Comb Filtering / Phase Cancellation Predictor mechanism

Model scope

The distance-based null formula is standard under the idealized two-source model, but the exact ambiguity requiring review is whether the input is Δd or Δt and what explicit formula and units apply to each. The peak expression, n range, and frequency-list limits must also be specified before implementation.

• The cancellation formula f_null = n*c/(2*Δd) is correct for positive odd integer n when Δd is a nonzero path-length difference.
• The peak formula is incomplete: it should explicitly be f_peak = n*c/(2*Δd) for positive even integer n, equivalently f_peak = m*c/Δd for positive integer m.
• The input is ambiguous because it says distance/time difference, but the stated formula uses distance only. For a time difference Δt, the corresponding formulas are f_null = n/(2*Δt) and f_peak = n/(2*Δt), or use Δd = c*Δt first.
• The valid domain and output frequency range are unspecified: n should be a positive integer, and the instrument should state how many harmonics or what maximum frequency to return.
• The model should specify that Δd is the absolute path-length difference; a negative signed difference produces the same frequency locations.

Units and conventions

• For distance-based calculations, Δd is in metres and c is in metres per second, producing frequencies in hertz.
• For time-based calculations, Δt is in seconds, producing frequencies in hertz.
• c is the propagation speed in the relevant medium; 343 m/s is assumed for air near room temperature.
• The two sources emit phase-coherent versions of the same signal, with equal effective amplitudes and matching polarity for exact nulls and peaks.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "delta_d_m": 0.5,
    "speed_of_sound_m_per_s": 343,
    "null_n": [
      1,
      3,
      5
    ],
    "peak_n": [
      2,
      4
    ]
  },
  "expected_outputs": {
    "null_frequencies_hz": [
      343,
      1029,
      1715
    ],
    "peak_frequencies_hz": [
      686,
      1372
    ]
  },
  "working": "Base frequency = c/(2*Δd) = 343/(2*0.5) = 343/1 = 343 Hz. Nulls use odd n: n=1 -> 1*343 = 343 Hz; n=3 -> 3*343 = 1029 Hz; n=5 -> 5*343 = 1715 Hz. Peaks use even n: n=2 -> 2*343 = 686 Hz; n=4 -> 4*343 = 1372 Hz."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The predictor reaches an undefined division-by-zero condition when the path-length difference is exactly zero and can produce physically invalid negative frequencies if a signed time or distance difference is used without an absolute-value convention.

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