SMA and EMA check
Fixed fictional reference; no market observations

Up to 240 prices, each greater than zero and at most 1,000,000,000, with at most 12 decimal places. At most 80 characters per line and 20,000 in the price input. The unit label has 1–24 permitted letters, numbers, spaces or . _ - /. Exact fractions are used without intermediate rounding.

1. Record the source instrument, unit, equal period length, session/time zone, closing-price field, adjustment policy and history start. Confirm the bars are closed and the series has no missing periods. The form cannot verify those facts.

2. Paste one positive price per line, no header or internal blank line. Set N and explicitly choose the EMA seed. Keep the original source record. α = 2/(N+1); β = 1−α. Do not round intermediate values.

3. Fictional reference: prices 100; 110; 90; 110; 100 USD and N = 3. SMA: unavailable; unavailable; 100; 310/3; 100. SMA-seeded EMA: unavailable; unavailable; 100; 105; 102.5. First-price EMA: 100; 105; 97.5; 103.75; 101.875. The final difference is 0.625 USD, not a percentage.

4. At row 5, SMA weights are 0; 0; 1/3; 1/3; 1/3. SMA-seeded EMA weights are 1/12; 1/12; 1/12; 1/4; 1/2; first-price EMA weights are 1/16; 1/16; 1/8; 1/4; 1/2. Each set sums to 1; weighted prices give 100; 102.5 and 101.875, respectively.

5. Spreadsheet: prices in B2:B6, N in H2 and α in H3 =2/(H2+1). First SMA in C4 =SUM(B2:B4)/$H$2. SMA-seeded EMA: D4=C4; D5=$H$3*B5+(1-$H$3)*D4. First-price EMA: E2=B2; E3=$H$3*B3+(1-$H$3)*E2. Copy the recurrences downward. N = 3 fixes these example start rows; another N changes them.

6. Import exact CSV fields as text to preserve long fractions and avoid dates. Spreadsheet floating-point precision can differ in final digits. Compare source history, sessions, adjustments and seed before claiming a mismatch. A matching calculation is not proof of a platform setting or strategy quality.

Your verification record
Source / instrument / price unit: ____________________
History start / period / session / time zone / closed bars: ____________________
N / alpha / seed / inspected row: ____________________
Missing or unverified data: ____________________
Arithmetic and weights checked by / on: ____________________

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