Source: https://guthlabs.ai/docs/instruments/serial-dilution-calculator/mechanism/

instrument mechanism / verified-clean

# Serial Dilution Calculator mechanism

The inspectable method record for Serial Dilution Calculator, kept separate from implementation and qualification.

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

## Model scope

The algebraic concentration formulas are standard, but the specification is incomplete for volume calculations. Define the dilution-factor convention, require final volume per step, distinguish direct from serial targets, and enforce concentration, volume, DF, and step-count constraints. Retain the stated lab-planning and not-medical-advice labeling.

- C1V1=C2V2 is the correct conservation-of-solute formula for a single dilution, but the specification does not provide the required final volume or an explicit formula for diluent volume: V_diluent=V2−V1.

- C(n)=C0/DF^n is correct only when DF means the dimensionless dilution ratio per step, defined as the previous concentration divided by the next concentration. Some protocols define dilution factor as the reciprocal dilution, so this convention must be explicit.

- The listed formulas do not specify the per-step transfer formula for a serial dilution. With a fixed final volume V_step and DF>1, V_transfer=V_step/DF and V_diluent=V_step−V_transfer.

- The inputs say target concentration(s), number of steps, and dilution factor without defining whether targets are independently calculated from the stock or are successive serial targets.

## Units and conventions

- Concentrations must use compatible units before applying C1V1=C2V2; for example, 500 micrograms/mL equals 0.5 mg/mL.

- Volumes must use one compatible unit throughout each calculation, such as mL.

- DF is assumed dimensionless and defined as C_previous/C_next, with DF>1 for an actual dilution.

- C0 is the starting concentration before step 1, and n is a nonnegative integer.

- For per-step volumes, a fixed final volume per tube must be supplied; the vectors assume no volume loss and exact pipetting.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "stock_concentration": "50 mg/mL",
    "target_concentration": "2 mg/mL",
    "final_volume": "25 mL"
  },
  "expected_outputs": {
    "stock_volume": "1 mL",
    "diluent_volume": "24 mL",
    "final_concentration": "2 mg/mL"
  },
  "working": "C1V1=C2V2. V1=(C2×V2)/C1=(2 mg/mL×25 mL)/(50 mg/mL)=50/50 mL=1 mL. V_diluent=V2−V1=25 mL−1 mL=24 mL. Check: 50 mg/mL×1 mL=50 mg; 2 mg/mL×25 mL=50 mg."
}
````

## Failure boundary

- Division by zero occurs if stock concentration C1 is zero in V1=(C2V2)/C1.

- DF=0 makes C0/DF^n undefined for n>0; DF must be positive, and an actual dilution generally requires DF>1.

- DF=1 produces no dilution and should be rejected or clearly labeled as a no-op.

- Negative concentrations, volumes, dilution factors, or non-integer negative step counts must be rejected.

- A target concentration greater than the starting concentration yields V1>V2 and is not a dilution; concentration-increasing operations require a different protocol.

- Rounding transfer volumes can change the achieved concentration, especially for small volumes or large dilution factors.

- The instrument is a planning aid only; sterile technique, material compatibility, mixing, carryover, evaporation, and protocol-specific minimum pipetting volumes are not represented.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/serial-dilution-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/serial-dilution-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/serial-dilution-calculator/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-tranche4/tranche4-results.json`