artatopics

Forecasting 251 research fields from planetary positions only. Every test: fit on data ≤1995, graded on 1996–2025 the model never saw, against do-nothing baselines. Scores: 1.0 = perfect, 0 = no better than the field's long-run average. Full code and data: github.com/ArtaQuest/artatopics.

1 · The deployed model — one receiver for all of science

y_field(t) = | b_field + A_field Σ_i a_i · e ^{i(θ_i(t) − p_field,i)} |²

What each symbol is. θ_i(t) is the position of planet i (Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, lunar node) in year t — known centuries ahead, which is the only reason a thirty-year forecast is possible at all. Each planet contributes an arrow rotating in the plane at its own orbital rate. The arrow lengths a_i are global: one spectrum, shared by every one of the 251 fields. A field owns exactly three personal things: a level b (its resting brightness), a gain A (how loudly it hears the shared spectrum), and seven phases p_i — where each planet must stand to push it hardest. The phases are the field's identity — its signs. The predicted share is the squared length of the total arrow: bright when the planets gang up on the field's phases, dim when they cancel.

Why the square matters. Squaring the total arrow expands exactly — not approximately — into a baseline, seven transit terms (2bA·a_i·cos(θ_i−p_i), one planet crossing the field's phase) and twenty-one aspect terms (2A²a_ia_k times the cosine of the pair's separation against the pair's phases). Those are linear in fixed functions of the date, so the model fits by least squares in closed form — no optimiser, no random seed; refit it anywhere and the same numbers come out. The per-field level and gain then solve exactly too: each is the root of a cubic. Two footnotes the fit forced on us, kept in the code: the slowest features barely move inside a 296-year window, so a small ridge (chosen on early origins only) is needed to keep the coefficients identifiable; and scale is each field's own historical level — measured from its data, never fitted.

How it is tested. Fit on everything up to 1995; forecast 1996–2025 blind; score against carrying the field's average forward — and repeat from twelve different cut-off years so no single lucky window decides anything. The same discipline as every number on this page.

The global arrows: mars 0.012 · jupiter 0.017 · saturn 0.035 · uranus 0.080 · neptune 0.050 · pluto 0.048 · node 0.022. Honest comparison: the best per-field model in this repository (each field also fitting its own arrow lengths) scores 0.88 / 0.80 on the same tests, and "carry today forward" scores 0.85 / 0.73 — this model beats carry-forward at the 30-year wall.

The data and the fit

Blue = the field's actual share of each year's citations. Gold = this model: solid where it was fitted (≤1995), dashed where it forecasts. The 8% Artificial Intelligence spike in 1868 is real data but thin evidence — 369 citations existed that year in total — and carries almost no weight in the fit.

Every field, same picture:

2 · The per-field reference model, 30-year forecast

3 · The share of attention across all fields at once

Copying yesterday wins. Fields drift one way (AI grows, old fields shrink); periodic signals cannot encode drift. Verified not to be a training issue: loss, model form, phase count and topic roster all varied — ranking unchanged.

4 · "Will it trend next year?" — one predictor per field, trained by least squares, called at the field's median

Controls: fast planets only → 48% (chance). Slow planets only → 59%. Calendar year alone → 67%, better than the sky. The accuracy is calendar signal carried by the slow planets, not planetary rhythm.

Per-field calls

5 · The competition — four GPU model families vs two do-nothing baselines

The whole campaign was then run as an open benchmark: a public Kaggle dataset, four competing model families trained on separate GPU accounts, scored blind on the ArtaQuest platform. Best selected model: a stack blending a damped trend with the sky receiver above (−2.09); a plain damped trend scores −2.04; every single-family GPU model loses to the baselines. The full board, the era-shift finding behind it, and a lab that rebuilds the winner in your browser (Pyodide): the ensemble stack →

6 · The exact phasor, solved analytically, on the daily record

The model above, |b + Σaᵢe^{i(θᵢ−pᵢ)}|², solved in closed form for b, aᵢ, pᵢ from the sky alone (kerykeion sidereal, cross-checked against three engines) and tested day by day on every arXiv submission since 1991: peak-detection AUC 0.49–0.50 across 127 categories, infeasible in 78% unregularised, and under L2 the inner walls shrink the arrows to nothing in 118 of 127. On the yearly share task the exact form scores −8.25 where the record's √-linear approximation scores −3.58 — the approximation was carrying it. A lab runs the closed-form solve in your browser: the exact phasor →