The source, checked

what the description says

The description defines the entry point two ways at once: a retracement ratio on the prior leg, and a projection from the origin point.

what the arithmetic gives

The two paths lead to different prices — the divergence reaches 17% of the move —, and one of the branches requires a retracement larger than the very move that produces it, which does not exist.

what the description says

That squaring the constant makes the slow extreme «equivalent to a 900-period trend», and, further on, that the line «varies from 25 to 900 (5² to 30²)».

what the arithmetic gives

3.5 to 480 periods. What gets squared is the smoothing CONSTANT, not the period — and sc² does not correspond to n².

what the description says

That higher volatility produces «an increase in the smoothing constant and consequently a SLOWER trend».

what the arithmetic gives

Faster. The chain has three links and the first two are right — higher volatility ⇒ higher ratio ⇒ higher constant —, but in exponential smoothing a higher constant is a faster trend.

what the description says

That the constant varies between a fast limit of 0.5 and a slow one of 0.05, with the rule «if the constant exceeds the slow limit, use the slow limit».

what the arithmetic gives

A FIXED 39-period exponential. The printed limiter locks the constant at 0.05 whenever it exceeds it — and the branch that would return the fast limit is cancelled by the next line.

what the description says

The rule twice: first as a formula, then rewritten in words as the «general form». The two versions give opposite results.

what the arithmetic gives

The printed formula returns the LONGER period when the market is quiet; the rewritten general form returns the SHORTER one.

what the description says

In both techniques, that the period responds to the LEVEL of volatility: «as volatility increases, the period will be shorter» and «as price becomes more volatile, a shorter period may be used».

what the arithmetic gives

They respond to CHANGE, not to the level. Both divide volatility by its own recent volatility, and the scale cancels out: a permanently violent market gets the same period as a permanently calm one.

what the description says

That the correction «succeeds in several ways, but at the cost of losing some of the most extreme cases».

what the arithmetic gives

It loses all of them. The corrected value stays between 36.7 and 63.3 — it never reaches 30 or 70. It follows from the printed formula: the oscillator is the average of ten daily closing positions, which clusters around 50, and the correction subtracts a five-period average of that.

what the description says

That the negative directional movement is «today's low minus yesterday's» — and states, in the next paragraph, that «on an inside day both the positive and the negative movement are zero».

what the arithmetic gives

The two statements cannot both be true. On an inside day the low is HIGHER than yesterday's, so the printed formula gives a positive number, never zero. The original definition has the terms inverted.

what the description says

That the true range of a bar is the largest of three values, and the third one is «today's close minus yesterday's low» — stating on the same line that «the true range is always positive».

what the arithmetic gives

That third term spans TWO bars, so it is not any bar's range at all. The missing term is the symmetric one — YESTERDAY's close minus TODAY's low —, which is what measures the downside gap.

what the description says

That you should only take long trades «when the average directional index is rising» — and, in the same paragraph, describes that index three incompatible ways, among them «an oscillator such that, when its value crosses above 50, the move is upward».

what the arithmetic gives

The index is defined in another chapter with an ABSOLUTE VALUE, and the same text comments on the effect: «the absolute value makes the index lose the information of which direction prices are going». An index that has discarded direction cannot pick the side of the trade.

what the description says

That the 14-period smoothed sum, defined as «yesterday's value, minus yesterday's value divided by 14, plus today's», «can also be produced using a smoothing constant of 0.071, which is an approximation of the fraction 1/14» — and prints «0.071 × yesterday's value plus today's».

what the arithmetic gives

The two forms are not the same. Subtracting 1/14 from yesterday's value leaves 13/14 of it, that is 0.929 — and that is the multiplier. The 0.071 is what gets SUBTRACTED, not what is left. Swapped, what was a 14-period sum becomes nearly the bar's raw value.

what the description says

That you go LONG if «the positive indicator crosses above the negative», and SHORT if «the negative indicator crosses below the positive».

what the arithmetic gives

The two conditions are the same. The negative falling below the positive is the positive being above the negative — the same inequality written backwards. As printed, the system signals both a buy and a sell on the same bar and never goes short.

what the description says

That traders use «0.382, the complement of 0.618, as a key retracement level» — and adds, in the same sentence, that «this is NOT a Fibonacci ratio».

what the arithmetic gives

0.382 is both things at once: it is the complement (1 − 0.618 = 0.382) AND it is the square of the ratio itself (0.618² = 0.38197). A power of the golden ratio is as derived from the sequence as the ratio itself. And the source itself derives it from the sequence a few pages later, when listing the ratios of the combined Fibonacci-Lucas sequence: «F_i/L_{i+2} = L_i/L_{i+2} = 0.382».

what the description says

That the fifth wave's target is found by solving for its value such that «Wave 1/Wave 5 = Wave 5/Wave 3 = 0».

what the arithmetic gives

A ratio of two lengths is only zero if the numerator is zero, that is, if the wave does not exist. As written, the target is a move of zero size. The surrounding text calls for the geometric mean — solving for Wave 5 such that Wave1/Wave5 = Wave5/Wave3, that is, Wave5² = Wave1 × Wave3 — and the «= 0» is a printing artifact over the equals sign.

what the description says

That the stop should be placed «just beyond each trade's maximum adverse excursion, determined by historical evaluation» — or at 2.5% of price, whichever is smaller.

what the arithmetic gives

A trade's maximum adverse excursion is the worst point it passed through, and is only defined after the trade ends. The rule asks, at the moment of entry, for a number that will only exist at the exit: it uses information from the trades it is supposed to protect. The «or 2.5%, whichever is smaller» does not fix it, because the smaller of the two still depends on the unknown value.

what the description says

That you go long when «condition A OR condition B» is true, and that you flatten the long when «not-A OR not-B» is true.

what the arithmetic gives

The two overlap. With A true and B false, the entry rule fires (A or B) and so does the exit (not-B) — it enters and exits on the same bar, and the pair is not executable without a precedence convention. The logical opposite of «A or B» is «not-A AND not-B», with AND, not OR.

what the description says

Presents, under the title «high-low volatility», a formula that sums the log of the ratio between consecutive closes, squared, multiplied by the constant 0.601.

what the arithmetic gives

The formula contains neither the high nor the low: it is a rescaled close-against-close measure. And the constant gives away what was intended — 0.601 is 1/(2·√ln2), the factor that converts the log of the HIGH/LOW ratio into a standard deviation. It has no function at all over a ratio between closes.

what the description says

Defines the mean A as (1/n) times the sum, from i = 1 to n, of ln(R_{t−1}); and the variance as (1/(n−1)) times the sum, over the same indices, of (ln(R_{t−1}) − A)².

what the arithmetic gives

The summed term does not depend on the sum's index. The average of n copies of the same number is the number itself, so A = ln(R_{t−1}) — and every term of the variance becomes (ln(R_{t−1}) − ln(R_{t−1}))². **The variance is identically zero**, and so is the standard deviation.

what the description says

When setting up the test procedure, it states that «the two trends used will be 10 and 60 days». One page later, and in every results table, the underlying system is a 40-day average.

what the arithmetic gives

The declared periods and the tested ones are disjoint sets: {10, 60} and {40}. No published number comes from the announced configuration, and the announced configuration has no published number.

what the description says

In the procedure, it says to enter «if today's volatility is ABOVE the LOW filter's threshold, or BELOW the HIGH filter's threshold». In the results, it calls «high-volatility filter» the one «that allows trades only ABOVE its threshold».

what the arithmetic gives

The two namings are opposite. In the procedure, the filter is named by the POSITION of the threshold, and the «low filter» admits high-volatility days. In the results, it is named by the REGIME it admits, and the «high filter» admits high-volatility days. Implementing by the wrong name inverts the filter.

what the description says

After comparing the average true range with annualised volatility, it states that «both can be converted into dollar values by multiplying by the current price».

what the arithmetic gives

It holds for annualised volatility, which is dimensionless because it is the standard deviation of returns. **The true range is already in price units** — it is a difference between prices. Multiplying it by price gives price squared, which is not a monetary quantity.