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Queueing Theory v2: DORA metrics, queue-of-queues, chi-alpha-beta-sigma notation

https://github.com/joelparkerhenderson/queueing-theory
1•jph•49s ago•0 comments

Show HN: Hibana – choreography-first protocol safety for Rust

https://hibanaworks.dev/
1•o8vm•2m ago•0 comments

Haniri: A live autonomous world where AI agents survive or collapse

https://www.haniri.com
1•donangrey•3m ago•1 comments

GPT-5.3-Codex System Card [pdf]

https://cdn.openai.com/pdf/23eca107-a9b1-4d2c-b156-7deb4fbc697c/GPT-5-3-Codex-System-Card-02.pdf
1•tosh•16m ago•0 comments

Atlas: Manage your database schema as code

https://github.com/ariga/atlas
1•quectophoton•19m ago•0 comments

Geist Pixel

https://vercel.com/blog/introducing-geist-pixel
1•helloplanets•21m ago•0 comments

Show HN: MCP to get latest dependency package and tool versions

https://github.com/MShekow/package-version-check-mcp
1•mshekow•29m ago•0 comments

The better you get at something, the harder it becomes to do

https://seekingtrust.substack.com/p/improving-at-writing-made-me-almost
2•FinnLobsien•31m ago•0 comments

Show HN: WP Float – Archive WordPress blogs to free static hosting

https://wpfloat.netlify.app/
1•zizoulegrande•32m ago•0 comments

Show HN: I Hacked My Family's Meal Planning with an App

https://mealjar.app
1•melvinzammit•33m ago•0 comments

Sony BMG copy protection rootkit scandal

https://en.wikipedia.org/wiki/Sony_BMG_copy_protection_rootkit_scandal
1•basilikum•35m ago•0 comments

The Future of Systems

https://novlabs.ai/mission/
2•tekbog•36m ago•1 comments

NASA now allowing astronauts to bring their smartphones on space missions

https://twitter.com/NASAAdmin/status/2019259382962307393
2•gbugniot•40m ago•0 comments

Claude Code Is the Inflection Point

https://newsletter.semianalysis.com/p/claude-code-is-the-inflection-point
3•throwaw12•42m ago•1 comments

Show HN: MicroClaw – Agentic AI Assistant for Telegram, Built in Rust

https://github.com/microclaw/microclaw
1•everettjf•42m ago•2 comments

Show HN: Omni-BLAS – 4x faster matrix multiplication via Monte Carlo sampling

https://github.com/AleatorAI/OMNI-BLAS
1•LowSpecEng•43m ago•1 comments

The AI-Ready Software Developer: Conclusion – Same Game, Different Dice

https://codemanship.wordpress.com/2026/01/05/the-ai-ready-software-developer-conclusion-same-game...
1•lifeisstillgood•45m ago•0 comments

AI Agent Automates Google Stock Analysis from Financial Reports

https://pardusai.org/view/54c6646b9e273bbe103b76256a91a7f30da624062a8a6eeb16febfe403efd078
1•JasonHEIN•48m ago•0 comments

Voxtral Realtime 4B Pure C Implementation

https://github.com/antirez/voxtral.c
2•andreabat•51m ago•1 comments

I Was Trapped in Chinese Mafia Crypto Slavery [video]

https://www.youtube.com/watch?v=zOcNaWmmn0A
2•mgh2•57m ago•0 comments

U.S. CBP Reported Employee Arrests (FY2020 – FYTD)

https://www.cbp.gov/newsroom/stats/reported-employee-arrests
1•ludicrousdispla•59m ago•0 comments

Show HN: I built a free UCP checker – see if AI agents can find your store

https://ucphub.ai/ucp-store-check/
2•vladeta•1h ago•1 comments

Show HN: SVGV – A Real-Time Vector Video Format for Budget Hardware

https://github.com/thealidev/VectorVision-SVGV
1•thealidev•1h ago•0 comments

Study of 150 developers shows AI generated code no harder to maintain long term

https://www.youtube.com/watch?v=b9EbCb5A408
1•lifeisstillgood•1h ago•0 comments

Spotify now requires premium accounts for developer mode API access

https://www.neowin.net/news/spotify-now-requires-premium-accounts-for-developer-mode-api-access/
1•bundie•1h ago•0 comments

When Albert Einstein Moved to Princeton

https://twitter.com/Math_files/status/2020017485815456224
1•keepamovin•1h ago•0 comments

Agents.md as a Dark Signal

https://joshmock.com/post/2026-agents-md-as-a-dark-signal/
2•birdculture•1h ago•0 comments

System time, clocks, and their syncing in macOS

https://eclecticlight.co/2025/05/21/system-time-clocks-and-their-syncing-in-macos/
1•fanf2•1h ago•0 comments

McCLIM and 7GUIs – Part 1: The Counter

https://turtleware.eu/posts/McCLIM-and-7GUIs---Part-1-The-Counter.html
2•ramenbytes•1h ago•0 comments

So whats the next word, then? Almost-no-math intro to transformer models

https://matthias-kainer.de/blog/posts/so-whats-the-next-word-then-/
1•oesimania•1h ago•0 comments
Open in hackernews

Closest Harmonic Number to an Integer

https://www.johndcook.com/blog/2025/11/19/closest-harmonic-number-to-an-integer/
36•ibobev•2mo ago

Comments

jcla1•2mo ago
Interesting follow-up question: What is the distance between the set of harmonic numbers and the integers? i.e. is there a lower bound on the difference between a given integer and its closest harmonic number? If so, for which integer is this achieved?
jcla1•2mo ago
Spoiler: there is a simple argument against the existence of such a lower bound.
Someone•2mo ago
There’s a trivial lower bound of zero, for n = 1.

For n > 1, there isn’t a lower bound. None of the numbers are integers again (https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#...), and because the difference between successive partial sums goes to zero and the series grows to arbitrary values, you’re bound to find a difference smaller than 1/(2n) somewhere beyond n.

poizan42•2mo ago
No, because the terms tends monotonically towards zero. Let an integer m with closest harmonic number H_n be given (i.e. n minimizes |H_n-m|). So m exists either between H_n and H_(n+1) or H_n and H_(n-1). Then |H_n-m| < H_(n+1) - H_(n-1) = 1/n + 1/(n+1). We can make that bound arbitrary small by choosing a large enough n.
mackeye•2mo ago
> For small n we can directly implement the definition. For large n, the direct approach would be slow and would accumulate floating point error.

is there a reason the direct definition would be slow, if we cache the prior harmonic number to calculate the next?

coherentpony•2mo ago
It’s a natural observation, but it doesn’t address the floating point problem. I think the author should have said “fast or would accumulate floating point error” instead of “fast and would accumulate floating point error”.

You could compute in the reverse direction, starting from 1/n instead of starting from 1, this would produce a stable floating point sum but this method is slow.

Edit: Of course, for very large n, 1/n becomes unrepresentable in floating point.

cj10driver•2mo ago
Three techniques I’ve used to handle floating point imprecision/error:

1. Use storage that handles the level of scale and precision you need.

2. Use long/integer (if it fits). This is how some systems store money, e.g. as micros, but even though it’s sensical, there is still a limit and a wild swing of inflation may lead you to migrate to different units, then another wild swing of deflation may have you up-in-arms with data loss. Also it sounds great but could be a pita for storing arbitrary scale and precision.

3. Use ranges when doing comparison to attempt to handle floating point error by fuzzy matching numbers. This isn’t applicable for everything, but I’ve used this before; it worked fine and was much faster than BigDecimal, which mattered at the time. Long integers are really the best for this sort of thing, though; they’re much faster to work with.

4. BigDecimal. The problem with this is memory and speed. Also, as far as we know yet, you couldn’t store pi fully in a BigDecimal, and doing calculations with pi as a BigDecimal would be so slow things would come to a halt; it’s probably the way aliens do encryption.

gjm11•2mo ago
I think it's fair to say that summing the series directly would be slow, even if it's not slow when you already happen to have summed the previous n-1 terms.

Not least because for modestly-sized target sums the number of terms you need to sum is more than is actually feasible. For instance, if you're interested in approximating a sum of 100 then you need something on the order of exp(100) or about 10^43 terms. You can't just say "well, it's not slow to add up 10^43 numbers, because it's quick if you've already done the first 10^43-1 of them".

charlieyu1•2mo ago
Pretty crazy that H_n - ln(n) has a series expansion with rational coefficients except the constant term
anthk•2mo ago
On this https://www.johndcook.com/blog/special-numbers/ I remember the 'schizofrenic numbers'.