Bit Depth Dynamic Range Calculator mechanism

Model scope

The formula is standard and appropriate for the stated theoretical PCM bit-depth calculation. The existing honest label correctly warns that real converters have lower effective dynamic range.

No additional formula finding is recorded.

Units and conventions

• bit_depth is a positive integer number of PCM bits per sample, not bytes or storage size
• The formula DR(dB) ≈ 6.02 × bits + 1.76 is the ideal quantization SNR for a full-scale sine wave with uniformly distributed quantization error
• dynamic_range_db is expressed in decibels relative to the quantization-noise floor; this is not a guarantee of real converter performance
• The 1.76 dB constant assumes the standard ideal sine-wave quantization model

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "bit_depth": 1
  },
  "expected_outputs": {
    "dynamic_range_db": 7.78
  },
  "working": "DR ≈ 6.02 × bits + 1.76\n= 6.02 × 1 + 1.76\n= 6.02 + 1.76\n= 7.78 dB"
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

An extreme positive bit-depth input overflows JavaScript arithmetic to Infinity, and the zero boundary produces a numerical result even though zero-bit PCM should be rejected or flagged as physically invalid.

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