Source: https://guthlabs.ai/docs/instruments/diffusion-time-fick-s-law-estimator-biological-scale/
instrument / verified-clean
# Diffusion Time / Fick's Law Estimator (biological scale)
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]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Biology, Medicine & Pharmacology (educational estimates only — every panel labeled not-medical-advice)
**Tranche**: tranche-7
**Evidence ID**: t7-116
**Ledger rows**: 1
No ledger note is attached.
## Review findings
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.
### Formula and scope findings
- 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.
### Unit assumptions
- 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.
## Boundary hardening
**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.
## 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": {
"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."
}
````
## 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-tranche7/tranche7-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`