Bitcoin's Power Law with a Narrowing Range: Floor, Trend, Top Band, Zones and the 2-Year Moving-Average Band

Abstract. We study 5957 daily closing prices of Bitcoin, from 18 July 2010 to 7 November 2026, against the published Power Law, price = 10^−16.493 × days^5.688, with days counted from the genesis block. The price range narrows from above only: measured against that line, the five cycle tops fell from 15.5 to 1.1 × while the bear-market lows stayed between 0.41 and 0.56 ×. We therefore describe the price with three nested lines. The floor is 0.42 × the published line, which forecast one to four years ahead better than five alternatives. The top band is fitted through the cycle tops and measured against the floor. It was 35 × the floor at the start, is 2.63 × in November 2026 and will be about 2 × in 2029 and 1.5 × in 2033; in the long run its distance to the floor on the log chart shrinks like days^−3, so it becomes ever smaller and never closes. The band passes within 13 % of each top. Five tops cannot choose its form. What decides is volatility: every year the price moves through a range of at least that year's volatility, which rules out a band that ends on the floor. The trend, the fair value, has no fitted number of its own. It is the Power Law line until 29 January 2022 and since then the middle between floor and top band on the log chart, 0.68 × the line in November 2026. Since 2022 it fits the closes clearly better than the straight line (0.156 against 0.195 in log10), and it was nearer to the closes it had not seen, but the evidence that the middle of the prices has left the line comes from one cycle. In dollars every line gets steeper each year, because each is a multiple of the floor; what shrinks is the distance between them. Valuation zones between the three lines separate the days that were followed by a higher price a year later (100 % in accumulation) from those that were not (6.3 % in the hot zone). The peaks of the price over its 2-year moving average halved from cycle to cycle (17.96, 9.96, 4.88, 2.48 ×), so the customary fixed ×5 upper line is no longer reached. Finally, we state a test that can prove the model wrong: if Bitcoin has not passed its October 2025 high by 2 December 2028, it will be below the floor.

Keywords: Bitcoin, power law, log-log regression, cycle tops, decaying bubbles, volatility, moving average, out-of-sample validation, quantile regression.

Version 3, 13 November 2026. Data up to 7 November 2026. In version 1 the trend was the straight Power Law line and the top band met it in May 2027. In version 2 the trend was the floor plus a premium fitted to all closes, and the top band came down onto the trend within a few years. Here the top band is measured against the floor and never reaches it, and the trend follows from the two. The live values of every line are on the Power Law page, and every formula, data source and update time is on the methodology page.

How to cite: Bitcoin Power Law Research (2026). Bitcoin's Power Law with a Narrowing Range: Floor, Trend, Top Band, Zones and the 2-Year Moving-Average Band. Version 3, 13 November 2026. https://bitcoin-powerlaw.com/en/magazin/power-law-paper

1 Introduction

The Bitcoin Power Law describes the price as a power of the time since the network started: on a chart with both axes logarithmic, the daily closes since 2010 lie along a straight line. The idea goes back to Giovanni Santostasi and to Harold Christopher Burger's "power-law corridor" (2019). Several public pages calculate the same line, and bitcoin-powerlaw.com shows it with a floor, a trend, a top band and five valuation zones.

Four things about the model were open. First, does the trend grow too fast? The last cycle was weaker than the ones before: on a linear chart the straight Power Law line runs through the last top, and the price has been below it for most of four years. Second, the top band. Drawn as a power law of its own through the cycle tops, it rose far above every recent price. Drawn so that it runs out on the trend, it ended in a kink, stayed flat for years on a linear chart and then rose with the trend like a hockey stick. Drawn as a premium over a trend that itself comes down, it sank onto the trend within a few years, and the middle of the prices would have become their ceiling. Third, the linear chart. If growth slows, why does every line still get steeper in dollars, and can the tops keep flattening the way they did? Fourth, the widely used 2-year moving-average band with an upper line at five times the average: the price has not reached that line since January 2018.

This paper answers these questions with one data set. The floor is the published formula. The top band is fitted by least squares through the cycle tops, and the trend follows from the two without a number of its own. We report how each line did on closes it had not seen, also where that speaks against our choice. Everything here can be reproduced from the data file in section 12.

2 Data

The data set has one closing price in US dollars per UTC day, without gaps, from 18 July 2010 to 7 November 2026 (5957 days):

• 18 July 2010 to 10 January 2018: Coin Metrics community data, PriceUSD.
• From 11 January 2018: OKX BTC-USDT daily candles, the close of each UTC day.

Time is measured in days since the genesis block, 3 January 2009 00:00 UTC. All logarithms are base 10 unless stated. The residual of a day is log10(close ÷ trend), and a multiple such as "2 × trend" means a residual of log10 2 ≈ 0.30.

3 The Power Law line

3.1 The formula

power law (USD) = 10^-16.493 × days^5.688

a = −16.493 and b = 5.688 are the published fit that other Power Law pages also use (bitcoinpower.law, btcpowerlaw.nl). They are fixed. On the full data set the formula has R² = 0.96 on log prices. On 8 November 2026 it gives $159’200.

3.2 Our own regression as a check

Least squares of log10(close) on log10(days), every day weighted equally, on the closes up to the end of each year:

Up to the end of 2025 the regression confirms the formula within about 1 %. We use it as a check, not as the model: refitted every day, it follows the market. In 2026, closes at about half the line took 9 % off it within ten months and moved every earlier day's values with it.

3.3 Six curves, tested on what they did not know

Each curve was fitted on the closes up to the end of a year from 2014 to 2022 and scored on the following four years: the mean of log10(model ÷ close), averaged in absolute value over the nine cuts.

A second test refitted three of them every six months from January 2014 to November 2024 (22 dates). It scored the 90 days around one, two and four years later as the root mean square of log10(close ÷ forecast), and counted how often the close was above the forecast:

The bending power law has bent downwards in every fit since 2015 and fits the past slightly better, but it never forecast better. The curve that levels off was too low four times out of five. This agrees with Baquero and Menezes: in sample a power law cannot be told from a stack of saturating curves, out of sample it is ahead at one to two years [1], and a bend cannot be told from none before the 2030s [2]. The published power law stays the backbone of the model, and the floor is a fixed share of it.

4 The floor

floor = 0.42 × power law

Measured against the Power Law line, the bear-market lows closed at 0.43 × (2011), 0.53 × (2015), 0.56 × (2018), 0.41 × (2022) and 0.41 × (June 2026). 3.7 % of all days closed below the floor, most of them in 2010, 2012 and 2015. A power law through the four bear-market lows alone has the exponent 5.71, the formula's is 5.688, and from the 2022 low to the 2026 low the price grew like days^5.68. The lows have not slowed down, so the floor keeps the published formula. A day's floor is the same as on other Power Law pages and never changes afterwards. On 8 November 2026 it stood at $66’900.

5 The trend

5.1 What the closes say

The tops have come down and the lows have not. Per halving epoch, the 95th percentile of close ÷ power law was 5.8, 6.3, 3.1, 2.8 and 1.2 ×, while the 5th percentile was 0.30, 0.41, 0.46, 0.49 and 0.45 ×. From one bear-market low to the next, the price closed above the line on 58 %, 37 %, 48 % and 24 % of days. Over the four years to November 2026 it averaged 28 % below the line and closed above it on 22 % of days. Every curve of section 3.3 fitted at the end of 2021 or 2022 was about 0.2 too high over the four years that followed. The straight line has become the upper edge of the prices rather than their middle.

Inside that range the prices have spread out. From the low of November 2022 to November 2026 the closes lie evenly between the floor and the cycle's top on the log chart: the 5th, 25th, 50th, 75th and 95th percentile of close ÷ floor are 1.08, 1.37, 1.83, 2.37 and 2.72, and the highest is 3.01. In the early cycles the price spent most days low in its range and reached the top in a short spike. A cycle's mean of ln(close ÷ floor) was 0.17 to 0.34 of its highest value in the first two cycles, 0.26 in the third, 0.46 in the fourth and 0.53 in the last, and the top stood 3.4, 2.6, 3.1, 2.1 and 1.5 standard deviations above the cycle's mean. The spikes have gone. The middle of the prices is now the middle between the floor and the top band.

5.2 The form

The trend, the fair value, has no fitted number of its own. It follows from the floor and the top band (section 7):

trend = the lower of the Power Law and √(floor × top band)

√(floor × top band) is the middle between the floor and the top band on the log chart. As long as the booms rose far above the Power Law line, that middle lay above the line, and the trend is the line. With the tops coming down, the middle fell below the line on 29 January 2022, and since then the trend is the middle. The trend is 2.38 × the floor until then (1 ÷ 0.42) and 1.62 × on 8 November 2026: $108’500, which is 0.68 × the Power Law line. It will be 1.54 × the floor in November 2027, 1.40 × in 2029, 1.24 × in 2033 and 1.08 × in 2045. It comes down toward the floor as the top band does and never reaches it, and it cannot cross the top band.

Trends compared. The fit is the root mean square of log10(close ÷ trend) over all closes, since 2018 and since 2022. The next column is the mean of ln(close ÷ trend) from the low of November 2022 on, and the last is the trend on 8 November 2026 as a multiple of the Power Law line:

The trend in bold fits all closes best, though no number of it is fitted to them. With a limit fitted to the closes in place of the Power Law line (2.46 × the floor, which is 1.035 × the line), the fit is 0.2947: the Power Law line is the limit the closes would choose themselves. Rounded corners in place of the kink (a smooth minimum, a tanh) fit worse (0.2973, 0.2992). A share of the way from floor to top band other than half, fitted to the closes (0.58 to 0.73), fits no better and forecasts worse. The middle on every day fits the years since 2018 as well, but not the early cycles, when the price spent most days far below the middle of its range.

Over the next twelve months the trend grows by 29 %, the floor by 36 % and the top band by 22 %. Two years from now the trend's growth is 27 % a year, four years from now 25 %. In 2014 it grew by 182 %, in 2018 by 82 % and in 2022 by 39 %.

5.3 How sure it is

On closes it did not know, the trend did better than the alternatives. The evidence is still thin, and a reader should know why.

For the test, the top band was fitted on the cycle tops known at the end of 2014, 2016, 2018, 2020, 2022 and 2024, and the trend that follows from it was measured on the closes of the four years after each date. The table shows the mean of ln(close ÷ trend) per cut, the mean of the six absolute values and the mean root mean square:

A trend fitted to the closes themselves found no bend before the last cycle and was then far off. The trend taken from the top band saw the bend coming with the tops of 2017 and 2021. That is why we calculate it from the tops and do not fit it to the closes.

The limits:

• One cycle of evidence. That the middle of the prices has left the Power Law line shows in the last cycle only. From one bear-market low to the next, the price averaged +0.25, −0.17, +0.09 and −0.08 (ln) around the trend and closed above it on 58 %, 37 %, 49 % and 46 % of days. Around the Power Law line the last cycle averaged −0.32.
• The lower half of the closes has not come down. Over all closes the 10th, 25th and 50th percentile are at 0.46, 0.55 and 0.80 × the Power Law line, and a quantile regression over time [5] has them drift up by 1 to 2 % a year, while the 75th and 90th percentile fall by 6 and 11 % a year. What came down is the upper half.
• The trend is only as sure as the top band. Five tops determine the band (section 7.6). A new cycle top moves the band, and with it the trend from January 2022 on. Before that date the trend is the published formula and never changes.

The fair value differs from the one other Power Law pages show ($108’500 against $159’200 on 8 November 2026); the floor is the same.

6 Residuals

Against the trend, the residuals have a mean of 0.01 and a standard deviation of 0.30 (a factor of 2 either way). 69.0 % of days lie within one standard deviation and 95.2 % within two. The highest residual was +1.19 on 8 June 2011 (15.5 × trend), the lowest −0.68 on 5 October 2010 (0.21 ×). On 7 November 2026 the residual was −0.15 (0.70 × trend).

Residuals are not independent noise. Their autocorrelation is 0.998 at one day, 0.90 at 30 days, −0.22 at one year and −0.38 at two years. A deviation fades within about a year and then tends to swing to the other side. That is the cycle: about four years from top to top. Daily closes therefore carry far less information than their number suggests. The record is five cycles, not thousands of independent observations, and every statement in this paper should be read with that in mind.

The spread of the residuals narrows from above more than from below. Per halving epoch, the 95th percentile of the residual was +0.77, +0.80, +0.49, +0.44 and +0.18, the 5th percentile −0.52, −0.38, −0.33, −0.25 and −0.19. Annual means were +0.24 in 2013, +0.35 in 2021 and −0.12 in 2026.

7 The top band

7.1 Cycle tops

A cycle top is an all-time high that stood for at least 365 days. The highs on the way up (April 2013, April 2021, March 2024) were passed within eight months and do not count.

Each top was a smaller multiple of the floor than the one before: 37, 26, 15, 6.6 and 2.7 ×. On the log chart a top's distance to the floor, ln(top ÷ floor), shrank by 0.35, 0.56, 0.82 and 0.90 from top to top, so the gap closed faster each cycle. From top to top the price grew like days^5.2, ^4.8, ^3.4 and ^2.3, while the floor grows like days^5.688.

7.2 The form

The top band is that distance as a curve, fitted by least squares on ln(top ÷ floor) through the five tops:

top band = floor × e^(3.56 ÷ (1 + (days ÷ 4692)³))

The distance starts at 3.56, which is 35 × the floor. Half of it is gone on day 4692 (8 November 2021), and in the long run it shrinks like days^−3: it becomes ever smaller and is never zero. The band was 31.8 × the floor at the start of 2013, 17.6 × in 2017, 7.1 × in 2021 and 2.63 × on 8 November 2026 (about $175’900). It will be 2.36 × in November 2027 (about $215’000), 1.97 × in November 2029 (about $318’000), 1.54 × in 2033, 1.34 × in 2037 and 1.16 × in 2045. The top band stays above the trend and the trend above the floor on every day: the three lines never cross, and each of them rises every day.

The band passes within 13 % of each top. 96 days (1.6 %) closed above it: 91 of them in 2021 (up to 1.19 × the band on 13 April 2021, a high on the way up), three in 2017 and two in 2011.

Its two numbers hardly moved as tops joined: 3.55 and 4749 with three tops, 3.53 and 4855 with four, 3.56 and 4692 with five. Fitted on the first three tops, the band was 7 % below the fourth. Fitted on the first four, it was 22 % above the fifth. Leaving out one top at a time, the other four predict it within 22 % (band ÷ top 0.86, 1.21, 0.95, 0.84, 1.22).

7.3 Forms compared

Nine forms with two fitted numbers, each fitted to the five tops by least squares on ln(top ÷ floor); the root mean square of log10(band ÷ top) is the fit. For the forecasts, each form was fitted on the tops before and had to predict the fourth and the fifth top (predicted ÷ actual). The last columns show where the band then stands, as a multiple of the floor:

Five tops cannot choose the form: several pass within 15 % of each top. The two that fit them most closely, a premium over the floor that fades like e^(−years²) or e^(−years^1.5), end on the floor. The first is 4 % above it in 2033, the second 15 % in 2033 and on it by 2045. The band of version 2, a premium over that version's trend, also fitted the tops more closely (0.028, within 11 % of each top), and it ended on the trend. Whether such an end can be right is decided by something the tops do not show: how far the price moves within a year.

7.4 Volatility decides

The yearly volatility of the daily returns fell from 142 % in the first halving epoch to 98 %, 82 %, 63 % and 45 % in the fifth. Tested on what it did not know, it is best described as falling like a power of the days, 0.59 × (days ÷ 5000)^−0.555: 51 % in November 2026, 47 % in 2029, 42 % in 2033 and 34 % in 2045. A straight extension of the last decade's fall, 7.6 % less every year, gives 42 %, 34 %, 27 % and 11 %.

In every year so far the price moved through a range on the log chart of at least once that year's volatility, and the cycle tops stood 1.9 to 3.6 times the volatility above the floor. A band 4 % above the floor in 2033 would be a tenth of a calm year's range. The price would be above it in most years, and it would not mark tops. That rules out the forms that end on the floor.

The band of this paper is 1.9 times the volatility above the floor in 2026, 1.4 in 2029, 1.0 in 2033 and 0.4 in 2045 if volatility falls as it did over the whole history, and 2.3, 2.0, 1.6 and 1.4 times if it keeps falling as in the last decade. So the band says: booms keep shrinking about as fast as volatility has fallen in the last ten years. If volatility falls more slowly, tops will be above the band from the 2030s.

Among the forms with a slow end, a distance that shrinks like a power of the days, the tops fit the third power best. Fitted as a third number, the power is 3.3. We fix it at 3, so that five tops determine two numbers and not three.

7.5 On a linear chart

Every line is a multiple of the floor, and the floor grows like days^5.688: by 36 % over the next twelve months, 25 % in 2033 and 16 % in 2045. A rate that falls this slowly, on an amount that keeps growing, still means more dollars every year. On a linear chart every line therefore gets steeper, the top band too.

In dollars the tops did slow: from top to top the price rose 39-fold, 17-fold, 3.4-fold and 1.85-fold. That cannot continue. From October 2025 to October 2029 the floor alone rises 3.4-fold, and it passes the 2025 top in December 2028 (section 10). A top band that kept flattening in dollars would be below the floor within three years. The floor has held where it was tested, with lows at 0.41 to 0.43 × the Power Law line in 2011, 2022 and June 2026. So the slowing of the tops is measured against the floor: 37, 26, 15, 6.6 and 2.7 × at the tops, 2.0 × in 2029 and 1.5 × in 2033. On the linear chart the top band stays above the trend and the trend above the floor on every day, and the three run closer together every year.

7.6 What the band cannot say

Five tops are few. That the next booms end at about twice the floor in 2029 and one and a half times in 2033 is what these five tops say when their pattern is carried on. Nobody knows it. The 2025 top was 13 % below the band, the widest miss of the five together with 2013. The last cycle did not reach the band, and the band has come down for it: the first four tops alone put it 22 % above that top. From October 2027 the band lies below the straight Power Law line, the fair value other Power Law pages show: the model then says that booms no longer reach that line. The 2021 top was 2.75 × it, the 2025 top 1.12 ×. The band also assumes that volatility keeps falling as in the last decade (section 7.4). It is fitted again whenever a daily close arrives, and a new cycle top moves it.

8 Zones

The zones lie between the model's own lines, not at fixed multiples of the trend:

√(floor × trend) is halfway from the floor to the trend on the log chart, √(trend × top band) halfway from the trend to the top band. Since January 2022 the trend is the middle of the band, so the bounds are the band's quarter points on the log chart: accumulation is the lowest quarter between floor and top band, fair the middle half, hot the top quarter. On 8 November 2026 the four bounds are 0.62, 0.79, 1.27 and 1.62 × the trend.

Every close is sorted using today's lines. For the 5592 days that have a close 365 days later, the table shows whether that later close was higher:

Below the trend the record hardly splits. In the first eight tenths of the way from the floor to the trend, the close a year later was higher on every day, in the ninth tenth on 99 % of days and in the last on 86 %, so accumulation is simply the half nearer the floor. Above the trend the record turns before the middle. Days in the first four tenths of the way from the trend to the top band were followed by a higher close in 55 to 92 % of cases, between four and five tenths in 18 %, and beyond the middle in 11 % and less. Halfway needs no fitted number. It leaves the fifth tenth in fair, which is why fair's record is 78 % and not higher. A bound at a third of the way would give 89 % for fair and 14 % for hot: a less sharp split for one more number.

The zones move with the lines: twice the trend was fair in 2017, hot in 2021 and is euphoria today. Three of the five cycle tops (2011, 2017, 2021) closed in euphoria, the other two in hot. The lines come closer together and the zones with them, each keeping its share of the band: in 2030 the four bounds are 0.72, 0.85, 1.18 and 1.39 × the trend, in 2045 0.93, 0.96, 1.04 and 1.08 ×. Fixed multiples of the trend could not stay, because from July 2033 the floor itself is more than 0.8 × the trend. These outcomes describe five cycles fitted with hindsight, not thousands of independent trials.

9 The 2-year moving-average band

The 2-year moving average (2Y MA) is the mean of the last 730 daily closes, available from 16 July 2012 (5228 days). The band is usually drawn with an upper line at five times the average.

9.1 A fixed ×5 is no longer reached

The price closed at or above 5 × its average on 251 days: 145 in 2013, 38 in 2014, 53 in 2017 and 15 in 2018, the last on 15 January 2018. The highest multiple since was 4.88 (February 2021). On 7 November 2026, five times the average was $447’000, or 4.1 × trend. Even when the price did reach it, ×5 was a poor top signal: a year after those 251 days the close was lower on 153 of them.

9.2 The peaks halve each cycle

A cycle's peak is the highest multiple of the 2Y MA between the cycle's low and its top.

Three times in a row the peak was about half the one before. That is a trend, not an anomaly of the last cycle. It began between 2013 and 2017, before the indicator was widely followed, so front running alone does not explain it. It follows from the Power Law itself: the tops come closer to the floor each cycle, and the Power Law line grows more slowly every year. One-year and three-year averages show the same halving. The peak usually came well before the top in dollars: 239, 260 and 572 days earlier in 2013, 2021 and 2024.

9.3 The level

A price that rises exactly with the Power Law line sits above its own 2-year average, because the average looks back:

level = power law ÷ its mean over the last 730 days = (b + 1) × x ÷ (1 − (1 − x)^(b + 1)),   x = 730 ÷ days

The level falls as the line's growth slows: 3.18 in April 2013, 1.83 in December 2017, 1.57 in February 2021, 1.44 in March 2024, 1.37 on 7 November 2026, 1.30 in 2030 and 1.24 in 2035. An upper line below the level would call plain Power Law growth a top.

9.4 The line

Each form was fitted on the first two and three peaks and had to predict the next:

The square-root line fits far better than any other shrinking form: the root of a peak's excess over the level fell by the same amount each year (0.26). Measured over 1 instead of the level it fits slightly better, but it would end on the average itself in September 2028, while the price has been above its average on 72 % of all days. The level is the one end point that agrees with the Power Law and needs no third parameter. A fixed multiple is beaten by every shrinking form from 2017 on.

upper line = 2Y MA × (level + (5.0401 − 0.0007178 × days)²)

R² 0.993 on the roots. The line was 17.96 × the average in July 2013, 9.81 × in 2017, 4.67 × in 2021, 1.91 × in 2025 and 1.50 × on 7 November 2026 (about $134’000). The root reaches zero on 25 March 2028, and from then on the line is the level. Leaving out one peak at a time, the other three predict it within 16 %.

The price closed above this line on 33 days (0.6 %), and a year after each of them it was lower. That is hindsight, because the line is fitted through those peaks; ×5, fitted to nothing, managed 153 of 251. The lower line, the average itself, needs no change. Of the 1171 days below it that have a close a year later, the price was higher on 1135 (97 %). The 2Y MA line marks a market that has run hot, not the top in dollars. For the top, the top band is the better tool.

10 A test of the model

The pattern of the tops and the pattern of the lows cannot both continue. Taken alone and in dollars, the tops level off: from top to top, log10(price) grew by 0.64, 0.31, 0.14 and 0.07 a year, half as much each cycle. A Gompertz curve on log10 price fits all five tops better than the top band (0.018 against 0.041) and levels off near $180’000. It is not a usable model, though. Fitted on the first three or four tops, it was 13 % too low for the next one, and it would be below the floor from August 2029. That is why the band is measured against the floor, and the trend lies between the two.

The two readings part soon. The floor passes the October 2025 high of $124’673 on 2 December 2028. If Bitcoin has not closed above that high by then, it is below the floor, and the Power Law in this form no longer describes it. If it has, the tops have stopped levelling off in dollars the way they did. Either way the model can be checked in public on a known date.

11 Limitations

• Few events. Five cycle tops and four 2Y MA peaks carry the bands. Each new top will test them, and the bands are refitted when one joins. The trend since January 2022 moves with the top band.
• One cycle. That the middle of the prices has left the Power Law line rests on the last cycle (section 5.3). The earlier cycles do not show it.
• Volatility. The top band assumes that booms keep shrinking about as fast as volatility fell in the last decade (section 7.4). If volatility falls more slowly, tops will be above the band from the 2030s.
• Dependence. The residuals are strongly autocorrelated (section 6). Shares of days and R² overstate how much independent evidence there is.
• Hindsight. Zone outcomes and the 2Y MA line's record are measured with lines fitted to the same history. The out-of-sample results (3.3, 5.3, 7.2, 7.3, 9.4) are the fairer evidence.
• Narrowing lines. In 2045 the top band is 16 % above the floor, and all four zone bounds lie within 8 % of the trend. The zones are then narrow strips, and whether the price will really move so little is the same assumption about volatility.
• No forecast of tomorrow. The model describes where the price stands relative to its history, not what it will do next. This is not financial advice.

12 Data and reproducibility

The daily closes with trend, floor and residual for every day are free to download as CSV: /power-law/btc-daily.csv, with the columns date, close_usd, days_since_genesis, trend_usd, floor_usd, residual_log10. The same data is available to programs and AI agents at /api/data and through the read-only MCP endpoint /api/mcp. The methodology page lists every formula with the parameters in use today; the top band is fitted again whenever a new daily close arrives, and the trend since January 2022 follows it. You are welcome to use, reproduce and extend this work. Please cite it as shown at the top.