= Amplification blank timing
<Amplification blank timing> specifies when background-generating material enters relative to the cycles of a <chemical multiplication reaction>. Earlier contamination can undergo more multiplication than later contamination. A detector blank and a full <chemical amplification blank> can therefore test different sources of response.
Let cycle $j$ have multiplier $K_j$ and let $b_k$ enter immediately after cycle $k$. Background $B_0$ present before the first cycle contributes
$$
B_n=B_0\prod_{j=1}^{n}K_j+\sum_{k=1}^{n}b_k\prod_{j=k+1}^{n}K_j.
$$
An empty product equals1: material introduced after the final cycle receives no further gain. This is an original bookkeeping model for the repeated-cycle setting described by IUPAC.<Classification and Use of Terms for Amplification and Related Reactions by D. T. Burns and others>[p.1332, ideal direct multiplication over repeated cycles.]{ref}
For four ideal doubling cycles, one background unit introduced before all cycles becomes16 units. The same unit introduced after cycles1,2,3 or4 becomes8,4,2 or1, respectively. Matching the final reagent composition does not reproduce these different histories.
An original diagnostic model assumes constant multiplier $K=2$, initial background $B_0$ and equal added background $b$ after each cycle. Then $B_1=2B_0+b$ and $B_2=4B_0+3b$. If mean blank responses are3 and7 in the model's amount units, $b=B_2-2B_1=1$ and $B_0=1$. Replicated cycle-count series can test this pattern; two values fitting two unknowns do not independently validate it.
A practical comparison processes blanks from the earliest relevant handling stage and includes deliberately later-entry controls. IUPAC distinguishes a procedural blank carried through the entire procedure from blanks covering only particular stages.<Blank material in the IUPAC Gold Book>[Entry08010, note4, procedural and stage-specific blanks.]{ref} Differences can help localize contamination or spontaneous reporter formation, but changing yield, matrix effects and nonlinear gain can create alternative explanations. Report entry stage and cycle count with the blank response and its variation.
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