Measured by the lab
100.143
Two coils that never touch, wound on one iron core: does the transformer equation V₂/V₁ = N₂/N₁ — plus everything a real transformer does (current stepping down as voltage steps up, power conservation, regulation under load, total deafness to DC, and the n² transmission-loss payoff that decided the War of the Currents) — emerge from nothing but flux-linkage magnetostatics, Faraday's law and Kirchhoff's loop rules integrated in time? And is the pre-1831 view — that a steady current should induce a steady current next door — actually false?
Units: dimensionless — the nameplate turns ratio N₂/N₁ of the 4 kV→400 kV grid step-up unit (V₂/V₁ = N₂/N₁, Faraday's law applied twice to one shared flux)
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Transformer: no-oracle → validated + honest module — Faraday's 1831 induction ring weighed on a simulated bench: with NOTHING coded but turn-counting magnetostatics (L = N²P, M = kN₁N₂P — Hopkinson), Faraday's EMF = −dλ/dt and Kirchhoff's two loop equations under RK4 (no V₂/V₁ = N₂/N₁, no phasors, no reflected impedance anywhere in the recovery), the lock-in terminal ratio of a real 4 kV→400 kV grid unit returns 99.9937 vs nameplate 100 (rel −6.3e-5 = the coded leakage k−1 plus the R₂ winding drop, both disclosed; vs the exact steady state of the SAME coded circuit the floor is 1.5e-10), the turns LAW lands slopes +1.000000/−1.000000 over ×16 in N₂ and ×4 in N₁, the ratio is frequency-flat (8e-7 over 25–400 Hz) and drive-flat (6e-14 over ×100), the rated 1 MW operating point grows the full transformer anatomy unprompted (0.387% regulation, I₂/I₁ = N₁/N₂ to 5.3e-5 — the k again, 99.38% efficiency with the power audit P_in = P_load + I²R closing to 5.1e-7, and R = 0 ⇒ P_out = P_in to 5.0e-7 — no free lunch), DC transforms NOTHING (a 246 kV edge pulse decays to 4.1e-6 of the AC amplitude: dΦ/dt = 0), Faraday's own pre-1831 steady-conduction rival V₂ = c·I₁ is rejected ×5.9e7 at DC and misses 25 Hz by 37% where the measured ratio moves < 8e-7, and a 3-loop grid chain MEASURES the War-of-the-Currents payoff: line loss 38.4% → 0.0062% (÷6219) while delivering 2.57× more power; module honesty debt retired — the on-screen 'recovery' was v2True = ratio·V1 (the law under test coded as the generator), now the identical ODE pipeline, pinned float-exact by gate N (screen 100.3 = this seed's disclosed ±2% read)
The generator is the raw coupled-coil circuit: λ₁ = L₁I₁ + MI₂ and λ₂ = MI₁ + L₂I₂ with L₁ = N₁²P, L₂ = N₂²P, M = kN₁N₂P (a current I through N turns drives ampere-turns NI through the core permeance P and each of the N turns links the flux — turn-counting is where N² comes from), closed by Vs = R₁I₁ + dλ₁/dt and 0 = (R₂+R_L)I₂ + dλ₂/dt, integrated by fixed-step RK4. Non-circularity is structural: the transformer equation, phasor algebra, reflected impedance, regulation and power-invariance formulas appear nowhere in the dynamics; the steps-per-cycle is the unit combination max(400, ceil(T·p_fast/0.8)) built from the circuit's own leakage pole p_fast = (R₂+R_L)/(σL₂) + R₁/(σL₁) (a stability scale, the rlc/emwave dt pattern); and every recovered number is a lock-in or mean-power measurement of the integrated currents. Real bench: a grid step-up unit — N₁ = 100, N₂ = 10000, P = 2 mH/turn² (silicon-steel core), k = 0.99995 (3.9% per-unit leakage), R₁/R₂ = 0.31% per-unit copper, 4 kV rms 50 Hz — measured at the standard 0.4%-load turns-ratio test and at the rated 1 MW point; the N-sweeps run per-unit-matched (R₂ = (N₂/N₁)²R₁, R_L = (N₂/N₁)²·4 kΩ) so the k-sag is common-mode and only the law moves the slope. The exact phasor steady state of the same coded circuit is computed ONLY to score (gate B), proving the −6.3e-5 nameplate gap is device physics, not integration error. 24 seeds re-read the ratio-test lock-in with ±2% uniform noise (the module's disclosed instrument class). 14 gates in scripts/transformer-derisk.mjs (~1.9 s); tamper ⇒ exit 1. ?world=transformer.
0.26
0.0198
The ideal-transformer relations V₂/V₁ = N₂/N₁ and I₂/I₁ = N₁/N₂ with V₁I₁ = V₂I₂ (Feynman II ch. 16 & 22; Griffiths §7.2.4), voltage regulation from leakage reactance + winding resistance, and the n² transmission-loss law behind AC power distribution — all from Faraday's 1831 induction-ring discovery (Phil. Trans. R. Soc. 122, 125 (1832), §1–59). Non-circular: N₁, N₂, P, k, R enter ONLY as the bench's parts list through turn-counting magnetostatics; the recovery path contains no turns-ratio formula, no phasors, no Lorentzian-equivalents — the ratio is read as lock-in |V₂|/|V₁| of RK4-integrated currents, the law is confirmed as measured log-log slopes ±1.000000, and the closed-form steady state appears only in scoring (gate B) to prove the nameplate gap is coded device physics (k, R₂ — each decomposed and matched to ~1e-6). The em.generator world proved a spinning loop MAKES the grid's AC; this world proves why that AC then wins: the same Faraday law, applied twice to a shared flux, moves power across 100× voltage steps at 99.4% efficiency and cuts line loss ÷6219 — measured, not asserted. The decisive discriminator is structural: the steady-conduction rival predicts a 135 MV DC secondary and frequency tracking; the sim measures 2.3 V and a million-fold-flat ratio.
The module's real-units panel was the dishonest piece — worse than rlc's: _recover() literally coded v2True = (N₂/N₁)·V₁, i.e. the law under test WAS the generator, then 'recovered' the ratio from its own assumption; the transmission payoff was the closed-form (P/V)²R arithmetic. THIS RUN REPLACED BOTH: the module now integrates the identical first-principles pipeline as the oracle (coupled-coil RK4 ratio test at the 0.4% load, 8+4 cycles → lock-in terminal ratio → one ±2% uniform read via its own mulberry32(0x713A); 3-loop grid-chain integration for the loss fractions), and gate N replays that pipeline verbatim, pinning the on-screen numbers float-exact: screen V₂ = 401.1 kV, recovered ratio 100.3 (+0.29% vs 100 — this seed's disclosed single ±2% draw, ~0.25 SE of the instrument class, not a bias: the 24-read mean sits 0.55 SE from known), chain loss 38.4% → 0.0062% (÷6219), line current 154 → 2.5 A — verified live headless (vite preview + playwright panel scrape, worktree-local). The dimensionless live view (glowing core, V₂ = 2·V₁ trace at the drawn 6:12 ratio) remains an explicitly disclosed forward-model display; every number in the '—— real grid transformer (live ODE) ——' block comes from the integrated circuit.
Rung climbed: no-oracle → validated + honest module (56 → 57 oracles). Tolerances from measured floors, never padded: nameplate 2e-4 vs measured −6.25e-5 (decomposed: k −5.0e-5 + R₂/R_L 1.25e-5); phasor/convergence 1e-8 vs 1.5e-10 floors (headroom = cross-platform libm scatter over 2.5M-step sums); freq spread 2e-6 vs the REAL 7.96e-7 (400 Hz leakage quadrature (X_σ/R_L)²/2 = 7.9e-7 — physics, not noise); linearity 1e-10 vs 6.3e-14; current ratio 1e-4 vs 5.3e-5 (k-dominated, disclosed); mc gates 3.5·SE / 8e-3 / 2.5e-2 vs measured 0.55 SE / 1.4e-3 / 1.98e-2. ONE science-fix attempt used (gate D): the first N-sweep bench held R₂ = 500 Ω fixed while the load scaled, so small-N₂ points carried a 5% winding drop (slope 1.0157) — fixed by per-unit-matching the bench (R₂ = (N₂/N₁)²R₁, R_L = (N₂/N₁)²·4 kΩ; a device wound for another voltage class keeps its per-unit copper), after which the slopes landed +1.000000/−1.000000. Zero tolerance edits. DESIGN LESSON (new): when sweeping a construction parameter of a DEVICE, sweep the whole device per-unit — holding an absolute non-ideality fixed while the impedance base moves injects a fake power law (the 5%-drop end dominates the slope). Tamper (known → 90): gates A/M/N fail, exit 1, recovery unchanged at 99.9937; restored by hand. Scope: scripts/oracles/transformer.reference.json + scripts/transformer-derisk.mjs (new), src/modules/TransformerModule.ts (recovery honesty), data/findings/transformer.json, fragment, loop-runs line — all world transformer; no shared files touched. Gates run: build + smoke + derisk (module touched, no shared files).
npm run derisk -- transformer (scripts/transformer-derisk.mjs)scripts/oracles/transformer.reference.jsonM. Faraday, 'Experimental Researches in Electricity', Phil. Trans. R. Soc. 122, 125 (1832), §1–59 (the 1831 induction ring — two coils on one iron ring, the first transformer). K. Zipernowsky, O. Bláthy, M. Déri (1885), the closed-core AC transformer; W. Stanley (1886), Great Barrington. D. J. Griffiths, Introduction to Electrodynamics (4th ed.), §7.2.4; R. P. Feynman, The Feynman Lectures on Physics, Vol. II, ch. 16 & 22. The 'War of the Currents' / Niagara AC plant (1895): I²R line loss falls as 1/V² at fixed delivered power.