Cool data embedded in the Bitcoin blockchain The largest transactions in the Bitcoin Blockchain by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16- bb41a757f405890fb0f5856228e23b715702d714d59bf2b1feb70d8b2b4e3e08 999,657 bytes. Joins a bunch of tiny inputs into a single output
- 623463a2a8a949e0590ffe6b2fd3e4e1028b2b99c747e82e899da4485eb0b6be and 5143cf232576ae53e8991ca389334563f14ea7a7c507a3e081fbef2538c84f6e both have 3,075 outputs of 1 satoshi each and a single input. We were not able to identify any meaningful data in it,
filejust saysdata, and there aren't long ASCII strings. However, the outputs were unspent as of 2021, which suggests that they might actually be data.
Analysis of some of them follows.
- dd9f6bbf80ab36b722ca95d93268667a3ea6938288e0d4cf0e7d2e28a7a91ab3 has 13107 with payload 256KB in size, but some of them at least have been spent: www.blockchain.com/btc/tx/dd9f6bbf80ab36b722ca95d93268667a3ea6938288e0d4cf0e7d2e28a7a91ab3 therefore it's not data.
filesays their payload is a DOS executable, but it must be a coincidence
Matrix congruence can be seen as the change of basis of a bilinear form by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis modifies the matrix representation of a bilinear form as:
So, by taking , we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.
Some nice insights at: Robert Noyce: The Man Behind the Microchip by Leslie Berlin (2006).
They are the finite projective special linear groups.
This was the first infinite family of simple groups discovered after the simple cyclic groups and alternating groups. The first case discovered was by Galois. You should understand that one first.
Used to explain the black-body radiation experiment.
Published as: On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'
TODO how can it be derived from theoretical principles alone? There is one derivation at; en.wikipedia.org/wiki/Planck%27s_law#Derivation but it does not seem to mention the Schrödinger equation at all.
Using de novo DNA synthesis to synthesize entire Chromosomes.
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