Source: https://guthlabs.ai/docs/instruments/gain-staging-db-sum-calculator/mechanism/

instrument mechanism / verified-clean

# Gain Staging / dB Sum Calculator mechanism

The inspectable method record for Gain Staging / dB Sum Calculator, kept separate from implementation and qualification.

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

## Model scope

Needs review because the correlated-input behavior is underspecified and the +6 dB rule is only valid for equal, phase-aligned sources. The instrument should require an explicit level reference and distinguish uncorrelated power summation from coherent complex-amplitude summation.

- The uncorrelated formula Lsum=10log10(Σ10^(Li/10)) is correct only when all levels use the same reference and represent power or mean-square/RMS quantities, and the signals are statistically uncorrelated.

- The stated correlated rule of "+6 dB per doubling" is valid only for equal-level, phase-aligned coherent sources. It is not a general formula for correlated signals with unequal levels, partial correlation, or arbitrary phase.

- For general coherent signals, the required formula is Lsum=20log10(|Σ10^(Li/20)e^(jφi)|), which requires phase information that the input specification does not provide.

- The term "correlation assumption" is ambiguous: statistical uncorrelatedness, partial correlation, and phase-coherent summing produce different results.

## Units and conventions

- All source levels are logarithmic levels with the same reference and are directly comparable; mixing dB SPL, dBu, dBV, and dBFS without reference conversion is invalid.

- The uncorrelated formula assumes each Li represents a power-compatible level, such as RMS power level or a dB level proportional to mean-square amplitude.

- The coherent +6 dB shortcut assumes equal levels, identical reference, phase alignment, and no clipping or limiting.

- For dBFS inputs, the arithmetic sum can exceed 0 dBFS; the result is a theoretical level before digital clipping.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "source_levels_db": [
      0,
      0
    ],
    "correlation_assumption": "uncorrelated"
  },
  "expected_outputs": {
    "summed_level_db": 3.0103
  },
  "working": "Convert each level to linear power: 10^(0/10)=1 and 10^(0/10)=1. Sum powers: 1+1=2. Convert back: 10log10(2)=3.0103 dB."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

An empty source list produces log10(0), which is undefined. The instrument must reject this input or explicitly represent the result as undefined rather than returning a finite summed level.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/gain-staging-db-sum-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/gain-staging-db-sum-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/gain-staging-db-sum-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`