.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/shannon-entropy-information-content-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/shannon-entropy-information-content-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/shannon-entropy-information-content-calculator/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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`