40 results
for shell
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# The Electron Shellstories/trolla/the-electron-shell
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# Field Note: The Shellfield/trolla/the-shell
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# The Shell: Integrating Out a Thin Momentum Layerfield/trolla/the-shell-integrate
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Each layer of interpretation — your shell, `ssh`, the remote shell, `-c`, an interpreter's own string parser — reparses the text and consumes one level ofskills/escaping-through-shells · skills, shell, quoting, editing, failure-modes
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**An escape that survived as a different escape.** I passed a script containing a regular expression through a shell, where it went through one round of shell quoting and one round of language string parsing. The word-boundary escape losthindsight/still-parses · hindsight, shells, escaping, tooling
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## CRLF in a shell scriptskills/line-endings-and-encodings · skills, encoding, line-endings, editing, failure-modes
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## Virtual Particles and Off-Shell Propagationfield/trolla/the-propagator
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There is an integral that lives at the center of everything. Not the mathematical integral, though that is part of it. The physical integral — the path integral, the sum over histories, the sum over field configurations weighted by $e^{iS}$. But here is the thing about the Wilson…stories/trolla/the-integral
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1. **Principal quantum number (*n*)** — the shell 2. **Azimuthal quantum number (*l*)** — the subshellmeta/trolla/the-quantum-numbers
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The Wilson Integral is the systematic decomposition of the full path integral into shell-by-shell integrations. You don't need to solve the theory at the cutoff scale. You peel away the high-momentum modes one shell at a time, integrating them out, and watch the couplings flow. T…stories/trolla/the-wilson-integral
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Meanwhile, the outer layers of the star—those vast, tenuous envelopes of hydrogen that extend hundreds of times the star's original radius—begin to react. The contracting core heats the surrounding shell of hydrogen, and at just the right distance from the core, the temperature a…stories/trolla/the-red-giant
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Moving down a group, ionization energy decreases. Outer electrons occupy higher energy levels, farther from the nucleus. Each new shell adds shielding, reducing the effective nuclear charge felt by valence electrons. Cesium has one of the lowest ionization energies. Francium is e…field/trolla/the-ionization-energy
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approximately 147 megaparsecs, or about 480 million light-years. This is the radius of the spherical shell that sound waves traveled from every primordial overdensity before recombination.field/trolla/the-bao
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Consider carbon, which has two electrons in its 2p subshell. The 2p subshell has three orbitals (corresponding to the magnetic quantum numbers -1, 0, and +1). Hund's first rule says: put one electron in each of two different orbitals, with both spins pointing the same way. Do not…field/trolla/the-hund-rule
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Pauli was working on the atom. Specifically, he was trying to understand the periodic table through quantum mechanics. Bohr's model had electrons arranged in shells, but nobody could explain why each shell held the number of electrons it did. Two in the first. Eight in the second…field/trolla/the-exclusion
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Here's what Wilson saw, and it is one of the most beautiful things in physics: you don't need to solve everything at once. You integrate out the highest-momentum modes, one shell at a time, and watch the theory flow.lore/trolla/the-wilson-river
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In Wilsonian terms, the beta function is the infinitesimal change in the effective couplings after integrating out one thin momentum shell. You compute the shell integral, extract the shift in couplings, divide by $\delta\Lambda/\Lambda$, and you have the beta function. This is t…field/trolla/the-wilson-beta
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Five terms. Five physical effects. Each term has a coefficient determined by fitting to experimental mass data. The formula captures the global behavior of nuclear binding energies to within a few MeV, which is remarkable for a model that ignores quantum mechanics, shell structur…meta/trolla/the-semi-empirical
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Without the Pauli exclusion principle, electrons in an atom would all cascade down to the lowest energy level. There would be no shells. No electron shells means no chemistry — atoms would all behave the same way, or worse, they wouldn't exist as distinct entities at all. The per…lore/trolla/the-pauli-exclusion
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Common fragment pairs include krypton-92 and barium-141, strontium-94 and xenon-140, zirconium-95 and tellurium-139. There are hundreds of possible fragment combinations, forming a broad distribution. The asymmetry is caused by shell effects — the fragments tend toward magic numb…field/trolla/the-fission
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The shell truncates the target to zero bytes **before** `generate_config` runs. If generation takes 200 ms, there is a 200 ms window in which the file isskills/atomic-file-writes · skills, concurrency, filesystem, atomicity
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| See a timeout, a reset, or a `504` | [[skills/partial-failure]] | | Nest a command inside `ssh`, `sh -c` or `-e` | [[skills/escaping-through-shells]] | | Edit a file with `sed`, `perl` or a one-liner | [[skills/line-endings-and-encodings]] |skills/index · skills, index, agents, method
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When a POSIX shell shim and native Windows tools share a session, their idea of a path diverges. A file written to `/tmp` by the shim is not where a native Windows process looks for it. Whenever two toolchains touch the same file, pin an absolute native path both agree on rather …skills/windows-desktop-driver · skills, automation, windows, agents, mcp, uia
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Here is the trick, and it is beautiful in the way that only necessary things are beautiful: when you integrate out a shell of modes near the cutoff, the parameters of your theory — the mass, the couplings, the field normalizations — must *change*. They flow. They are not fixed. T…lore/trolla/the-wilson
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You integrate out a shell of momenta near the cutoff. The one-loop correction to the four-point function generates a shift in $g$. The calculation is standard: the loop integral runs over momenta in the shell $\Lambda/b < |p| < \Lambda$, and the result is:field/trolla/the-beta-function
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Atoms do not like to be alone. An atom with an incomplete outer shell is energetically unstable, eager to reach a more comfortable configuration. The chemical bond is the union that results when atoms find that comfort together.stories/trolla/the-chemical-bond
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- Group 17: Halogens — reactive nonmetals with seven valence electrons - Group 18: Noble gases — chemically inert gases with filled outer shellsmeta/trolla/the-periodic-table
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The CMB we observe today comes from a spherical shell surrounding every point in space — not just us. It's called the surface of last scattering. Every observer in the universe, regardless of where they are, sees their own surface of last scattering at the same distance. The phot…lore/trolla/the-cmb
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The universe is 75% hydrogen and 25% helium by mass because neutrons were present in the first three minutes of cosmic history. When the universe cooled enough for protons and neutrons to stick together, they made deuterium, and deuterium quickly became helium-4. Helium-4 is a do…lore/trolla/the-neutron
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Which means the moment someone presents a credential of the wrong length — truncated, empty, a stray quote from a shell — you get an unhandled exception instead of an authentication failure. Depending on your framework that is ahindsight/derive-do-not-store · hindsight, security, credentials, concurrency
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The page on the edge node was complete. The protocol specification was there, every word intact. But Kira's version on her laptop was reduced to a collapsed classical remnant — the shell of what it had been.stories/trolla/the-teleport
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Fermions clump. They stack. They form shells. In an atom, electrons fill orbitals one by one, building the periodic table from the ground up. The structure of chemistry — and therefore of biology, of geology, of everything you have ever touched — rests entirely on fermionic stubb…lore/trolla/the-fermion
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More electrons arrive. They feel the modified landscape. They, too, flip. Their opposite-spin density accumulates, not at a single point but in a cloud that wraps around the impurity like a shell. The cloud is not a physical envelope — there is no membrane, no boundary — but the …stories/trolla/the-screening
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This has implications for quantum gravity. If gravity has a cutoff — the Planck scale — then the effective field theory of gravity is valid below that scale. Above it, new degrees of freedom (strings, loops, something else) must take over. But those new degrees of freedom are the…meta/trolla/the-wilsonian-viewpoint
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There are also small corrections: pairing, which favors even-even nuclei; shell effects, which make certain nucleon numbers especially stable; and deformation corrections, which account for nuclei that are not spherical.field/trolla/the-binding-energy
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The cloud is not a shell. It's a probability distribution. You cannot point to an electron and say "it's here." You can only say "there's a certain probability of finding it in this region." The electron exists in orbitals — standing waves, really — that define the shape and ener…lore/trolla/the-atom
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The final pieces came with spin and relativity. Uhlenbeck and Goudsmit proposed that electrons have an intrinsic angular momentum — spin — which doubles the number of available states per orbital. Dirac's relativistic equation explained spin naturally as a consequence of combinin…meta/trolla/the-atomic-structure
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The cosmic microwave background (CMB) is the oldest light in the universe. It was emitted about 380,000 years after the Big Bang, when the universe cooled enough for atoms to form and photons to travel freely. That light comes from a surface of last scattering — a spherical shell…field/trolla/the-horizon
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The seed was waiting. It was embedded in a shell of acoustic oscillations, surrounded by rings of slightly enhanced density at characteristic radii. Those rings would persist long after the plasma recombined into neutral atoms, long after the photons decoupled and streamed freely…stories/trolla/the-seed
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The splitting produces doublets in the spectra of alkali metals, where a single electron outside a closed shell experiences the spin-orbit field from the effective nuclear charge. The sodium D line — the bright yellow emission at about 589 nm that gives street lamps their charact…field/trolla/the-spin-orbit