---
slug: how-magnets-work
passed: 2026-10-18
by: the assay line (research/assay-line/claude-1018/), Claude fixer (claude-opus-5-5) directed by claude-assaying-boyle-1014; source record by a Claude agent (claude-sonnet-5-5), checked by a Claude agent (claude-opus-5-5)
checked: 86
confirmed: 77            # 69 CONFIRMED lines + 8 MINOR lines (near-misses, all fixed, counted here)
wrong: 1
unverifiable: 3
observed: 5
stale: 0
---
# Claims pass: What Holds a Magnet Together

This pass was the assay line's batch claude-1018 on /strata/how-magnets-work/: a source record of the page's claims, a checker who took every entry back to its source (Kittel's Introduction to Solid State Physics 8th edition, CODATA 2018, Crossref, Wikipedia, the Feynman transcript) and recomputed every figure, a triage that re-read each finding, and this fix. Of 86 claims, 69 held, 5 are OBSERVED (the check placard's measurements and the 7/7 run, recreated), 3 are UNVERIFIABLE (a comparative over all accounts online; Blundell's book, which exists with the right section but whose words were not read; and the quotation "magnetism is relativity." attributed to the Feynman Lectures, Vol. II, which no source found carries), 1 is WRONG and 8 are MINOR. The WRONG one was the "Ride with the charge" readout, which gave the lab-frame force as the force in the charge's frame; it now reads 1.13058×10⁻⁴ N in that frame, the figure research/how-magnets-work/verify.mjs prints, and carries a dated Corrected line. The eight MINOR lines were fixed in place with no line on the page. After the fix the layer's verifier prints "ALL CHECKS PASS (7 passed, 0 failed)", and its seventh check now takes ε₀ from CODATA 2018 and fails when that value is perturbed by 1.4e-9 (tried).

## Claims
- CONFIRMED | Ask how a magnet works and you'll be told opposite poles attract. | https://en.wikipedia.org/wiki/Magnet | opposite-poles: "Since opposite poles (north and south) attract" is there; the page itself says this is true and explains nothing.
- CONFIRMED | Every iron atom is already a tiny magnet; its electrons carry spin, and spin is magnetic. | https://en.wikipedia.org/wiki/Bohr_magneton | iron-atom-magnet: "the inherent rotation, or spin, of the electron has a spin magnetic moment"; the iron-specific part is Kittel Table 1, Fe n_B(0 K) = 2.22 Bohr magnetons per atom.
- CONFIRMED | A bar of iron contains some 10²³ of them. | https://web.archive.org/web/2021id_/https://physics.nist.gov/cuu/Constants/Table/allascii.txt | bar-1e23: Avogadro 6.022 140 76 e23 mol^-1 (exact); with 55.845 g/mol, 10^23 atoms is 9.3 g and 1 cm³ (7.874 g) is 8.5e22, so a small bar is 10^23 and a 100 g bar about 10^24; order of magnitude holds for a small bar.
- CONFIRMED | Below a sharp temperature the pull wins and patches of atoms lock into step: domains. | https://en.wikipedia.org/wiki/Magnetic_domain | domains: "When cooled below a temperature called the Curie temperature, the magnetization of a piece of ferromagnetic material spontaneously divides into many small regions called magnetic domains."
- CONFIRMED | in two dimensions Lars Onsager solved it exactly in 1944 | https://en.wikipedia.org/wiki/Ising_model | onsager-1944-exact: "was only given an analytic description much later, by Lars Onsager (1944)"; Crossref 10.1103/PhysRev.65.117 issued 1944-02-01.
- CONFIRMED | the tipping point sits at Tc = 2/ln(1+√2) = 2.2692… | https://en.wikipedia.org/wiki/Ising_model | tc-2d-value: "the critical temperature Tc occurs at the following point Tc = 2J/(k ln(1+√2)) = (2.269185…) J/k"; recomputed 2.269185314.
- CONFIRMED | L. Onsager, "Crystal Statistics. I.", Phys. Rev. 65, 117 (1944), the exact 2D Ising solution; Tc = 2/ln(1+√2). | https://api.crossref.org/works/10.1103/PhysRev.65.117 | tc-2d-value-onsager-paper: Crossref title "Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition", Onsager, Physical Review 65, 117-149, 1944 (page gives the title's first part only).
- CONFIRMED | Heat past it and the alignment collapses to zero. | https://en.wikipedia.org/wiki/Curie_temperature | heat-collapses: "spontaneous magnetism only occurs below the Curie temperature"; the page's own update rule run headless at N = 120 gives mean net alignment 0.97 (T 1.7), 0.79 (T 2.2, Onsager's exact value is 0.79), 0.034 (T 2.6), 0.023 (T 3.0), the finite-grid residue of zero.
- CONFIRMED | every ferromagnet has a Curie temperature where it simply stops being a magnet. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | every-ferromagnet-curie: Kittel ch. 12 states it generally: "The Curie temperature Tc is the temperature above which the spontaneous magnetization vanishes; it separates the disordered paramagnetic phase at T > Tc from the ordered ferromagnetic phase"; Wikipedia's "certain materials" means ferromagnets.
- CONFIRMED | This is a real Ising model, the simplest honest cartoon of a ferromagnet. | https://en.wikipedia.org/wiki/Ising_model | cond-ising-cartoon: "one of the simplest statistical models to show a phase transition. Though it is a highly simplified model of a magnetic material"; the page script is a genuine Metropolis Ising update, dE = 2*s*(up+dn+lf+rt), accept exp(-dE/T), periodic 120 x 120.
- CONFIRMED | Iron (Fe) 1043 K (770 °C) | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | curie-fe: Table 1 "Fe 1707 1740 2.22 1043"; 1043 - 273.15 = 769.85 °C.
- CONFIRMED | Cobalt (Co) 1388 K (1115 °C) | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | curie-co: Table 1 "Co 1400 1446 1.72 1388"; 1114.85 °C. (Wikipedia's table says 1400 K; the page cites Kittel.)
- CONFIRMED | Nickel (Ni) 627 K (354 °C) | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | curie-ni: Table 1 "Ni 485 510 0.606 627"; 353.85 °C.
- CONFIRMED | Gadolinium (Gd) 292 K (19 °C) | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | curie-gd: Table 1 "Gd" row ends "2060 7.63 292"; 18.85 °C (Wikipedia: 293.2 K).
- CONFIRMED | Representative values, Kittel, Introduction to Solid State Physics. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | kittel-representative: "Table 1 gives representative valnes [OCR] of the saturation magnetization M,, the ferromagnetic Curie temperature, and the effective magneton number".
- MINOR | Gadolinium's is near room temperature; it stops being a fridge magnet in your warm hand. | https://en.wikipedia.org/wiki/Gadolinium | gd-hand: the Curie point is right (292 K per Kittel; "Gadolinium below its Curie point of 20 °C (68 °F) is ferromagnetic, with an attraction to a magnetic field higher than that of nickel"), but gadolinium is never a fridge magnet: below its Curie point it is attracted to a magnet, it does not hold its own magnetization; and at 19 °C a typical room is already at or above it, so the demonstration needs it cooled first.
- CONFIRMED | Two atomic dipoles a lattice-spacing apart in iron interact with an energy of about μ₀/4π · m²/r³. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | dipole-energy-formula: Kittel p. 324 "a magnetic ion produces a field ~ μB/a³ [OCR 'up/a°'] or about 10³ G = 0.1 T at a neighboring lattice point"; field times moment is the page's order-of-magnitude energy; the page's numbers give 0.135 T, consistent.
- CONFIRMED | Put in iron's real numbers (r = 0.248 nm, moment 2.22 Bohr magnetons) | https://en.wikipedia.org/wiki/Iron | iron-r: infobox "a = 286.65 pm (at 20 °C)", bcc; (√3/2)a = 0.24825 nm.
- CONFIRMED | Put in iron's real numbers (r = 0.248 nm, moment 2.22 Bohr magnetons) | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | iron-moment: Table 1 n_B(0 K) for Fe is 2.22 per formula unit.
- CONFIRMED | and that energy is 2.8×10⁻²⁴ J, which, as a temperature, is 0.20 K. | research/how-magnets-work/verify.mjs | energy-2.8e-24-0.20K: verify.mjs prints "U_dipole ≈ 2.771e-24 J = 1.729e-5 eV → 0.201 K"; independent Python with CODATA 2018 gives 2.7707e-24 J and 0.20068 K.
- CONFIRMED | If magnetism were the glue, iron would scramble above a fifth of a degree above absolute zero. | research/how-magnets-work/verify.mjs | scramble-fifth-degree: 0.2007 K is a fifth of a kelvin; the inference is the page's order-of-magnitude argument, which Kittel makes the same way (exchange field 10³ T against 0.1 T from neighbouring dipoles).
- CONFIRMED | Instead it holds its alignment all the way to 1043 K | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | holds-to-1043: Table 1 Fe Curie temperature 1043 K.
- CONFIRMED | about 5,200× stronger than magnetism can account for. | research/how-magnets-work/verify.mjs | ratio-5200: recomputed 1043 / 0.200683 = 5197.26; rounds to 5,200.
- CONFIRMED | U_dipole = (μ₀/4π)·(2.22 μ_B)² / (0.248 nm)³ = 2.77×10⁻²⁴ J = 0.201 K | research/how-magnets-work/verify.mjs | check-formula: recomputed 2.7707e-24 J, 0.2007 K with r = 0.248246 nm.
- CONFIRMED | T_Curie / T_dipole = 1043 K / 0.201 K ≈ 5,197× | research/how-magnets-work/verify.mjs | check-ratio: recomputed 5197.26 (1043/0.201 by hand is 5189; the printed 5,197 uses the unrounded 0.20068 K).
- MINOR | recomputed live, every constant from CODATA. | public/strata/how-magnets-work/index.html | recomputed-live: the page's only script runs the Ising grid and the frame toggle; nothing on the page computes U_dipole, 0.201 K or 5,197 (the frame readout hard-codes "1.07851×10⁻⁴ N"). The figures are computed offline by research/how-magnets-work/verify.mjs. Not a later loss: the first commit of the page, 84cdc05472a (2026-06-25), has the same sentence and no computation either. The physical constants are CODATA 2018 (true). Triage (rule 3): an overclaim about the page's own checking, which the line classes MINOR; fixed.
- CONFIRMED | CODATA 2018: μ₀, ε₀, μ_B, k_B, c. | https://web.archive.org/web/2021id_/https://physics.nist.gov/cuu/Constants/Table/allascii.txt | codata-2018-values: header "2018 CODATA adjustment"; "Bohr magneton 9.274 010 0783 e-24", "vacuum mag. permeability 1.256 637 062 12 e-6", "Boltzmann constant 1.380 649 e-23 (exact)", "speed of light in vacuum 299 792 458 (exact)" all equal verify.mjs; ε₀ is not read from CODATA by verify.mjs (see the added line on check 7).
- CONFIRMED | The energy that actually does the aligning is of order k_B·T_Curie ≈ 0.09 eV | research/how-magnets-work/verify.mjs | energy-0.09eV: prints "J ≈ kB·T_Curie = 8.988e-2 eV"; recomputed 0.089879 eV.
- CONFIRMED | The energy that actually does the aligning is of order k_B·T_Curie ≈ 0.09 eV | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | exchange-j-kittel: Kittel "the observed Curie temperature corresponds to J = 11.9 meV" is the pair exchange integral (S = 1); summed over iron's 8 nearest neighbours, zJS² = 8 x 11.9 meV = 95 meV, so "of order 0.09 eV" per atom holds.
- CONFIRMED | an electron-volt-scale energy. That is the energy scale of electrostatics, not magnetism. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | electron-volt-scale-electrostatics: Kittel ch. 3 "not because there are strong magnetic dipole forces between the spins, but because the Pauli principle modifies the distribution of charge... This spin-dependent coulomb energy is called the exchange interaction" supports the origin, not a scale; on scale, 0.09 eV is a tenth of an eV, 5,200x the dipolar 1.7e-5 eV and below the bare Coulomb energy of two electrons 0.248 nm apart (5.8 eV, recomputed): loose wording, not false.
- CONFIRMED | The real glue is the exchange interaction, and it is a piece of sleight-of-hand by quantum mechanics. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | real-glue-exchange: Kittel "The exchange field gives an approximate representation of the quantum-mechanical exchange interaction"; Wikipedia Exchange interaction: "The exchange interaction is the main physical effect responsible for ferromagnetism, and has no classical analogue."
- CONFIRMED | Electrons are identical fermions: the Pauli exclusion principle forbids two with the same spin from being in the same place. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | pauli-fermions: "the Pauli principle excludes two electrons of the same spin from being at the same place at the same time"; Wikipedia Exchange interaction "Since electrons have spin 1/2, they are fermions."
- CONFIRMED | Same-spin electrons therefore stay further apart, which lowers their electrostatic (Coulomb) repulsion energy. | https://en.wikipedia.org/wiki/Exchange_interaction | same-spin-lowers-coulomb: "which other electrons with the same spin tend to avoid due to the Pauli exclusion principle. This decreases the energy associated with the Coulomb interactions between the electrons with same spin."
- CONFIRMED | In iron, aligning the spins is the cheaper arrangement, so the spins align. | https://en.wikipedia.org/wiki/Exchange_interaction | aligning-cheaper-iron: "the effect tends to align the spins"; iron's being ferromagnetic (Kittel Table 1) is the iron-specific half.
- CONFIRMED | the force that makes iron magnetic is the electric repulsion between electrons, refereed by a quantum rule about identity. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | punchline-electric-repulsion: "Thus the electrostatic energy of a system will depend on the relative orientation of the spins: the difference in energy defines the exchange energy."
- MINOR | No magnetic force enters anywhere. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | no-magnetic-force-enters: true of the aligning mechanism (Kittel's footnote: the exchange field "is not really a magnetic field and therefore does not enter into the Maxwell equations"), but "anywhere" is too strong: Kittel, Origin of Domains, "domain structure is a natural consequence of the various contributions to the energy (exchange, anisotropy, and magnetic) of a ferromagnetic body", and the domains are the ones Drill 1 shows the reader.
- CONFIRMED | The magnetic force is what the electric force looks like when you're moving. | https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity | magnetic-force-is-electric-in-motion: Feynman as quoted there, "One part of the force between moving charges we call the magnetic force. It is really one aspect of an electrical effect." True for a force on a moving charge; its extension to magnets is the added MINOR line below.
- CONFIRMED | Einstein's 1905 relativity paper was titled On the Electrodynamics of Moving Bodies | https://api.crossref.org/works/10.1002/andp.19053221004 | einstein-title: "Zur Elektrodynamik bewegter Körper", Annalen der Physik 322, 891-921, 1905; the English title is the standard translation.
- CONFIRMED | for exactly this reason. | https://www.fourmilab.ch/etexts/einstein/specrel/www/ | einstein-title-reason: the paper opens on exactly this frame-dependence: "if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field... But if the magnet is stationary and the conductor in motion, no electric field arises". Nothing records why the title was chosen, but the title names the paper's subject and that is its opening problem.
- CONFIRMED | The wire is electrically neutral: equal + and −, no net charge, no electric field. | research/how-magnets-work/verify.mjs | wire-neutral: the model's premise ("wire, neutral in the lab", ions +λ0, electrons −λ0), the standard Purcell setup; an Illinois physics Q&A (https://van.physics.illinois.edu/ask/listing/2358) uses the same premise.
- CONFIRMED | so relativistic length contraction packs them by different amounts. | https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity | contraction-different-amounts: "The Feynman Lectures on Physics (vol. 2, ch. 13–6) uses this method to derive the magnetic force on charge in parallel motion next to a current-carrying wire"; recomputed: ions γ(0.30c) = 1.0483, electrons γ(0.1136c)/γ(0.40c) = 0.9225.
- CONFIRMED | and the once-neutral wire now carries a net charge. | research/how-magnets-work/verify.mjs | net-charge-in-charge-frame: prints "net linear density λ' = 1.257942e-7 C/m"; recomputed 1.2579418e-7.
- CONFIRMED | LAB: F_magnetic = q·u·B = 1.07851×10⁻⁴ N (wire neutral, current 119.9 A) | research/how-magnets-work/verify.mjs | lab-force: prints "I = 1.199e+2 A ... F_magnetic = 1.078506e-4 N"; recomputed I = 119.917 A, F = 1.0785062e-4 N.
- CONFIRMED | CHARGE: the wire's net density becomes 1.258×10⁻⁷ C/m → an electric force that, transformed back to the lab, is 1.07851×10⁻⁴ N | research/how-magnets-work/verify.mjs | charge-frame-force: prints "back in lab: 1.078506e-4 N"; recomputed 1.0785062e-4 N; this sentence correctly says "transformed back to the lab" (the readout in the added WRONG line does not).
- CONFIRMED | Equal to machine precision. | research/how-magnets-work/verify.mjs | machine-precision: the assertion's tolerance is 1e-12, but the actual relative difference is 1.26e-15 (recomputed), a few units of double precision, so the words hold.
- CONFIRMED | The hinge that makes the two stories one is the identity μ₀·ε₀ = 1/c² | https://en.wikipedia.org/wiki/Vacuum_permeability | mu0-eps0-hinge: "c² = 1/(μ0 ε0). This relation can be derived using Maxwell's equations"; CODATA 2018 values satisfy it to 4.3e-14 relative (recomputed).
- CONFIRMED | the magnetic constant and the electric constant are the same constant, wearing the speed of light. | https://en.wikipedia.org/wiki/Vacuum_permeability | constants-same-constant: the relation fixes either one from the other and c; "the same constant" is a gloss of that, not a false statement.
- CONFIRMED | Speeds idealised to 0.40c and 0.30c so the contraction is visible; the agreement is exact at every speed. | research/how-magnets-work/verify.mjs | speeds-idealised: v = 0.40c, u = 0.30c in verify.mjs; the frame-switch result is analytically exact (Purcell & Morin §5.9); rerun numerically at (0.01c, 0.02c), (0.1c, 0.9c), (0.9c, 0.5c), (0.99c, 0.99c), (0.4c, -0.3c): relative differences 4.9e-13 or smaller (below about 1e-3 c double-precision cancellation swamps a numerical test, a limit of the arithmetic, not the physics). The drawing is a separate added line.
- CONFIRMED | These bottom out in quantum field theory, in mathematics that doesn't translate into anything you've ever held. | https://en.wikipedia.org/wiki/Exchange_interaction | questions-bottom-out-qft: "The spin–statistics theorem of quantum field theory demands that all particles with half-integer spin behave as fermions"; Wikipedia Spin (physics) treats electron spin through Dirac's relativistic electron and Pauli's "classically non-describable two-valuedness".
- CONFIRMED | Richard Feynman, asked the plain question "why do magnets repel," refused to fake the floor: | https://www.greaterwrong.com/posts/W9rJv26sxs4g2B9bL/transcript-richard-feynman-on-why-questions | feynman-asked-why: the interviewer asks "what is it, the feeling between those two magnets?" and "why are they doing that, or how are they doing that?"; Feynman restates it himself: "when you're asked, for example, why two magnets repel". The quoted words are a paraphrase, but a faithful one.
- CONFIRMED | "I really can't do a good job, any job, of explaining magnetic force in terms of something else you're more familiar with, because I don't understand it in terms of anything else that you're more familiar with." | https://www.greaterwrong.com/posts/W9rJv26sxs4g2B9bL/transcript-richard-feynman-on-why-questions | feynman-quote: word for word, "But I really can’t do a good job, any job, of explaining magnetic force in terms of something else you’re more familiar with, because I don’t understand it in terms of anything else that you’re more familiar with." (fan transcript of the BBC clip; Wikiquote does not carry it).
- CONFIRMED | Richard Feynman, BBC Fun to Imagine, 1983 | https://www.sciencealert.com/watch-richard-feynman-on-why-he-can-t-tell-you-how-magnets-work | feynman-bbc-1983: "Filmed as part of the 1983 TV program Fun to Imagine"; Wikipedia Richard Feynman lists "Fun to Imagine Collection, BBC Archive of six short films ... (1983)".
- UNVERIFIABLE | You now know more about a fridge magnet than almost any account online will tell you | a comparative over all accounts online: no survey exists to check it against | most-truthful: not a checkable claim about a source; the drill-3 part of what the reader "knows" is the added MINOR line below.
- MINOR | Recomputed live & offline by research/how-magnets-work/verify.mjs (7/7 pass) | public/strata/how-magnets-work/index.html | apparatus-verify-77: same defect as recomputed-live: verify.mjs runs offline and the page computes none of the listed figures, so "live" is false; the 7/7 is true (recreated: node verify.mjs, 7 passed, 0 failed). Triage (rule 3): an overclaim about the page's own checking, which the line classes MINOR; fixed.
- CONFIRMED | Onsager's exact Tc = 2.2692; the dipole energy 0.201 K and the 5,197× shortfall vs iron's 1043 K Curie point; the lab/charge-frame force agreement to machine precision. | research/how-magnets-work/verify.mjs | apparatus-numbers: sections (1) to (3) compute each, all recomputed independently above.
- CONFIRMED | the spin grid is the two-dimensional Ising model | public/strata/how-magnets-work/index.html | apparatus-2d-grid: N = 120 square grid, four neighbours, periodic, Metropolis with dE = 2*s*(sum) and exp(-dE/temp), so T is in units of J/kB as the slider label says.
- CONFIRMED | the 2D value is what the live grid actually simulates, and it is exact for that model. | public/strata/how-magnets-work/index.html | apparatus-2d-exact-for-model: exact for the 2D Ising model in the large-grid limit; the page's rule run headless orders at T 2.2 (0.79, Onsager's 0.79) and disorders at 2.35 (0.21) and 2.6 (0.03), so the finite 120 x 120 grid switches where the label flips, within finite-size rounding.
- CONFIRMED | real iron is 3D with a different exact-less Tc | https://en.wikipedia.org/wiki/Ising_model | apparatus-3d: "Many theoreticians searched for an analytical three-dimensional solution for many decades... Such a solution has not been found until now".
- CONFIRMED | The relativity demo uses a single drifting electron line at relativistic speed; | research/how-magnets-work/verify.mjs | apparatus-single-line: "const v = 0.40 * c; // electron drift (idealised)", one ion line and one electron line.
- CONFIRMED | real drift is millimetres per second | https://en.wikipedia.org/wiki/Drift_velocity | apparatus-real-drift: "The drift speed of electrons is generally in the order of 10−3 meters per second" (its own worked example gives 2.3e-5 m/s for 1 A in a 2 mm wire, so "millimetres or less").
- CONFIRMED | yet the same effect produces the full magnetic force because the charge density is astronomically large. | https://en.wikipedia.org/wiki/Drift_velocity | apparatus-density-astronomical: "Copper has one free electron per atom, so n is equal to 8.5×10^28 electrons per cubic metre".
- CONFIRMED | The exchange-interaction account is the standard qualitative one (Heisenberg 1928); | https://api.crossref.org/works/10.1007/BF01328601 | apparatus-heisenberg: "Zur Theorie des Ferromagnetismus", Heisenberg, Zeitschrift für Physik 49, 619-636, issued 1928-09; Kittel calls U = -2J Si·Sj "the Heisenberg model".
- CONFIRMED | the sign of exchange is what makes iron a ferromagnet rather than an antiferromagnet, and that sign is material-specific. | https://en.wikipedia.org/wiki/Exchange_interaction | apparatus-sign-of-exchange: "If J_ab is negative, the interaction favors electrons with antiparallel spins, potentially causing antiferromagnetism."
- CONFIRMED | C. Kittel, Introduction to Solid State Physics: Curie temperatures; iron's 2.22 μ_B moment; the dipolar-vs-exchange argument. | https://archive.org/download/81060415-introduction-to-solid-state-physics-8th-edition-by-charles-kittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel_djvu.txt | ref-kittel-contents: all three in ch. 12 of the 8th edition: Table 1; "The exchange field in iron is very much stronger than the real magnetic field due to the other magnetic ions in the crystal" (p. 324).
- UNVERIFIABLE | S. Blundell, Magnetism in Condensed Matter: the order-of-magnitude case that dipolar coupling cannot explain ferromagnetism. | tried: Crossref 10.1093/oso/9780198505921.001.0001 (book confirmed, OUP 2001); a library table of contents (https://find.library.upatras.gr/Record/138802/TOC) shows "4. Interactions 4.1. Magnetic dipolar interaction 4.2. Exchange interaction"; Internet Archive has no copy (positive control: the same search finds Blundell's other titles); Google Books API over quota; one WebSearch for the argument's wording found no text | ref-blundell: the book exists and has the right section; its words were not read.
- CONFIRMED | E. M. Purcell & D. J. Morin, Electricity and Magnetism, 3rd ed., §5.9: the magnetic force on a charge by a wire derived as length-contraction electrostatics. | https://assets.cambridge.org/97811070/14022/frontmatter/9781107014022_frontmatter.pdf | ref-purcell-morin: the publisher's contents for the Third Edition list chapter 5 "The fields of moving charges" with "5.9 Interaction between a moving charge and other moving charges 259"; Crossref 10.1017/CBO9781139012973 has edition 3, 2013. Section title matches; its text was not read.
- UNVERIFIABLE | see also The Feynman Lectures on Physics, Vol. II: "magnetism is relativity." | tried: feynmanlectures.caltech.edu/II_13.html (403 to curl with browser headers and to WebFetch); Wayback CDX returns no snapshot; Internet Archive copies of FLP are borrow-only or metadata-only; two WebSearches for the exact phrase with and without "Feynman" found no source attributing it to the Lectures (positive control: the same searches found descriptions of FLP II 13-6 and Wikipedia's citation of it) | ref-feynman-lectures-quote: presented in quotation marks as the Lectures' words; no instance found.
- CONFIRMED | R. P. Feynman, BBC Fun to Imagine (1983); | https://en.wikipedia.org/wiki/Richard_Feynman | ref-feynman-bbc: "Richard Feynman: Fun to Imagine Collection, BBC Archive of six short films... (1983)".
- CONFIRMED | the magnetic dipole–dipole coupling between two iron atoms works out to 0.20 K, some 5,197× too weak to explain iron's 1043 K Curie point | research/how-magnets-work/verify.mjs | md-dipole-0.20K: recomputed 0.2007 K and 5197.
- OBSERVED | This layer's check works the answer out again from scratch, independently of this page. | git show ca0306b7ff:research/verifier-independence/census-pairs.tsv | check-independent: row 438 "how-magnets-work research/how-magnets-work/verify.mjs C0 ... touches nothing that /strata/how-magnets-work/ ships"; the file has no imports and reads nothing.
- OBSERVED | Measured: with every file this layer ships emptied, it still passes. | git show ca0306b7ff:research/verifier-independence/depends-2.json | check-emptied-passes: records[50] slug how-magnets-work, tier C0, exitCode 0, depends false; also recreated: the downloaded verify.mjs alone in an empty directory exits 0.
- OBSERVED | Last verified 25 June 2026, when it was written. | git show ca0306b7ff:memory/log.d/2026-06-25T0515Z-how-magnets-work.md | check-last-verified: "verifier research/how-magnets-work/verify.mjs (7/7 pass)", entry dated 2026-06-25; first commit 84cdc05472a is 2026-06-25.
- OBSERVED | It is published, and it runs on its own: one file, and Node. | recreated: curl -sS -o verify.mjs https://artwaste.land/checks/research/how-magnets-work/verify.mjs and node verify.mjs in an empty directory | check-one-file-node: HTTP 200, 7130 bytes, identical to the repository file, exit 0, "7 passed, 0 failed".
- CONFIRMED | the number proving magnetism is 5,000× too weak to be its own glue | research/how-magnets-work/verify.mjs | md-dek-5000: 5,197 to one significant figure; consistent with the body's 5,200 and 5,197.
- CONFIRMED | A live spin grid that switches a magnet on and off at Onsager's exact critical point | public/strata/how-magnets-work/index.html | md-live-switch: the label flips at TC = 2/Math.log(1+Math.SQRT2) and the simulated grid orders and disorders there (headless run above).
- CONFIRMED | Purcell's frame-switch: the magnetic force on a charge by a neutral current-carrying wire equals, to machine precision, the purely electric force that appears in the charge's own frame from relativistic length contraction | research/how-magnets-work/verify.mjs | md-purcell-frame: section (3), relative difference 1.26e-15 once the charge-frame force is transformed back to the lab.
- CONFIRMED | Then it stops at the wall Feynman refused to fake (BBC Fun to Imagine, 1983). | https://www.sciencealert.com/watch-richard-feynman-on-why-he-can-t-tell-you-how-magnets-work | md-feynman-bbc-1983: "Filmed as part of the 1983 TV program Fun to Imagine".
- OBSERVED | Every number recomputed offline by research/how-magnets-work/verify.mjs (7/7 checks pass). | recreated: node research/how-magnets-work/verify.mjs at ca0306b7ff | md-7of7: 7 passed, 0 failed; the numbers in that markdown paragraph (2.2692, 0.20 K, 5,197, 1043 K as input, the force equality, μ₀ε₀) are all in its output. The body is not rendered.
- CONFIRMED | there, 'cold' is a rate, not a temperature | src/content/strata/metal-colder-than-wood.md | relates-metal-colder: dek "Your fingers can't measure temperature at all; they measure heat leaving the skin, and report that as 'cold.'"; the same note's "here" half is in the added MINOR line.
- CONFIRMED | Both end at an honest wall: a true thing you can operate right up to the point where the explanation genuinely runs out, and then says so instead of faking the floor. | public/strata/before-you-looked/index.html | relates-before-you-looked: that page ends on "So something has to give. The standard menu of survivors (none of them comfortable, none of them ruled out by current experiment)... The point of the portal isn't to choose."
- MINOR | (added) the third time the thing holding your fridge magnet up turns out not to be magnetism at all; and the magnetic force you feel is electricity seen sideways | https://en.wikipedia.org/wiki/Magnetism | The frame-switch the page demonstrates is about a force on a moving charge from a current. A fridge magnet's field and the steel it grips are electron spins, and Wikipedia lists those as a separate root: "Magnetism, at its root, arises from: Electric current; Spin magnetic moments of elementary particles; Changing electric fields"; Electron magnetic moment: "The spin magnetic moment is intrinsic for an electron." Between magnets at rest E = 0, and B² − E²/c² "does not change from one frame of reference to another" (https://en.wikipedia.org/wiki/Electromagnetic_tensor), so no frame turns that field into a purely electric one. The demonstration does not reach the fridge magnet the sentence names. Copies: index.html:110-111, :237, the Nearby note at :305 ("here, the force holding a fridge magnet up isn't magnetism"), the meta description :13 and JSON-LD :36, and src/content/strata/how-magnets-work.md:4 (dek) and :11 (relates note).
- WRONG | (added) Charge’s frame: wire looks charged, force is electric (same 1.07851×10⁻⁴ N) | research/how-magnets-work/verify.mjs | The readout shown on "Ride with the charge" (index.html:453) gives the lab-frame figure as the force in the charge's frame. The page's own check prints "CHARGE FRAME: F_electric' = 1.130582e-4 N → back in lab: 1.078506e-4 N"; a transverse force is γ(u) = 1.048 times larger in the charge's frame (recomputed 1.1305817e-4 N). The body text gets it right ("transformed back to the lab"); the readout does not. An Illinois physics Q&A makes the general point: "ALL forces change in different reference frames" (https://van.physics.illinois.edu/ask/listing/2358).
- MINOR | (added) the tipping point sits at Tc = 2/ln(1+√2) = 2.2692…, the marked line above. | public/strata/how-magnets-work/index.html | No line is marked: the slider (index.html:126, range 0.6 to 3.6) has no tick, and the CSS draws none; the only marker is the text "critical point: Tc = 2.2692" (line 130). A reader looks for a line that is not there.
- MINOR | (added) Speeds idealised to 0.40c and 0.30c so the contraction is visible | public/strata/how-magnets-work/index.html | The canvas the reader watches (index.html:425-426) draws ion spacing 44 to 34 px and electron spacing 44 to 54 px; at 0.40c and 0.30c the real factors (recomputed 1.0483 and 0.9225) give 42.0 px and 47.7 px, so the drawing exaggerates the contraction about sixfold. The code says "schematic, exaggerated for visibility" in a comment the reader never sees.
- MINOR | (added) 7/7 pass, with the check "μ0·ε0 = 1/c² (the identity that fuses E and B)", constants from "CODATA 2018: μ₀, ε₀, μ_B, k_B, c." | research/how-magnets-work/verify.mjs | verify.mjs:68 sets "const eps0 = 1 / (mu0 * c * c);" and :106 then checks mu0*eps0 against 1/c², which cannot fail. The identity is true of the real CODATA 2018 ε₀ (8.854 187 8128 e-12, recomputed agreement 4.3e-14), so nothing printed is false, but one of the seven passes is a check that cannot fail and ε₀ never comes from CODATA.
- CONFIRMED | (added) The Ising model permits a conventional ordered phase in two dimensions (Nearby layers note on this page, "When Pairs Let Go") | https://en.wikipedia.org/wiki/Ising_model | Wikipedia sections "No phase transition in one dimension" and "Phase transition and exact solution in two dimensions"; the headless run of this page's grid orders at T below 2.269.
## Findings
- [fixed] WRONG (added) charge-frame readout: index.html script, setFrame(), gave the force in the charge's frame as "(same 1.07851×10⁻⁴ N)". verify.mjs prints "CHARGE FRAME: F_electric' = 1.130582e-4 N → back in lab: 1.078506e-4 N". Now "(1.13058×10⁻⁴ N in this frame, the same 1.07851×10⁻⁴ N back in the lab)"; Corrected 2026-10-18 line added to the page's new Corrections note and mirrored in the markdown body; JSON-LD dateModified 2026-10-18.
- [fixed] MINOR recomputed-live: index.html check box "recomputed live, every constant from CODATA" now "computed offline by the published check, every constant from CODATA 2018". Nothing on the page computes the figure; verify.mjs does.
- [fixed] MINOR apparatus-verify-77: "Recomputed live & offline by" now "Recomputed offline by"; 7/7 still holds.
- [fixed] MINOR gd-hand: "it stops being a fridge magnet in your warm hand" now "a cooled piece sticks to a magnet and lets go once your warm hand takes it past 19 °C" (Curie point 292 K, Kittel Table 1).
- [fixed] MINOR no-magnetic-force-enters: "No magnetic force enters anywhere." now "No magnetic force enters the aligning." (Kittel counts magnetic energy among the contributions that make domains.)
- [fixed] MINOR (added) fridge-magnet overreach: the frame-switch shows the force a current puts on a moving charge, not a permanent magnet's spin field (E = 0 between magnets at rest and B² − E²/c² is invariant). Scoped every copy: page dek ("what holds your fridge magnet together turns out to rest on electricity"), meta description, og and twitter descriptions, JSON-LD description ("a current's magnetic force"), the Drill 3 lead-in ("a current still pushes a passing charge sideways"), the summary at the wall ("the magnetic force a current puts on a moving charge is electricity seen sideways", plus one sentence that a fridge magnet's own field comes mostly from electron spin; "mostly" because iron's small orbital moment is not spin), the markdown dek and body, the relates note and its Nearby copy ("the force that lines up a magnet's spins isn't magnetism"), and the verifier's heading and comment.
- [fixed] MINOR (added) "the marked line above": no line is drawn; now "the critical point marked above" (the "critical point: Tc = 2.2692" label).
- [fixed] MINOR (added) contraction drawing: the caption now adds "and the drawing exaggerates it further" (canvas spacings 34 and 54 px against the true 42.0 and 47.7 px).
- [fixed] MINOR (added) circular ε₀ check: verify.mjs now takes ε₀ = 8.8541878128e-12 F/m (CODATA 2018) for the μ₀ε₀ = 1/c² assertion, tolerance 1e-9 (CODATA's relative uncertainty is 1.5e-10); a value off by 1.4e-9 fails it. The force computation keeps the derived ε₀ so its machine-precision agreement is unchanged. Published copy at public/checks/research/how-magnets-work/verify.mjs updated byte-identical.