Sigma-pi and equivalent-orbital models are concepts from molecular and solid-state physics that deal with the electronic structure of molecules and materials. ### Sigma-Pi Models 1. **Sigma Bonds (σ Bonds)**: These are covalent bonds formed when two atoms share electrons in an overlapping region of their atomic orbitals along the axis connecting the two nuclei. Sigma bonds are generally stronger because they involve direct overlap.
By Ciro Santilli:
- 2021-04-13 twitter.com/cirosantilli/status/1382067162492366854: main initial announcement on Twitter. twitter.com/mikko, who has 209.9K followers and a Wikipedia page: Mikko Hypponen hearted the tweet s2
- 2023-01-21 twitter.com/cirosantilli/status/1749172304259535063: improvements to the Prayer wars
- 2024-02-07 twitter.com/cirosantilli/status/1755378931446739373: large-ish update with new items and improved organization
- 2024-03-31 twitter.com/cirosantilli/status/1774531934305071295: binwalk discoveries, start poking a bit into ordinal ruleset inscriptions
- 2024-04-04 twitter.com/cirosantilli/status/1775805941885108392: largest text ordinal inscription
By others:
- 2021-04-15 news.ycombinator.com/item?id=26801067 (96 points) on Hacker News. Reached position 16 at one point: archive.ph/L0Fte and led to about 5k views total. Ah, Ciro could watch that Google Analytics realtime view go bling all day long. Narcissism is a bitch.
- 2021 cryptonewmedia.press/tankman-image-on-bitcoin-blockchain/ by user igadjeed
- 2022-01-23 news.ycombinator.com/item?id=30050479 "Abuse and Harassment on the Blockchain", comment-mid thread
- 2022-01-24 www.reddit.com/r/Buttcoin/comments/sbw0se/when_i_heard_about_nfts_i_thought_they_were/hu2uk8g "When I heard about NFTs, I thought they were stupid, but then I watched a video explaining how they work, it really changed my perspective", comment mid-thread
- 2023-02 lots of Twitter backlinks as a result of ordinal ruleset inscriptions:
- 2023-02-03
Video 1. Source. Features Marijuana plant and Rickrolling sections. He seems to be a finance guru. - 2023-02-07 twitter.com/privateid_ntity/status/1622814063331004421
- 2024-01-18 twitter.com/pete_rizzo_/status/1748049913286447355 by Rizzo, The Bitcoin Historian (81k followers, mid-thread)
- 2024-12-29: x.com/lopp/status/1873453363523932630 by Jameson Lopp (492k subscribers)
- ? cloudhiker.net/ A hand curated and categorized list of interesting links by Kevin Woblick. Only allows users to visit a random one per category, so we can't get proof of backlink, this was noticed through Google Analytics.
- 2025-03-18 Bitcoin Burn Addresses: Unveiling the Permanent Losses and Their Underlying Causes
The mention of this project is brief:Announced at:Ciro Santilli maintains a Web page listing arbitrary data embedded in the Bitcoin blockchain. This is the most complete and up-to-date list of arbitrary data we are aware of. However, he does not specifically focus on burn addresses, but on the stored contents.
- 2025-03-28 x.com/punk3606/status/1905295370227155344 quick "this was already discovered" mention on thread x.com/I____felix____I/status/1905291048798106061 where a dude rediscovers Figure "Warren Buffet"
- 2025-07-20 www.youtube.com/watch?v=oFrK2tpat8c Uncovering Hidden Messages in Bitcoin by Th3M0rn1ng5h0w
Related:
There are infinitely many prime k-tuples for every admissible tuple.
Generalization of the Twin prime conjecture.
In informal contexts, it usually refers to the phase of ice observed in atmospheric pressure, Ice Ih.
This is the most important technical tutorial project that Ciro Santilli has done in his life so far as of 2019.
The scope is insane and unprecedented, and goes beyond Linux kernel-land alone, which is where it started.
It ended up eating every system programming content Ciro had previously written! Including:
so that that repo would better be called "System Programming Cheat". But "Linux Kernel Module Cheat" sounds more hardcore ;-)
Other major things that could be added there as well in the future are:
- github.com/cirosantilli/algorithm-cheat
- computer architecture tutorials with gem5
Due to this project, some have considered Ciro to be (archive):which made Ciro smile, although "Linux kernel documenter God" would have been more precise.
some kind of Linux kernel god.
[ 1.451857] input: AT Translated Set 2 keyboard as /devices/platform/i8042/s1│loading @0xffffffffc0000000: ../kernel_modules-1.0//timer.ko
[ 1.454310] ledtrig-cpu: registered to indicate activity on CPUs │(gdb) b lkmc_timer_callback
[ 1.455621] usbcore: registered new interface driver usbhid │Breakpoint 1 at 0xffffffffc0000000: file /home/ciro/bak/git/linux-kernel-module
[ 1.455811] usbhid: USB HID core driver │-cheat/out/x86_64/buildroot/build/kernel_modules-1.0/./timer.c, line 28.
[ 1.462044] NET: Registered protocol family 10 │(gdb) c
[ 1.467911] Segment Routing with IPv6 │Continuing.
[ 1.468407] sit: IPv6, IPv4 and MPLS over IPv4 tunneling driver │
[ 1.470859] NET: Registered protocol family 17 │Breakpoint 1, lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 1.472017] 9pnet: Installing 9P2000 support │ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 1.475461] sched_clock: Marking stable (1473574872, 0)->(1554017593, -80442)│kernel_modules-1.0/./timer.c:28
[ 1.479419] ALSA device list: │28 {
[ 1.479567] No soundcards found. │(gdb) c
[ 1.619187] ata2.00: ATAPI: QEMU DVD-ROM, 2.5+, max UDMA/100 │Continuing.
[ 1.622954] ata2.00: configured for MWDMA2 │
[ 1.644048] scsi 1:0:0:0: CD-ROM QEMU QEMU DVD-ROM 2.5+ P5│Breakpoint 1, lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 1.741966] tsc: Refined TSC clocksource calibration: 2904.010 MHz │ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 1.742796] clocksource: tsc: mask: 0xffffffffffffffff max_cycles: 0x29dc0f4s│kernel_modules-1.0/./timer.c:28
[ 1.743648] clocksource: Switched to clocksource tsc │28 {
[ 2.072945] input: ImExPS/2 Generic Explorer Mouse as /devices/platform/i8043│(gdb) bt
[ 2.078641] EXT4-fs (vda): couldn't mount as ext3 due to feature incompatibis│#0 lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 2.080350] EXT4-fs (vda): mounting ext2 file system using the ext4 subsystem│ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 2.088978] EXT4-fs (vda): mounted filesystem without journal. Opts: (null) │kernel_modules-1.0/./timer.c:28
[ 2.089872] VFS: Mounted root (ext2 filesystem) readonly on device 254:0. │#1 0xffffffff810ab494 in call_timer_fn (timer=0xffffffffc0002000 <mytimer>,
[ 2.097168] devtmpfs: mounted │ fn=0xffffffffc0000000 <lkmc_timer_callback>) at kernel/time/timer.c:1326
[ 2.126472] Freeing unused kernel memory: 1264K │#2 0xffffffff810ab71f in expire_timers (head=<optimized out>,
[ 2.126706] Write protecting the kernel read-only data: 16384k │ base=<optimized out>) at kernel/time/timer.c:1363
[ 2.129388] Freeing unused kernel memory: 2024K │#3 __run_timers (base=<optimized out>) at kernel/time/timer.c:1666
[ 2.139370] Freeing unused kernel memory: 1284K │#4 run_timer_softirq (h=<optimized out>) at kernel/time/timer.c:1692
[ 2.246231] EXT4-fs (vda): warning: mounting unchecked fs, running e2fsck isd│#5 0xffffffff81a000cc in __do_softirq () at kernel/softirq.c:285
[ 2.259574] EXT4-fs (vda): re-mounted. Opts: block_validity,barrier,user_xatr│#6 0xffffffff810577cc in invoke_softirq () at kernel/softirq.c:365
hello S98 │#7 irq_exit () at kernel/softirq.c:405
│#8 0xffffffff818021ba in exiting_irq () at ./arch/x86/include/asm/apic.h:541
Apr 15 23:59:23 login[49]: root login on 'console' │#9 smp_apic_timer_interrupt (regs=<optimized out>)
hello /root/.profile │ at arch/x86/kernel/apic/apic.c:1052
# insmod /timer.ko │#10 0xffffffff8180190f in apic_timer_interrupt ()
[ 6.791945] timer: loading out-of-tree module taints kernel. │ at arch/x86/entry/entry_64.S:857
# [ 7.821621] 4294894248 │#11 0xffffffff82003df8 in init_thread_union ()
[ 8.851385] 4294894504 │#12 0x0000000000000000 in ?? ()
│(gdb) is a hyperparameter, and are common choices when doing dataset exploration, as they can be easily visualized on a planar plot.
The mapping is done by projecting all points to a dimensional hyperplane. PCA is an algorithm for choosing this hyperplane and the coordinate system within this hyperplane.
The hyperplane choice is done as follows:
- the hyperplane will have origin at the mean point
- the first axis is picked along the direction of greatest variance, i.e. where points are the most spread out.Intuitively, if we pick an axis of small variation, that would be bad, because all the points are very close to one another on that axis, so it doesn't contain as much information that helps us differentiate the points.
- then we pick a second axis, orthogonal to the first one, and on the direction of second largest variance
- and so on until orthogonal axes are taken
www.sartorius.com/en/knowledge/science-snippets/what-is-principal-component-analysis-pca-and-how-it-is-used-507186 provides an OK-ish example with a concrete context. In there, each point is a country, and the input data is the consumption of different kinds of foods per year, e.g.:so in this example, we would have input points in 4D.
- flour
- dry codfish
- olive oil
- sausage
Suppose that every country consumes the same amount of flour every year. Then, that number doesn't tell us much about which country each point represents (has the least variance), and the first PCA axes would basically never point anywhere near that direction.
Another cool thing is that PCA seems to automatically account for linear dependencies in the data, so it skips selecting highly correlated axes multiple times. For example, suppose that dry codfish and olive oil consumption are very high in Portugal and Spain, but very low in Germany and Poland. Therefore, the variation is very high in those two parameters, and contains a lot of information.
However, suppose that dry codfish consumption is also directly proportional to olive oil consumption. Because of this, it would be kind of wasteful if we selected:since the information about codfish already tells us the olive oil. PCA apparently recognizes this, and instead picks the first axis at a 45 degree angle to both dry codfish and olive oil, and then moves on to something else for the second axis.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact