Source: https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/mechanism/

instrument mechanism / verified-clean

# Bit Depth Dynamic Range Calculator mechanism

The inspectable method record for Bit Depth Dynamic Range Calculator, kept separate from implementation and qualification.

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

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-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`