9. A Strongly Aperiodic Monotile in Three Dimensions (arxiv.org)

Socolar and Taylor asked for a single, simply connected three-dimensional prototile that forces nonperiodicity by shape alone, admitting no weakly nonperiodic tiling; the Schmitt-Conway-Danzer biprism and the three-dimensional Socolar-Taylor tile admit screw motions or a periodic stacking direction. We exhibit a rational polyhedral $3$-ball $Q$, which we call Chair44 (R44): a seven-cube chair whose $24$ exposed unit panels carry tiny square-pyramid features, and prove, as a proof submission, that $Q$ admits tilings of $\mathbb{R}^3$ by congruent copies, reflections allowed, and that every such tiling has no translational period and a symmetry group of order at most $24$; every tiling is homochiral and carries a unique infinite hierarchy of nested supertiles. The solid was designed to a reading of the aperiodic-monotile phenomenon reached with the Six Birds emergence calculus (Section 3.3), and the construction turns on a single finite test, checked by machine: the tile's own contact rule survives coarsening, so that the decoded parent tiling obeys the tile's rule and no other. The proof combines a written geometric argument, that the features force every tiling onto a registered lattice, with exhaustive finite enumerations; the companion census is replayed by two independent implementations, every finite gate is kernel-checked in Lean 4 (modulo a named compiler hook per native_decide theorem), and the written geometric lemmas and the logical assembly are Lean theorems as well, so that the theorem is kernel-checked modulo the named compiler hooks; the written proofs remain as exposition.

Researchers have developed a new three-dimensional tile, called Chair44, that uniquely enforces nonperiodicity through its shape alone, without allowing for any periodic arrangements. This discovery could have significant implications for the study of aperiodic tiling in higher dimensions.

10. Show HN: Yagi DSP Modulation SIM (brian-armstrong.github.io)

Explore digital modulation and channel impairments in the browser.

Yagi DSP is a new library that ports the popular liquid-dsp C library to Rust, showcasing its capabilities through a browser demo that illustrates modem performance in noisy environments. With over 95% test coverage and a recent major refactor, it promises to be a solid tool for those interested in digital signal processing.

14. FCSS 2: Utility CSS that reads like CSS (github.com)

Functional CSS: utility classes named after real CSS properties. One class, one declaration, zero runtime. Works with Vite, Next.js, Astro and Angular. - meerita/FCSS2

FCSS 2 introduces utility classes that mimic real CSS properties, simplifying styling with one class per declaration and no runtime overhead. It’s compatible with popular frameworks like Vite, Next.js, Astro, and Angular, making it a practical choice for developers looking to streamline their CSS workflow.

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