Bitcoin touched the bottom power law support and its current value proposition comes by very rarely. Most people have given up and are too scared to make the correct moves here. Watch my latest video:
youtu.be/dBEQUh_SMcE
Excellent; we appreciate the independent confirmation
Of Bitcoin discrete scale invariance (log periodicity) together with continuous scale invariance (power law).
@ScientificBTC
Dr. Perrenod — I reproduced your log-periodic analysis on my own data (BitcoinMagazinePro daily closes, 2010–2026) and wanted to share what I found.
My own power-law fit gives β = 5.65.
From the residuals, I recovered the log-periodic structure two independent ways:
•
Shannon worked out the entropy of information. Base 2 it’s entropy in bits, for base e it’s called nats.
John Kelly worked with Shannon at Bell Labs and adapted the formula and Shannon’s work on channel capacity for gambling outcomes and finance. Kelly growth rate is a relative entropy.
Surprising finding is Kelly optimal allocation fraction f* for Bitcoin should grow with time, not fall, given power law and the observed ~ reciprocal decline in volatility. open.substack.com/pub/stephenper…
In 1937, a 21-year-old MIT student sat in a quiet library, mapping abstract philosophical logic onto electrical circuits to pass the time.
By the time he finished his thesis, the young man had mathematically proven that mechanical telephone switches could perform complex
The emergence of global consensus without centralized control was once considered impossible. Bitcoin demonstrated that impossibility claims sometimes have expiration dates.
Bitcoin is encapsulated energy and the first true energy-based standard for monetary technology.
Its inspired highly scalable hashing protocol incentivizes more energy into the Bitcoin network. This provides it with a higher surface to interoperate with, integrate into, and optimize the existing energy grid infrastructure.
A useful scientific question: "What properties must a monetary network possess to survive for centuries?" Bitcoin may be our first opportunity to study the answer in real time.
We didn't give it the name Power Law, it is the definition of a mathematical relationship y ~ x^β, an independent variable raised to some power, some exponent of repeated multiplication. It's simply the correct name used by scientists and mathematicians.
Some famous examples:
Newton’s gravitation
F ~ r^{-2}
(inverse-square law, a special power law)
Kepler’s Third Law
T^2 ~ a^3
Stefan-Boltzmann Law
L ~ T^4
Blackbody radiation (Rayleigh-Jeans limit)
another power-law regime.
Physicists were already accustomed to calling these “laws” because they appeared fundamental.
Saying “gravity is just a theory” is like saying “music is just a theory.” The notes are real; the theory explains how they fit together.
Some notes are better muted.
What's your favorite theory of gravity? General relativity, loop quantum gravity, scalar-tensor-vector, emergent (entropic)...?
To date general relativity has passed every test, so alternatives must reduce to general relativity under known circumstances.
I have the feelings than the PMI only and the 4-year cycle only camps are both wrong.
A log periodic model with a main dominant frequency and 2 additional observed frequencies close (but not exactly) to the 2nd and 3rd harmonics can explain most of the Bitcoin oscillations.
Nature often discovers robustness through redundancy. Bitcoin does the same. Thousands of nodes store the same truth so no single failure can erase it.
@ScientificBTC It had to be an algorithmic process multiple steps removed from human intervention, in order to allow for an absolutely finite and scientifically precise monetary standard.
We were expecting major resistance at $80k, and the rejection came as expected. For those with a long-term vision, the most exciting part of the cycle is about to begin.
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