Shannon Entropy / Information Content Calculator mechanism

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

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