Source: https://guthlabs.ai/docs/instruments/deep-water-wave-speed-period/mechanism/

instrument mechanism / verified-clean

# Deep-Water Wave Speed & Period mechanism

The inspectable method record for Deep-Water Wave Speed & Period, kept separate from implementation and qualification.

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

## Model scope

The formulas are correct for deep-water linear wave theory with period input and SI units. The product should not claim to accept wavelength input until the missing inverse formulas and unit behavior are specified. The honest label should clearly state that the approximation is not valid for shallow or intermediate water and that depth applicability is not currently validated.

- The supplied formulas are standard deep-water linear wave-theory formulas when period T is the input: c = gT/(2π), L = cT, and c_g = c/2.

- The input description says 'wave period (or wavelength)', but no wavelength-input formula is supplied. For wavelength input, the corresponding deep-water formulas would be c = sqrt(gL/(2π)) and T = sqrt(2πL/g).

- The instrument has no depth input, so it cannot verify the stated applicability condition depth > L/2 for the calculated wavelength.

## Units and conventions

- Wave period T is in seconds unless explicitly converted before calculation.

- Wavelength L is in metres, phase speed c is in metres per second, group velocity c_g is in metres per second, and gravitational acceleration g is in metres per second squared.

- Standard gravity g = 9.80665 m/s² is assumed.

- π = 3.141592653589793 is assumed.

- The deep-water approximation is assumed valid only when water depth exceeds half the wavelength, as stated by the honest label.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "period_s": 6,
    "g_m_s2": 9.80665
  },
  "expected_outputs": {
    "phase_speed_m_s": 9.364660936,
    "wavelength_m": 56.187965616,
    "group_velocity_m_s": 4.682330468
  },
  "working": "c = gT/(2π) = (9.80665 × 6)/(2 × 3.141592653589793) = 58.8399/6.283185307179586 = 9.364660936 m/s. L = cT = 9.364660936 × 6 = 56.187965616 m. c_g = c/2 = 9.364660936/2 = 4.682330468 m/s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The literal plain-arithmetic implementation overflows at a period of 1e308 s even though the phase-speed expression can be algebraically rearranged to produce a finite value; it also lacks a supplied non-deep-water branch and does not define handling for negative periods.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/deep-water-wave-speed-period/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/deep-water-wave-speed-period/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/deep-water-wave-speed-period/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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`