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: • Lomb-Scargle → λ ≈ 2.04 • FFT / 3-mode DSI → λ ≈ 2.06 Both land right where you reported (~2.05). The DSI 3-mode clearly tracks the residual peaks where a linear 3.5-year cycle drifts off — consistent with your finding that the structure is logarithmic, not calendar-time. Thank you for publishing the method clearly enough that someone outside academia could replicate it. I treat λ as "near 2," not exact — and none of this as a price predictor. Just wanted to confirm your work holds up on independent data. 🫡 — a student of the power law, from South Korea

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 calculations. Instead of just routing phone calls, they were destined to become thinking machines. He had just discovered the mathematical trigger for digital computing. But when he published his work, the leading engineers of the industrial world paid little attention, viewing his mathematics as a mere academic parlor trick. His name was Claude Shannon. It would take years for the industrial establishment to fully realize he was right and adopt the binary logic that now powers every computer, smartphone, and network on Earth. His breakthrough against traditional engineering is the ultimate lesson in what happens when rigid practices clash with unexpected philosophical reality. In the early 20th century, engineers believed they understood circuit design. They knew that as telephone networks grew, they needed more physical wires and relays. But traditional engineering offered no universal science; it was a manual process of brute-force trial and error. The systems would grow into a chaotic, tangled mess of blueprints and copper lines. The entire industrial establishment agreed: every circuit, no matter how complex, had to be wired by manual experimentation. It was a tedious, costly formula. But in that library, Shannon realized the establishment had left a massive variable out of their equations: 19th-century symbolic philosophy. Shannon recalculated the engineering, factoring in what happens when you treat an electrical switch using the laws of Boolean algebra. What he found shattered the industrial consensus. He proved that an electrical switch has only two possible states: it is either closed and letting power through, or open and blocking the current. This was mathematically identical to True (1) and False (0). The circuit could evaluate logical statements. There was no limit to what it could compute. It could automate human thought, transforming physical electricity into digital logic. When Shannon presented this concept, mainstream electrical engineers were skeptical. They couldn't accept that an abstract philosophical concept could solve real-world hardware bottlenecks. Shannon was initially ignored. The establishment stuck to their traditional wiring methods. Instead of fighting a rigid, closed system, Shannon quietly expanded his work into Information Theory, proving that all data could be compressed into a universal currency called the "bit." Decades later, when the global tech revolution exploded, the world realized the 21-year-old student had been right all along. The philosophical blueprint Shannon left behind is a vital truth for navigating complex problems and institutional pushback: Comforting traditions will always be more popular than disruptive innovations. Trust the system's underlying logic anyway. Most of us approach our careers and projects seeking the validation of current experts or established guidelines. When we propose a radical new idea or try to change a broken system, and the authorities tell us we are wrong, our instinct is to assume our logic is flawed. We abandon our data to fit the consensus. But Shannon’s legacy proves that traditional industry consensus is not the same thing as truth. Gatekeepers are human; they protect their own methods, their own training, and their own comfort. What is a bottleneck, a project, or a direction you’ve abandoned just because an expert or a boss told you it wouldn't work? What happens if you stop looking for their permission and trust the structural logic of your own work?

The gap between these bars is arguably the largest asymmetry in Bitcoin right now

Gravity is just a theory, it’s not a law…