Source: https://guthlabs.ai/docs/instruments/pcr-cycle-amplification-calculator/mechanism/

instrument mechanism / verified-clean

# PCR Cycle / Amplification Calculator mechanism

The inspectable method record for PCR Cycle / Amplification Calculator, kept separate from implementation and qualification.

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

## Model scope

The amplification equation is conditionally standard. The Ct equation needs an explicit 100% efficiency and assay-comparability assumption, or an efficiency-adjusted alternative. Retain the existing educational and not-medical-advice labeling, and display the efficiency-unit convention prominently.

- N_final=N0×(1+E)^cycles is correct only for a constant per-cycle efficiency E expressed as a fraction; the allowed range and cycle-count constraints are not specified.

- N0=N_ref×2^(Ct_ref−Ct) is correct only under the ideal 100% efficiency assumption, with comparable assays and Ct values defined on the same scale. For efficiency E other than 1, the base should generally be 1+E rather than 2.

- The output fold amplification is not explicitly defined. It should be stated as (1+E)^cycles, or equivalently N_final/N0 only when N0 is nonzero.

## Units and conventions

- Efficiency E is a dimensionless fraction: 90% must be entered as 0.90, not 90.

- Cycle count is a dimensionless nonnegative integer.

- Ct values are dimensionless cycle numbers.

- N0, N_ref, and the computed quantities use the same copy-number units.

- The Ct formula assumes equal target/reference behavior and 100% amplification efficiency unless an efficiency-adjusted formula is supplied.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mode": "amplification",
    "initial_copies": 1000,
    "efficiency": 1,
    "cycles": 10
  },
  "expected_outputs": {
    "final_copy_number": 1024000,
    "fold_amplification": 1024
  },
  "working": "1. Convert efficiency: E=1, so 1+E=2. 2. Compute fold amplification: 2^10=1024. 3. Compute final copies: 1000×1024=1,024,000."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

An efficiency of -2 with a fractional cycle count of 0.5 makes the amplification base negative and raises it to a non-integer power, producing no real-valued result. The calculator should reject this input or explicitly return undefined rather than silently returning an invalid quantity.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/pcr-cycle-amplification-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/pcr-cycle-amplification-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/pcr-cycle-amplification-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`

- `BOUNDARY_HAZARD_CATALOG.json`