Source: https://guthlabs.ai/docs/instruments/microphone-polar-pattern-proximity-effect-reference/

instrument / verified-clean

# Microphone Polar Pattern / Proximity Effect Reference

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/microphone-polar-pattern-proximity-effect-reference/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/microphone-polar-pattern-proximity-effect-reference/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/microphone-polar-pattern-proximity-effect-reference/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/microphone-polar-pattern-proximity-effect-reference/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Audio, Music, Photography & Color

**Tranche**: tranche-6

**Evidence ID**: t6-063

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The three polar formulas are standard idealized textbook patterns, consistent with the existing honest-label warning. Verdict is NEEDS_REVIEW because the angle unit and figure-8 signed-versus-magnitude semantics are unspecified, and the proximity-effect portion is not mathematically defined.

### Formula and scope findings

- The cardioid formula 0.5 + 0.5 cos(theta) is the standard idealized normalized cardioid response.

- The omni formula 1 is correct for an idealized normalized omnidirectional pattern.

- The figure-8 formula cos(theta) is correct as a signed transfer response, where the rear lobe has opposite polarity. If 'relative sensitivity' means nonnegative pickup magnitude, the displayed quantity should instead be abs(cos(theta)); this signed-versus-magnitude choice is unspecified.

- The proximity-effect claim has no formula, distance model, frequency assumption, or quantitative output, so it cannot be verified or deterministically plotted from this specification.

### Unit assumptions

- Angles must be explicitly defined; the vectors below use degrees converted to radians before evaluating JavaScript cosine functions.

- Sensitivity is dimensionless and normalized to 1.0 on-axis.

- Angles are interpreted modulo 360 degrees.

- For figure-8, expected values use signed sensitivity. A magnitude-only display would use the absolute value instead.

- The proximity-effect note is qualitative only; no distance units or bass-boost units are specified.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A very large JSON angle such as 1e309 becomes Infinity in JavaScript, causing Math.cos(Infinity) to return NaN for cardioid and figure-8. The instrument should reject non-finite angles but may instead render undefined or corrupted plot data. The unspecified angle unit also permits materially different sensitivity values.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "pattern": "cardioid",
    "angle_deg": [
      0,
      90,
      180
    ]
  },
  "expected_outputs": {
    "sampled_points": [
      {
        "angle_deg": 0,
        "relative_sensitivity": 1
      },
      {
        "angle_deg": 90,
        "relative_sensitivity": 0.5
      },
      {
        "angle_deg": 180,
        "relative_sensitivity": 0
      }
    ],
    "key_curve_features": {
      "maximum": {
        "angle_deg": 0,
        "value": 1
      },
      "rear_null": {
        "angle_deg": 180,
        "value": 0
      },
      "range": [
        0,
        1
      ]
    }
  },
  "working": "theta=0 degrees=0 radians: cos(0)=1; sensitivity=0.5+0.5*1=1.000000. theta=90 degrees=pi/2 radians: cos(pi/2)=0; sensitivity=0.5+0.5*0=0.500000. theta=180 degrees=pi radians: cos(pi)=-1; sensitivity=0.5+0.5*(-1)=0.000000. The cardioid maximum is at 0 degrees and the rear null is at 180 degrees."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`