P(t) = 10A · t3β × saturation(W) × ζ·[euphoria(de) − panic(dp)]
Compiled in August 2026 · observed through early August 2026 · everything to the right is computed
Three layers stitched together: the Metcalfe exponent sets the slope of the power-law growth; a monetary ceiling sets the height that growth runs into; and that same ceiling, by straightening the trend, turns one and the same cycle into deeper drawdowns and weaker rallies. Each layer owns its own time scale: the first governs decades, the second governs how it all ends, the third governs the four-year waves inside.
From the H4 peak to the H6 halving — detail
The same data as on the upper panel, but on a linear scale and across one whole cycle: from the October 2025 peak through the trough, the April 2028 halving, the H5 peak and trough — up to the H6 halving. The model's nodes are labelled: the observed/computed boundary, the halving, the peak, the trough and the end of the window. Left of the boundary the orange line is fact, to the right it is calculation only, at the current slider positions. The blue band runs the owner ceiling ±40% and opens up noticeably by the end of the window.
Three lines. The grey dashed one carries the trend: a power law with saturation, cycles removed. The dashes work as a spine the asset keeps returning to, and by themselves predict nothing. The blue one multiplies that spine by the cycle overlay. The orange one shows what happened.
The upper panel runs on a logarithmic scale. The lower one carries the residual, measured in dex. Dex expresses “how many times” in logarithmic form: +1 dex puts the price ten times above the trend, −0.3 dex roughly halves it, zero lands exactly on the spine.
Everything else on both panels is markup. The grey bands are the halving epochs H0–H8. The dashed vertical separates fact from calculation: observations to the left, model only to the right, at the current slider positions. The thin lines at ±0.5 dex below are the regime band from falsification criterion 5.
As of August 2026 the residual holds around −0.36 dex, that is, the price sits a little below half the trend. This looks worse than it behaves: every post-halving trough parked between −0.24 and −0.38 dex. A trough is supposed to look like that. The alarming signal would be a residual that leaves the ±0.5 dex band and stays out: that is falsification criterion 5, which has never fired for longer than five months.
| Epoch | Halving | Peak | Trough | a — peak, dex above trend | b — trough, dex below trend | Drawdown |
|---|
Amplitudes for the computed epochs are shown as effective, that is, already multiplied by ζ. A euphoric peak needs headroom above the trend, while swings among those who already own require none, so the amplitude has two sources: ζ = d_e + (1 − d_e)·φ, where φ is the share of the trend's travel that the ceiling lets through. The multiplier is constant within an epoch and is taken at its peak. Epochs H0–H4 are not touched at all: there φ = 1.00 to within half a percent, and there is nothing to rewrite in a measurement.
Epochs H0–H4 are calibrated against observed data; the lower node of H4 is calibrated to the late-June 2026 minimum, $57,950, so the model matching it there checks nothing. The dex amplitudes are fixed at β = 1.897; move the β slider and the dollar nodes travel with the trend, ceasing to coincide with the observed extremes — that is the visible part of the same check. H5 onward are computed from two sliders independently, after which both amplitudes are multiplied by ζ: a is projected by the euphoria decay, b by the panic decay. The drawdown follows from their combination, not from a common swing.
The peak and trough in the table are model nodes, that is, the trend of the corresponding month multiplied by the calibrated amplitude. The drawdown follows directly from them, as 1 − trough / peak, and stays smaller than the swing: the trend itself grows in the time between peak and trough. The observation series on the chart runs on month closes, while the nodes run on intra-month extremes, which produces small discrepancies between the table and the orange line.
Three layers multiplied by one another. The first two are independent, the third is tied to the second by the multiplier ζ: the amplitude of the cycle needs headroom above the trend, and saturation is exactly what eats that headroom.
Early intuition about bitcoin often said “exponential growth”, but that would be a strong oversimplification. An exponential doubles over equal intervals: a year, another year, another year. A power law needs an ever longer stretch for the same multiple.
The formula P ∝ t3β reads as follows: the price grows as the age of the network raised to 3β, with age counted in days from the genesis block of 3 January 2009. The exponent 5.69 is measured straight off the price, and it has a separately measured decomposition into two quantities, each with its own physical reading:
| 3.046 | The number of non-zero addresses grew roughly as the cube of the network's age, R² = 0.977 over the whole history. The estimate rests on the early years: over the data of the last decade the growth is noticeably slower — discussed in the objections. |
| 1.838 | The value of a network grows faster than the number of participants — Metcalfe's law in generalised form. Each new participant adds not only themselves but the connections to everyone else. The measured value lies between textbook Metcalfe (n²) and Odlyzko (n log n). |
| 5.60 | The product of the two measured quantities: 3.046 × 1.838. It differs from the slope read straight off the price by 1.6% — and that discrepancy is worth keeping in mind. |
| 5.69 | The slope measured directly from the price, R² = 0.961. The model computes with it rather than with the product; the β slider shows 5.69 / 3 = 1.897, that is, the Metcalfe exponent at which the product would come out exact. |
Hence the logarithmic scale on the chart, where each division means a factor of ten. A power law straightens out on such a scale, and departures from it become visible to the eye. Proportions are preserved too: a fall from $100 to $50 looks like a fall from $100,000 to $50,000, because for the owner both mean a half.
Layer 1 carries two fitted numbers: the exponent and a multiplier. Those two have to reproduce 194 monthly observations spanning six orders of magnitude in price, and the residual leaves ±0.5 dex in only 14 of them — almost exclusively on the blow-offs of 2011 and 2013/14, where the price itself behaved abnormally.
Those same 14 out of 194 are what the miss counter under the β slider shows, so the claim “β was measured, not chosen” is not to be taken on trust. Move the β slider to 1.70 and the misses become 26, with more than half of the new ones falling on 2010–2012: the early history falls off first, because it is what sets the slope. Nearly doubling on a shift of two tenths is what the words “narrow corridor” amount to.
When β changes, the curve is recalibrated through a reference point at the logarithmic centre of the observations — day 2971 from genesis, February 2017. The rotation happens around the centre of mass of the data rather than around an arbitrary end, otherwise the slider would break the fit for a reason having nothing to do with the exponent itself.
Whether all of this counts as evidence or as curve fitting is discussed below, in the objections, since it comes up first thing every time.
Cubic growth runs into the obvious: both the people on the planet and the money they have are finite. Every network — telephone, internet, payment — goes the same way: acceleration first, then slowdown, then a plateau. An S-curve.
In the model this is arranged as soft braking: P = Ptrend · L / (Ptrend³ + L³)⅓, where L is the plateau level. The mechanics are simple: far below the plateau the braking is almost imperceptible, closer to it the braking drags. The cubic power governs how soft the transition feels, stretching it over years instead of a step.
The plateau level is a monetary constraint. Terminal capitalisation is made up of the number of owners and how much falls to each owner on average, and the price comes from dividing by the coin supply: plateau = W · A / S, where A = $8,447 of terminal holding per person and S ≈ 20.7M coins in circulation by the mid-2030s. The ceiling enters linearly: an error by a factor of two moves the plateau by a factor of two.
The $8,447 itself comes from a division, not from a measurement. Of the three quantities — ceiling, average holding size, plateau level — only two are independent, the third is computed from them. The outer two are pinned. The base ceiling is 1610 million owners: the middle of the plausible corridor of 1300–1900 and about 27% of adults. The base plateau is $657k, that is, a terminal capitalisation of $13.6T, a little under half the value of all the gold ever mined. From there A = $13.6T / 1610M = $8,447 per owner. After that A is fixed and the slider moves only W: capitalisation and plateau follow it linearly, while the average holding size stays as it was.
On its own A is not measured. It is the calibration base expressed per person, and arguing with the plateau level makes sense precisely through it: $8,447 per owner is of the same order as an average retail brokerage account, and it either looks plausible or it does not.
The Metcalfe exponent is absent here, and that is deliberate. The temptation to run the plateau through the same β is strong, but the arithmetic does not survive it: at 106M owners as of mid-2026 and a trend of $144k, growth of the network to 1610M would give a multiplier of 15.19β ≈ 174, that is, a plateau on the order of $25M. The power law describes the acceleration, not the place where acceleration ends; what it runs into is the size of world wealth. So β lives only in the slope of the first layer, and the second layer counts money.
Sensitivity to all of this is what the “owner ceiling” slider exposes. Move it: the whole right-hand part of the chart travels up and down — and not by level alone. The ceiling enters the cycle by a second route, through the multiplier ζ, so the amplitude travels along with the plateau: at the base decays the H5 drawdown runs from 23% at a ceiling of 700M to 40% at 3200, and at the lower edge the troughs almost flatten out. Two things stay untouched: the historical part of the chart, where φ = 1.00 and saturation has not yet kicked in, and the whole of the first layer — the ceiling does not turn the slope of the power law. The travel of the slider measures what share of the 2030s rests on a quantity nobody has yet counted.
Today (August 2026) roughly 106M owners map onto 57M non-zero addresses, and the ratio is falling: custodial services and exchange-traded funds recruit holders who never touch an address on the chain. Measuring the size of the network in addresses makes less sense with every year.
As long as the decay reads as moderate, the contradiction is tolerable. If the decay is irreversible, the contradiction becomes direct: you cannot claim at once that euphoria died because the composition of holders changed and count the ceiling as if the ratio of addresses to owners had stayed historical. So the plateau is computed from the number of owners. The number of addresses does not enter the calculation at all.
Historically the same sequence followed every halving: acceleration, a euphoric peak about a year and a half later, a crash, a long trough.
The explanation through the reduction of issuance, however, adds up poorly: the market knows the date of the halving years in advance, and a fully anticipated change in issuance should be priced in continuously, without a delayed impulse in the eighteenth month. Here the model leans on a sentiment-phase explanation:
The next sustained rise begins when the majority of new participants have finally stopped believing in a rise. The next sustained fall begins when the majority have absorbed the belief that the rise is endless.
The logic is that at the trough the beliefs of participants are maximally heterogeneous: everyone has their own reasons for scepticism, there is no single narrative. Such a state is unstable and prone to reassembling around a new idea. At the peak it is the other way round: everyone believes the same thing, and precisely because of that everyone's exit thresholds coincide, so one nudge triggers simultaneous selling. Unanimity looks like strength and works as fragility.
Technically the cycle is set by three nodes: a peak 18 months after the halving, a trough at 26–30, a return to the trend by the next halving. Between the nodes runs a smooth cosine interpolation.
The timing of the nodes is taken from history. Peaks arrived in months 13, 17, 18 and 18 after the four halvings, that is, the lag lengthened and then settled, and 18 is carried forward. The maximum falls arrived in months 26, 29, 30 and 26. The timing turned out to be far more stable than the amplitude, and the amplitude looks like it is collapsing.
The proportion between top and bottom inverted over those same four cycles. In the early ones almost all of the swing went upward: in H1 the peak rose 1.03 dex above the trend while the trough fell only 0.28 — four fifths of the swing belonged to euphoria. After that the share of the top fell monotonically: 77% in H2, 55% in H3 and only 14% in H4, where the peak barely left the trend while the trough went to the usual −0.37.
Here a second maturation indicator shows through, independent of the general compression of amplitude: the market loses its capacity for euphoria noticeably faster than its capacity for panic.
It follows that top and bottom are two different sequences rather than one with a fixed proportion. Peaks: 1.03, 0.81, 0.46, 0.06, a monotonic fall. Troughs: −0.28, −0.24, −0.38, −0.37, no trend at all. The model therefore projects them with two sliders, and neither determines the other. They do share the common multiplier ζ: it says how much travel the cycle has left in general, and so it scales top and bottom together, leaving the proportion between them untouched. In practice this means the euphoria slider also moves the H5 trough — from −0.24 to −0.28 dex across its full travel — but does not change what the lower slider asserts about the trough.
Asymmetric decay — the top fading much faster than the bottom — is the signature of institutionalisation: the composition of holders changed, euphoric buyers were replaced by funds and custodians, panic stayed with those who still hold directly.
Symmetric decay — both phases fading — is a clear sign that the source of judgement has changed. A deep trough is assembled out of many people selling each for their own reason: one believed in a ban, another in a competitor, a third simply got tired of waiting. The sentiment-phase mechanism requires exactly that discord — the trough is assembled out of it. If participants check against one and the same reliable source (say, a strong publicly available AI), they no longer have separate reasons, and there is nothing to assemble such a state from. This is the only known process that is obliged to damp panic together with euphoria.
Only the asymmetry has been observed so far. Symmetry is testable only in September 2030.
The lower panel removes the growth itself and leaves only the departure from the trend. The humps compress in sequence: 1.03 → 0.81 → 0.46 → 0.06 dex.
The December 2013 peak stood ten times above the trend. The December 2017 one, six times. The November 2021 one, three times. The October 2025 peak overshot the trend by 15% — the first cycle in the asset's history where an explicit euphoric phase effectively did not happen.
Hence the fork this part of the model is built around. Either the decay is irreversible — and then bitcoin leaves the speculative category and settles into an ordinary mature network asset with moderate swings. Or the collapse was temporary — and then peak height returns to some degree as soon as the environment around the market changes.
But it will not return at the former size, because there is a third decay that neither hypothesis speaks about: the headroom runs out. A euphoric peak is an overshoot above the trend, and a trend that has come up against the monetary ceiling leaves no room above itself. A change of environment around the market does not lift the ceiling. This is the multiplier ζ.
The upper slider therefore does two jobs at once. It switches hypotheses: zero — euphoria left “for good”, one — “temporarily”. And it also decides how much the cycle depends on the headroom at all: at zero the cycle rested on it entirely and fades along with it, at one it is not tied to the ceiling and survives the approach without losses. The base sits near zero but not at it, and why exactly is in the section on the dials. The bottom lives by its own rules (though it shares the multiplier ζ with the top), and the second slider is set aside for it.
There are four sliders in all, and they are not equal. The two decays, to a greater extent, govern the next five years. The ceiling affects the height of the H5 peak moderately — the plausible range moves it from $373k to $404k — but it rules the 2030s single-handedly and decides how much travel the cycle has left at all by the following epochs. β is not meant for tuning: it stands here as a check.
The sliders are moreover not independent of one another. The links between them are described in prose on this page and checked by the coherence indicator above the chart, because a link can be broken in one movement while the result looks perfectly normal in the numbers.
There are five checks. Top and bottom — the cause that put out euphoria is obliged to reach panic too. Decay and ceiling — institutional custody kills euphoria and removes the barrier to entry at the same time, so a low decay together with a low ceiling pulls one consequence away from the other. What the cycle rests on — whether the cycle of the 2030s rests on the headroom or on the assumption that speculativeness survived. Scale and regime — whether the ceiling takes capitalisation to a level requiring a change of monetary regime, which the model does not contain. β and institutionalisation — custodial holding thins the graph of links and pulls the Metcalfe exponent toward n log n by the same process that puts out euphoria and lifts the ceiling, so a shift of β to the left with a live cycle and a shift to the right with a high ceiling both pull cause away from consequence. The checks that have fired are listed under the status, and each one is explained in the tooltip beside it.
The indicator has to be read carefully. It checks for the presence of a mechanism, not the soundness of a setting. The most vivid of the hard combinations is euphoria fading irreversibly while panic does not fade at all. The indicator marks it red not because the observation is wrong, but because there is no explanation for it: the cause that killed the top is obliged sooner or later to reach the bottom. The colour changes continuously as it does so: each check has a tension between zero and one, and the slider moves it smoothly rather than switching it. None of the five has steps — a setting is never coherent up to exactly some value and incoherent after it.
The reverse holds too. A compatible setting is not a well-founded one. “Cycle never broke” passes the check almost without remarks, but it requires treating H4 as a fluke, and there is (so far) no independent evidence for that. Hence the neutral colour of the indicator rather than green: it catches a mismatch, it does not grade.
The scale is capitalisation itself: the plateau is terminal capitalisation divided by the coin supply, and gold stands alongside as a distantly similar non-digital analogue. By the mid-2030s about 20.7M coins will be in circulation, and all the gold ever mined is worth roughly $31T as of 2026. At 6 billion adults the ruler looks like this:
| 1000 | plateau $408k · capitalisation $8.4T · 27% of gold · 17% of adults — adoption continues, bitcoin stays a niche asset |
| 1300 | plateau $530k · $11.0T · 35% of gold · 22% of adults — the lower edge of the plausible |
| 1610 | plateau $657k · $13.6T · 44% of gold · 27% of adults — base, ≡ $8,447 of holding per owner |
| 1800 | plateau $735k · $15.2T · 49% of gold · 30% of adults — the upper edge of the plausible |
| 2600 | plateau $1.06M · $22.0T · 71% of gold · 43% of adults — requires a change of monetary regime, which the model does not contain |
The familiar anchor is the share of adults owning equities, 15–25%. But that share is low for two reasons: most people have no investable surplus, and there is a barrier to entry — a broker, literacy, trust in the procedure. The second reason is removed over a decade by an adviser available to everyone (AI), the first is widened by growth itself. An upper bound of 25% with the friction removed looks more like a lower one, hence 22–32% and a range of 1300–1900 million owners.
The ceiling moreover governs more than the plateau level. Through the multiplier ζ it sets what share of the cycle survives into the 2030s: the lower the ceiling, the sooner saturation eats the headroom and the amplitude with it. The proportion for epochs H5–H7 is shown in the “Cycle · support” block directly under the slider.
These figures are recomputed live under the chart, in the “What this requires of money” block. There the same capitalisation is shown not only at the plateau but along the way to it: how much has to be added on average per year and how much over the next twelve months. It is also visible there that issuance amounts to less than one percent of the required increase and keeps falling: the halving as a supply mechanism stops meaning anything quantitatively by 2028, and the cycle is left entirely to demand.
An increase in capitalisation is not an inflow of money. To get the second, the first has to be divided by the capitalisation multiplier: how many dollars of market value a dollar of net buying adds. Empirical estimates range from 2 to 25, so no number is displayed anywhere — the model does not know this multiplier and does not use it. For scale: all the gold ever mined is $31T, the world equity market is on the order of $130T. Issuance is computed from the protocol: 210,000 blocks per epoch, the supply at a halving is known exactly, and linearly in between.
Three reference positions:
| 0.00 | the decay runs at a halving per cycle: the H5 peak rises 0.03 dex above the trend, after which peaks fade almost completely along with the headroom |
| 0.50 | the decay has slowed: the H5 peak around 0.11 dex, twice as high as H4 |
| 1.00 | H4 was an anomaly and the log-linear H1–H3 trend wants to return: H5 peak = 0.21 dex |
Four cycles of evidence. The fact of the decline itself rests on all four observations at once and holds firmly. The sharpness of the last step rests on one observation — on H4 — and nothing more is known about it.
Hence the slider position of 0.15. Going further left is possible but pointless: continuing the break would lift the H5 peak 1.5% above the trend instead of 6%, and that difference is fifteen times smaller than the monthly scatter. No observation will tell them apart, and both settings assert nearly the same thing. Going right is possible, but it has to be paid for with an assumption — H4 has to be declared partly accidental. There is (so far) no evidence for that: it does not follow from the price itself, an external source is needed. Further down the page this assumption is called the H4 caveat.
The slider does, however, have a second reading, through the multiplier ζ: it sets what share of the cycle lives on after the headroom to the ceiling is exhausted. And here a position at zero is too strong a claim: nothing periodic remains, ever, at all. That does not happen even to mature assets whose number of holders is not growing. There are no observations under this reading: φ = 1.00 in all four historical epochs, saturation never once kicked in.
The base therefore stands at 0.15 — the minimal meaningful step away from the extreme. The upper bound on that step is not a matter of taste: at de ≈ 0.22 the effective amplitude of the H5 peak catches up with the observed amplitude of H4 (0.061 against 0.060), and the model starts to assert not a slowing of the decline in peaks but its reversal.
The irreversibility of the decay rests on a specific mechanism: institutionalisation. Euphoric buyers were replaced by funds and custodians, and the market's capacity to overheat disappeared with them.
That mechanism has its own observable trace, unconnected to the price — the ratio of non-zero addresses to owners. A holder through a fund never touches an address, so the further the replacement has gone, the lower the ratio. It has been falling for years and stands at about 0.54 as of mid-2026: roughly 57M addresses against 106M owners.
Hence a test that can be run monthly and without any model. If the ratio stops falling while the peaks stay dead, institutionalisation stops explaining the decay — and under the zero position of the slider no mechanism remains at all, only four trend observations. Continued falling works the other way: it is an argument for the irreversibility of a larger decay, taken from data that has nothing to do with the price.
The ratio here is a trace of this mechanism: the market could have matured for other reasons — deeper derivatives, less leverage — and then the ratio is entitled to stand still while the decay persists. A flat ratio refutes the explanation, not the slider itself.
There is not a single piece of evidence here. Four troughs over fifteen years stand at roughly the same depth, no movement is visible in them, and the direct reading says to set zero: the bottom did not fade before and will not start fading by itself later.
What can work against zero is, for instance, the logic of the mechanism. The near-zero upper slider asserts that euphoria disappeared for a reason rather than by chance. And the reason may be various — the composition of holders changed, custody went to institutions, participants gained access to a shared reliable source of information — but any of them is obliged by mechanism to reach the bottom sooner or later.
The lag is explicable, though. The top of the cycle is made by arriving participants, the bottom by those who stay, and the composition of the latter changes far more slowly. So the decay of panic ought to run behind the decay of euphoria, but it ought to run all the same.
Because of this the combination “zero on top, zero at the bottom” turns out to be internally contradictory. It means that the cause which killed euphoria acts on exactly half the cycle and does not touch the bottom's own mechanism, and there is at present nothing to explain such selectivity.
| 0.00 | H5 trough at −0.32 dex. The premise “the bottom did not change and will not”, minus the share saturation takes away |
| 0.50 | H5 trough at −0.24 dex, at the very shallow edge of the H1–H4 corridor, −0.24…−0.38 |
| 1.00 | H5 trough at −0.16 dex, shallower than anything observed. The bottom fades level with the top |
| ζ | all three numbers are given at the base ceiling and base euphoria decay. Through the common multiplier ζ they drift slightly with those too: at de = 0 the trough at 0.50 goes to −0.23, at de = 1 to −0.28 |
The H5 trough is projected for September 2030. The four previous troughs stood in the corridor −0.24…−0.38, but the observation can no longer be compared with that corridor directly: by 2029 saturation by itself lifts the trough, and with panic undamped the model expects −0.32 dex. Evidence of panic decay would be a trough shallower than −0.16 dex — that is what the right edge of the slider gives at the base ceiling and base euphoria decay. Anything between −0.32 and −0.16 reads as partial decay and is handled by the slider.
A trough in the familiar corridor means the opposite: only euphoria was fading, the mechanism of the cycle stayed human, the panic slider has to be set to zero and the red indicator has to be lived with as a recorded anomaly.
The only substantive objection to the value 1.897 is that institutional custody thins the graph of connections between participants and ought to shift the scaling toward n log n. The objection is right by mechanism and refutable by data: move the slider and watch the miss counter. The range over which the fit holds is very narrow, and that is the answer.
The buttons above the chart set all the sliders at once. The values are computed at β = 1.897.
| Scenario | Owner ceiling | Euphoria decay | Panic decay | Plateau | H5 peak, Oct 2029 | H5 trough, Sep 2030 | H5 drawdown |
|---|---|---|---|---|---|---|---|
| Cycle faded | 1800 | 0.00 | 1.00 | $735k | $379k | $301k | 21% |
| Quiet cycle base | 1610 | 0.15 | 0.50 | $657k | $394k | $245k | 38% |
| Cycle returns | 1350 | 0.50 | 0.25 | $551k | $432k | $209k | 52% |
| Cycle never broke | 1300 | 1.00 | 0.00 | $530k | $542k | $169k | 69% |
The names answer one question: what the four-year cycle looks like by 2030. The price here follows from the answer rather than setting it.
| Cycle faded | Both phases have almost disappeared. Euphoria decay at zero asserts not only that the break in H4 was real, but a second, stronger thing as well: once the headroom to the ceiling is exhausted, nothing periodic remains. An H5 drawdown of 21% — like a large technology stock rather than like a cryptocurrency. The number of owners is the highest, a third of adults, mostly through funds and custodians, plateau $735k. It requires a shared trustworthy source of information among participants — a publicly available AI, for instance: the heterogeneity of beliefs out of which the trough is assembled stops coming together. |
| Quiet cycle | Euphoria has gone almost irreversibly: the decay stands at 0.15, and zero would mean the cycle disappearing entirely along with the headroom. Panic fades with a lag, by the requirement of coherence: the cause that killed the top is obliged sooner or later to reach the bottom. The H5 trough at −0.24 dex, at the very shallow edge of the H1–H4 corridor, a 38% drawdown — a bad year on the stock market rather than a crypto crash. The upper setting is derived from data and moved off zero, the lower one rests on reasoning. |
| Cycle partly returns | H4 was partly a fluke. Euphoria tries to come back halfway, panic is almost untouched. The peak is higher than in the “quiet cycle” — $432k — but so is the drawdown at 52%. The ceiling is 1350, below the base one: if the decay is reversible, then institutionalisation has not gone that far and the barrier to entry has partly remained. A position for those who bet neither on the irreversibility of the decay nor on a full return of the amplitude; the coherence indicator answers it with two caveats. |
| Cycle never broke | Nothing changed in the market itself apart from saturation, the break in H4 was a ripple. All this time the decay ran at an even step of ×0.67 per cycle, and peak height returns to the H1–H3 line — not to the former values, but to the former rate of decline. The highest peak of the four and the lowest trough, a drawdown of nearly 69% — comparable to the 78% of H3. The ceiling sits at the lower edge of the plausible corridor, 1300. Bitcoin stays for a while longer in the stage of a cyclical speculative asset, and this is the only scenario where the cycle does not weaken by itself in the 2030s either: with euphoria returned it barely depends on the headroom to the ceiling. |
Of the four scenarios the second button from the left is chosen as the base, and the page opens on it by default. Below is the choice itself and its price; the justifications are discussed above, each in its own section.
Euphoria — 0.15. The slider has two readings. Under the first — was the break in H4 real — the data say yes, there is no point moving further left, and moving right only comes with the H4 caveat. Under the second reading — how much of the cycle lives on once the headroom is exhausted — there is no data at all, and zero would mean that nothing periodic remains either, ever and at all. That does not happen to any mature asset. 0.15 is the minimal step away from that extreme, and it stays far from the boundary of 0.22 beyond which the model starts to assert a reversal of the decline in peaks.
Panic — a half. That setting rests on the requirement of coherence: the cause that put out the top is obliged in time to reach the bottom. A half means the process is taken to be under way while the question of how far it has gone is left open.
Ceiling — 1610 million. It follows from the same premise as the two previous settings: if the cause — institutionalisation, for instance — went far enough to kill euphoria, it also removed the barrier to entry and moved a noticeable share of holdings to custodians.
The price of the choice. Two sliders out of three rest on reasoning. Panic entirely: there is not a single piece of evidence, and the first will arrive in September 2030. Euphoria halfway: its position is derived from data under the first reading and chosen under the second, where there is no data and none can appear until saturation starts to bite. This accumulates, and it is worth keeping in mind when reading any number beyond 2030.
The four scenarios are four points on one axis. The axis answers a single question: how irreversibly bitcoin stopped being a speculative asset. Maturity on the left, speculation on the right.
Three sliders move along this axis coherently, and the same mechanism sits under each linkage. Institutional custody damps euphoria because it changes the composition of buyers. It also raises the owner ceiling because it removes the barrier to entry: the lion's share of people do not own an asset of this class because of the broker, the literacy and the trust in the procedure, not because of a lack of interest. One process, both consequences. β stays at its measured value in all four scenarios.
The owner ceiling works on this axis as headroom. It counts how much road to the plateau is still left, and at the left edge there is the most of it. What damps the cycle is the upper slider: it sets what share of that headroom turns into euphoria. On the left there is plenty of travel and it barely converts. On the right there is less travel, but it is spent in full. Because of this, at the left edge of the axis the cycle has a little over twice as much travel left as at the right. It is dead there for a different reason: the headroom stopped turning into euphoria.
Hence the monotonicity in both columns at once:
| Plateau | $735k → $657k → $551k → $530k. The more mature the asset, the wider the terminal ownership and the higher the saturation level. On the right the step shrinks: the column runs into the lower edge of the plausible corridor of 1300–1900 million. |
| Drawdown | 21% → 38% → 52% → 69%. An obvious rise in speculativeness. |
The peak column grows to the right along with the drawdown: $379k → $394k → $432k → $542k. The peak here is a product of two factors moving toward each other: the remaining headroom falls to the left, the share converting into euphoria grows to the right, and on the 2029 horizon the second quantity wins, because saturation has barely kicked in by that date. Hence a property awkward to read: the 2029 peak is higher in the scenarios that are more optimistic by mechanism and more pessimistic in substance. It has to be read this way: a high 2029 peak points to a live cycle, to be followed by the usual crash. In the “Cycle never broke” scenario the peak is 38% higher while the trough is one and a half times lower.
Moving right along the axis changes not only the height of the cycle but what it rests on. On the left the cycle of the 2030s follows the headroom: the travel runs out, the cycle fades, and this is visible directly in the price. On the right, by 2033 an eighth of the headroom remains while the cycle keeps its full amplitude, and the euphoria slider carries the difference — that is, the premise that the asset's speculativeness survived on its own. The diagnostic under the ceiling slider shows this proportion for epoch H6.
And hence also the way to use the buttons. They are not “optimistic — base — pessimistic”: by the 2035 price the left edge is optimistic, by the October 2029 price the right edge is. Choosing between them is choosing a hypothesis about what happened to the market, not choosing a desired number.
The colour of the label shows how far the objection is accepted: grey — answered · orange — partly · red — entirely.
Answered in part
The exponent is read straight off the price, but it has an independent decomposition: addresses against time (3.046) and value against addresses (1.838), a product of 5.60 against the measured 5.69. The decomposition confirms the order of magnitude and does not replace the fit — caveat below. Layer 1 carries two free numbers in total, set against 194 monthly points across six orders of magnitude. The useful check looks at the structure of the residual; the quality of the fit decides little here. The residual does have structure: humps tied to the halvings, shrinking monotonically. Fitting artefacts do not produce those.
The question would be closed by falsification criterion 5: the residual leaves ±0.5 dex and does not return for two years. The criterion is set for use — if it fires the model is thrown out, and recalibration would be cheating.
Conceded, there is no answer inside the model
The strongest objection on the list, and I have nothing to set against it. Every network that died also had an early growth phase resembling a power law, and curves are only fitted to the survivor. The model is conditional by construction: it describes bitcoin while the current regime holds and assigns no probability at all to its ending. Read as an unconditional expectation, it misleads. Read as “if the adoption mechanism holds, the shape looks like this”, it works, with the probability of the premise supplied from outside.
Half agreed
Here the model agrees more than it argues, and puts a number under the agreement: H4 rose 0.06 dex above the trend against 1.03 for H1. The euphoric top died. The other two parts of the cycle outlived it. The timing held — 18 months to the peak, the same as H3. And the bottom did not decay at all: the troughs of the four cycles stand at −0.28, −0.24, −0.38, −0.37 dex, with no trend whatsoever. The formula “the cycle is dead” lumps three different things into one. One of them has gone, the other two remain.
Conceded
Yes. The lower node of H4 is taken from the observed minimum of $57,950, so the match there is tautological and checks nothing. The cycle table says so right where it happens, without burying it in footnotes. Falsification criterion 1 exists for the same reason: if the price settles below $58,000, the node was not a trough, and the amplitude calibration everything downstream depends on falls apart. Put plainly: the H4 amplitude is a measurement, and all the predictive content of the model begins with H5.
Conceded — the weak link
The objection was correct in the first version of the model (discussed below), and it took the form of a rebuild. The plateau is no longer counted in addresses: it is taken from the number of owners through the average size of a terminal holding, W · $8,447 / 20.7M, and the number of addresses has been removed from the calculation entirely.
The uncomfortable part survived the rebuild: the same institutionalisation that explains the decay of the cycles simultaneously breaks the measuring instrument. One process produces both effects. The difference is that the model no longer leans on a shrinking instrument: the decay of the cycles and the level of the plateau have stopped depending on one and the same breaking quantity.
Still open: neither the number of owners nor the average holding size is measured separately. 106M is a summary of industry estimates, not a census; $8,447 per owner is the calibration base expressed per person.
Partly conceded — it is indeed derived
Santostasi & Perrenod (2026) measure two quantities separately: an address growth exponent of 3.046 ± 0.012 and a Metcalfe exponent of 1.838. Their product gives 5.60, while the slope read straight off the price is 5.69 — a discrepancy of 1.6%, which the authors attribute to scatter in the estimates of the components. The model on this page computes with 5.69 and decomposes it into a flat three and 1.897 = 5.69 / 3. That is, 1.897 is not a third independent measurement but the remainder of a division, and the label under the slider says “reference value” rather than “measured”.
What remains of the objection: neither 1.838 nor 1.897 was chosen for the beauty of the chart, and both lie between textbook Metcalfe n² and Odlyzko n log n. What does not remain: the claim that the slope was obtained by multiplication and was not fitted to the price. It was fitted, and that is visible in the same miss counter.
β enters the calculation once, in the slope of the power law, and in the first version of the model its sensitivity was shown nowhere. Now it is: β is exposed as a slider, and the miss counter under it counts the months outside the ±0.5 dex band. The check works both ways. It confirms that 1.897 was computed sensibly, and it also shows how narrow the admissible corridor is.
Conceded — the decomposition does not hold
The exponent 3.046 in Santostasi & Perrenod is measured over the whole history and rests on the early years, where the network grew from nothing. It does not reproduce on fresh data. The number of non-zero addresses per public summaries: about 18M in August 2017, 28M in January 2020, 40M in February 2022, on the order of 57M by mid-2026. Over nine years that is growth by a little over three times, whereas the cube of the network's age would require growth by eight and a half. The exponent implied by that window is about 1.6, and over the last four years only 1.2.
Something unpleasant follows: the decomposition 5.69 = 3 × 1.897 works more as a note on where the number came from than as a live check. The power law in the price itself holds — 14 misses out of 194 over fifteen years — but it holds as a regularity in the price, not as the product of two quantities measurable today. The instrument broke on the same side it broke on under the ceiling: custodial services and exchange-traded funds recruit holders who create no addresses.
Partly conceded
The blue band runs the ceiling ±40%, carries no statistical content, and the page labels it exactly that way. The historical monthly scatter around the central trajectory is about 0.32 dex (1σ), so an honest 1σ envelope for any single month would be roughly four times wider and would completely swallow the ceiling band until the 2030s. Showing the spread from a parameter rather than from the variance was a deliberate choice: the reader can argue with an estimate of the ceiling, and can do almost nothing with the variance.
Depends on which half you are disputing
These two complaints are worth separating, because the model answers them differently. The 2029 peak falls in the confident half: from $379k to $542k across all four scenarios, a spread of 1.4 times, since saturation has barely kicked in at that horizon. Most of that spread comes from the euphoria slider; the owner ceiling moves the H5 peak moderately, from $373k to $404k, and what it decides is something else — how much of the cycle remains by the following epochs. Disputing the figure means disputing the power law itself. The 2030s are the fragile half: the same four scenarios give a plateau from $530k to $735k, the spread is wider, and the ceiling is reasonably disputed beyond that range in either direction. Disagreement about 2035 is cheap and expected. Disagreement about 2029 requires an argument about the exponent.
Partly conceded
The mechanism justifies the shape of the cycle, but the shape itself is calibrated to observed timings and amplitudes and would look exactly the same if the original explanation were purely mechanical. The narrative layer therefore does interpretive work; take it out and the model computes exactly the same numbers. What the story buys is a reason to expect decay at all: as the heterogeneity of beliefs at the trough declines along with rising institutional participation, reassembly around a single narrative weakens. That is a directional prediction specifically about euphoria, and euphoria is what collapsed. No more than a suggestive consideration, carried down into the limits.
Five conditions, from the nearest to the furthest:
| 1 | The price settles below $58,000. Then late June 2026 was not the trough of the cycle, and with it the lower node of H4 falls apart — the very node the decay amplitude is set by. Testable in the coming months. as of Aug 2026 — $64k |
| 2 | The drawdown of the current cycle goes deeper than 70% from the October 2025 peak, that is, below ≈$37,900. The shallowest fall of the previous cycles was 78% in H3, so at 70% H4 stops differing from them qualitatively and the whole extrapolation of the decay loses its footing: essentially one observation holds it up. as of Aug 2026 — 54% |
| 3 | The H5 trough stops shallower than −0.16 dex. The only item on the list the model survives: panic faded following euphoria, the panic slider goes right, the mechanism of the cycle has stopped being purely human. The threshold has moved from −0.24: part of the shallowing of the trough is now explained by saturation through the multiplier ζ, and −0.16 dex is what the right edge of the panic slider gives at the base ceiling. September 2030. |
| 4 | The drawdown of cycle H5 goes deeper than 60% at zero euphoria decay. Rejects irreversible decay in favour of a temporary collapse. At the base ceiling, zero euphoria decay and panic decay of 1 the model gives 20%; with the reverse arrangement, 68%. |
| 5 | The residual log₁₀(observed / trend) leaves ±0.5 dex and does not return for more than two years running. It means the power-law regime is broken and the model must not be used at all. Over the whole history the longest excursion outside that band lasted five months — the winter of 2013/14. never fired |
The threshold is set by the history of drawdowns, with no fondness for round numbers. H1, H2 and H3 fell 85, 84 and 78 percent; H4 stands at 54 as of August 2026. Twenty-four points separate it from the shallowest of the earlier cycles, and exactly that margin is what fills the claim “H4 is built differently” with content. A threshold of 70% leaves a small gap: below it the formal difference still survives, but there is nothing left to explain it with.
It does not predict the price of a particular month. The scatter around the central line within a year is comparable to the line itself, and trying to read it as “in March it will be such and such” is an abuse.
It does not account for discontinuities: regulatory bans in major jurisdictions, cryptographic threats, macro shocks. All three layers describe the behaviour of a system that stays in the current regime.
It does not separate cause from effect in the sentiment-phase mechanism. The observed link between heterogeneity of beliefs and reversals is real, but it remains an empirical regularity with no proven mechanism under it.
It does not model the supply side at all — lost coins, the behaviour of long-term holders, exchange balances, mining economics. Everything to do with supply is implicitly folded into the two fitted constants of the first layer.
The plateau is tied to a structure of world wealth recognisably like today's: the ceiling scale is read through a share of the value of all the gold ever mined. The cycles assume a market of human participants with heterogeneous beliefs, working through to 2040. Both premises are a bet that no transformative technological discontinuity occurs within the model's horizon.
The premise is nowhere set as a parameter, but it is stronger than the exponent β and stronger than the estimate of the ceiling: an error in those moves the numbers, while an error in it cancels applicability altogether. The panic decay slider is the place on this page where it becomes observable, because a shared trustworthy source of information for all participants at once — a strong publicly available AI, for instance — is exactly the discontinuity that would give itself away through the decay of the bottom.
The original model was published in April 2026 and gave one number: a plateau of about $565,000 by the mid-2030s. Its calibration started from a spot of $74,500, already stale by August. Here the model has been rebuilt in three places.
| What | Was | Now |
|---|---|---|
| Plateau | One number, $565k | A range: audience ceiling × average holding size |
| Ceiling | A fixed 800M addresses | Number of owners, 700–3200M |
| Addresses | The basis of the plateau calculation | Removed from the calculation |
| Cycles H5–H8 | A single decay trajectory | Two independent decays plus the multiplier ζ tying the cycle to the headroom left to the ceiling |
| Metcalfe β | A hidden constant | A slider with a live miss counter |
| Resolution | Phases of several months | Monthly, 372 points |
| Diagnostics | None | Three indicators checking the reader's settings |
| Falsification criteria | None | Five, including the panic decay marker |
| Testability | A forecast to 2035 | An explicit observed/computed boundary, history overlaid since 2010 |
The rebuild aimed at the form of the result. The central trajectory barely moved: the middle of the plausible ceiling corridor gives a plateau of $653k against the original $565k, a difference of 16%. In place of a point forecast there is now a claim with its uncertainty marked and with a note on which measurement would narrow that uncertainty.
Two conceptual problems were fixed along the way. First: addresses served as a measure of network size, whereas the link between addresses and living people is breaking down — 106M owners correspond to about 57M non-zero addresses, and the ratio falls as custodial services and exchange-traded funds grow. Now the plateau is computed from owners, and addresses are removed from the calculation.
Second: the cycle was described by one number with a fixed split between top and bottom. In the data these are two different sequences — peaks fall monotonically, troughs do not — and collapsing them into a single parameter erased the only meaningful signal. Now they are separated into two sliders, and a dedicated indicator checks the compatibility of their settings.
The model takes about fifty lines of JavaScript in the page source. The only dependency is Chart.js for drawing, and it sits next to the page rather than being loaded from a third-party server. The page is entirely static: everything is computed in the browser, not a single request goes out, and it works offline. To check or extend it:
pure(t, β) — the power law with recalibration through a reference point at day 2971 from genesissat(p, L) — the saturation envelope, p·L / (p³ + L³)^⅓plateau(W) — W · A / S, the plateau level from the number of owners through the average holding size; β does not enter hereamps(d_e, d_p, W, β) — separate projection of peak and trough amplitudes onto H5–H8, computed three times: for the central trajectory and for both edges of the ceiling band; euphoria is interpolated between 0.030 = 0.06 · 0.50 and 0.207 = 0.46 · 0.67² dex, panic is divided by 1 − 0.5·d_p each cycle, after which both are multiplied by the ζ of the corresponding epochcoherence(d_e, d_p, W, β) — five coherence checks; each returns a continuous tension from 0 to 1, they combine as independent, and the result colours the indicator without thresholdsphiAt(t, W, β) — the share of the trend's travel that the ceiling lets through; zetaAt — the share of the cycle that remains: d_e + (1 − d_e)·φfuelState(W, d_e, β) — what the cycle of the 2030s rests on: headroom checked against amplitude on H5–H7EPOCHS — the halving table with per-epoch amplitudes a (peak, dex above trend) and b (trough, dex below trend)modAt(i, A) — the cycle overlay, cosine interpolation between halving, peak, trough and the next halvingOBS — the observed monthly series since July 2010The OBS array contains approximate month closes compiled from public sources. That is enough for the shape of the residual and not enough for anything requiring precision; before any serious use, replace it with a verified series from one consistent source.