Diffusion Time / Fick's Law Estimator (biological scale) mechanism

Model scope

The arithmetic and dimensional form are correct under a one-dimensional free-diffusion convention. Verdict is NEEDS_REVIEW because 'characteristic diffusion time across a cellular distance' does not specify dimensionality or the environmental conditions corresponding to each preset. At least two vectors use exact, widely tabulated standard-value rows: O2 in water at approximately 25 °C and glucose in water at approximately 25 °C.

• t = x²/(2D) is the standard one-dimensional mean-square-displacement estimate only when x is a one-dimensional RMS displacement or characteristic distance. For an isotropic three-dimensional RMS radial displacement, the corresponding relation is t = x²/(6D). The instrument must state which convention it uses.
• The listed formula assumes free diffusion in a homogeneous, unbounded medium. Cellular crowding, binding, obstacles, membrane barriers, tortuosity, and reactions can substantially change the effective transport time.
• Preset diffusion coefficients are condition-dependent; each preset needs explicit temperature, solvent or cellular compartment, viscosity, and molecular form assumptions.

Units and conventions

• Distance is converted to meters before calculation.
• Diffusion coefficient D is in m²/s.
• Output time is in seconds; milliseconds are obtained by multiplying seconds by 1000.
• The factor 2 assumes one-dimensional diffusion. If the displayed distance is intended as a three-dimensional radial distance, the factor must be 6 instead.
• Distances must be finite and nonnegative; D must be finite and strictly positive.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "distance": 10,
    "distance_unit": "µm",
    "preset": "O2 in water at 25 °C"
  },
  "expected_outputs": {
    "diffusion_time_s": 0.025,
    "diffusion_time_ms": 25
  },
  "reference_data": {
    "preset": "O2 in water at 25 °C",
    "D_m2_per_s": 2e-9,
    "source_convention": "widely tabulated standard value; dilute aqueous oxygen diffusion coefficient at approximately 25 °C"
  },
  "working": "Convert distance: x = 10 µm × 10^-6 m/µm = 1.0×10^-5 m. Square it: x² = (1.0×10^-5)² = 1.0×10^-10 m². Denominator: 2D = 2×(2.0×10^-9) = 4.0×10^-9 m²/s. Time: t = (1.0×10^-10)/(4.0×10^-9) s = 2.5×10^-2 s = 0.025 s. Convert: 0.025×1000 = 25 ms."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The zero-diffusion-coefficient input produces an undefined division by zero, and the specification does not state an input-rejection rule. Negative D also yields a mathematically defined but physically invalid negative diffusion time.

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-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json