DC BitMax

Studying Bitcoin through the lens of Power Law.
StackSats&StayHumble. English version Power_Law_Chart
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[DC BitMax @DCBitMax]

This is the most rigorous Bitcoin paper
I've read. I've been studying —
and testing — it for 20 days.
https://t.co/mCfJQpJTbE

Dr. Santostasi and Dr. Perrenod gave us the ruler —
and the imagination to see the oscillator.
Together: the most falsifiable framework
in crypto economics.

The Power Law isn't just a model —
it's the most precise ruler we have
for measuring where Bitcoin stands.

Most models describe the past.
The Power Law keeps passing tests
it was never designed for.

"Isn't β=5.69 just curve-fitting?"
Fair question.
So I ran a test the paper didn't.

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Materials & Methods
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Data: Daily closing price and non-zero balance
address count (BitcoinMagazinePro,
2010-08-17 to 2026-06-04, n=5,771).

Model: log₁₀P(t) = log₁₀A + β·log₁₀(t)
where t = days since Genesis Block (2009-01-03).

Out-of-sample design:
The power law was fitted exclusively on data
up to the freeze date, with zero observations
from the test period used in estimation.

Two freeze points were tested:

① Freeze at 2016-07-08 (2nd halving)
Training: n=2,153 | Test: n=3,617 (10 years)

② Freeze at 2020-05-10 (3rd halving)
Training: n=3,555 | Test: n=2,215 (6 years)

Residuals computed as:
ε = log₁₀(P_observed / P_predicted)
normalized by in-sample σ.

Mean residual and area integrals
(trapezoidal rule) applied to test period only.

The out-of-sample test was my idea.
Computation and analysis executed with
Claude Opus 4.8 (Anthropic).
━━━━━━━━━━━━━━━━━━━━━━

Froze the power law using data up to 2016 only (β=5.717).
Then measured the following 10 years it had never seen.

Result: mean residual −0.05σ. Effectively zero.
Frozen at 2020 instead → next 6 years, −0.13σ.
Same story.

The line drawn in 2016 ran straight through the next decade.
That's not fitting. That's forecasting.

The Power Law: powerful because it can be broken —
and hasn't been.
Knowing where we are won't tell us when things will happen — but it tells us exactly what to do now.

Buy Bitcoin Now.

@Giovann35084111 @moneyordebt @ScientificBTC
@saylor @natbrunell
#Bitcoin #PowerLaw

[Giovanni's BTC_POWER_LAW @Giovann35084111]

If you didn't read it yet. 10 k downloads. https://t.co/DYFWLDNXeQ

[unusual_whales @unusual_whales]

SK Hynix is considering a U.S. share listing on Nasdaq, per Bloomberg.

[The Kobeissi Letter @KobeissiLetter]

BREAKING: SpaceX stock, $SPCX, surges over +30% to a fresh record high and hits $2.3 trillion in market cap.

SpaceX is now the 6th largest public company in the world.

[Reuters Business @ReutersBiz]

WATCH: South Korean memory chipmaker SK Hynix is looking to choose the Nasdaq for its planned US listing, two sources familiar with the matter told Reuters, opting for the technology-heavy bourse to capitalize on investor appetite for AI-linked stocks https://t.co/MKUNcn0AL0

[Hendrik_Z @Hendrik__Z]

Bitcoin Noise Model:
Separating Slow Cyclical Drift from True Daily Noise

In price space, slow cyclic drift and daily noise are entangled. Any volatility estimate inevitably averages over a moving offset.

What you get are messy mixture distributions, where cyclic behaviour or regime changes overlap.

This looks different in the space of daily exponents.

There we see:
🔸 cleaner distribution functions, well approximated either by Student-t (already shown by @Giovann35084111) or by Laplace distributions
https://t.co/492RfyUDWI
🔸a relatively stable mean μ(t), slightly different from cycle to cycle
🔸strong but slow intra-cyclical drift, which is essentially is the signal
https://t.co/6LIoM1vddu
https://t.co/KdYNuPxKGO
🔸enormous additional daily stochastic noise, superimposed on that, with max. exponents up to ±1000 or more

This last point makes clear why a cycle mean of n around 6 is so meaningful despite the huge daily noise.

In short: with the daily exponents, we have probably found a clean observable of Bitcoin. On top of that, we can test the stability of the noise model assumptions, Laplace vs Student-t, after applying them to the price space.

The idea is simple: model the price as a Power Law with μ(t) as the exponent and add the noise whose "shape" we already know from the fits in the exponent-space.
We can use a Monte Carlo simulation with a 1-day horizon and determine the width of all simulated paths.

This reveals the daily noise band, as cleanly separated as possible from local bubbles, crashes or wild market regimes!

The interesting part is that noise acts multiplicatively in price space, so it also depends on the absolute price level.

As price anchor, a smoothed price curve can be used and the simulated noise band can be drawn around it. The noise width is therefore automatically adapted both to the current price level and to the distribution width of the current cycle.
Decoupling from the price level also is easy: the noise band is drawn around a theoretical Power-Law Mean instead of the current price.

There are more interesting things one can do. With conventional methods, it is almost impossible to determine the evolution of noise or extrapolate it precisely. With this approach, we can even theoretically determine the function by which future noise should evolve.

Results:
🔸daily noise level decay ~1/t relative to the price level, currently around 7%, will be ~6.5% 04/2028
🔸absolute noise levels will rise, since PL rises: from currently ±8k to ±15k within the next 2 years

Fig1: Q99.9% since 2013, log-log-chart
Fig2: Q99.0% since 2017, linear chart
Fig3: rel. and abs. noise level evolution and extrapolation. Since the '13-cycle noise level was a bit lower, a global fit was not possible, but since halving 2 we see nearly identical levels (semi-global fit in red).

Remarks:
n: exponent of a power law y~t^n
µ: the mean of value of a probability distribution

So if µ is a fit parameter of a probability distribution, it is refered to as µ and not n.

[Giovanni's BTC_POWER_LAW @Giovann35084111]

This is the secret sauce guys. Who understands it, truly understands Bitcoin.

[Giovanni's BTC_POWER_LAW @Giovann35084111]

The point is truth. Bitcoin is truth. You like bs the why not 1 BTC= zillion?

[Bitcoin Magazine @BitcoinMagazine]

JUST IN: Elon Musk's SpaceX $SPCX is now officially trading live on the NASDAQ.

They hold 18,712 BTC on their balance sheet 🚀

[Evan @StockMKTNewz]

SpaceX $SPCX just passed Taiwan Semiconductor $TSM and is now the 6th largest public company in the world

[Fox News @FoxNews]

WATCH: SpaceX CEO Elon Musk rings the NASDAQ opening bell as the company officially goes public, setting him up to be the world's first trillionaire.

[James E. Thorne @DrJStrategy]

Don’t bet against Elon.

Historic achievement, many more to come.

[The General @GeneralMCNews]

BREAKING: Elon Musk becomes the world's first trillionaire.

[SA2CO @kis03004]

스페이스X 곧 옵니다.
스타트가 남다르네ㅋㅋ

[DC BitMax @DCBitMax]

팔란티어도 그래
한잔해

[unusual_whales @unusual_whales]

Palantir CEO Alex Karp: "I'm bullish on Space if the person doing it knows what they're doing. Bullish on Elon and Space, yes.

[unusual_whales @unusual_whales]

Palantir CEO Alex Karp: "I'm bullish on Space if the person doing it knows what they're doing. Bullish on Elon and Space, yes.

[Prof @TheProfInvestor]

Happy SpaceX day. 🚀

We have loved Tesla for years
We will do the same for SpaceX

When things settle- we will buy and sit on those shares for ever.

[The Kobeissi Letter @KobeissiLetter]

BREAKING: SpaceX, $SPCX, shares are now indicated to open at $151 per share, 12% above the IPO price of $135 per share.

We expect further price indications before shares officially begin trading shortly.

Turn on our post notifications at @KobeissiLetter for real time analysis.

[Hendrik_Z @Hendrik__Z]

@moneyordebt @CFidget70375 @david_eng_mba @saylor @dgt10011 @GrantCardone @MicroStrategy @Giovann35084111 @Giovann35084111
There's no test with Laplace in these articles, so why not repeat the test with Laplace?

Seeing not a triangle shape in log(y)-lin(x) is like denying the straight line of the power law bottom in a log-log plot.

https://t.co/5oSYWshrOF
But here with linear y:

[Giovanni's BTC_POWER_LAW @Giovann35084111]

Scientific way of distinguishing regimes in Bitcoin, not using price relative to reference price but looking at the dynamics of returns.

[DC BitMax @DCBitMax]

ㅋㅋㅋ

[Bitcoin Magazine @BitcoinMagazine]

JUST IN: Bitcoin pumps up to $64,133 🚀