PCR Cycle / Amplification Calculator mechanism

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

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