Predictions

This page carries six numbered entries, and they are not all the same thing. Three are falsifiable predictions — #4, #5 and #6, the deep-time ones — each differing from the standard reading by a measurable amount at a dated epoch and naming the observation that would end it. Of the rest: #3 is withdrawn by its own pre-registered test and kept as the record; #1 is a consequence, not a discriminator (it agrees with Laskar and separates only from truncated convenience fits, which nobody defends outside their stated range); and #2 has no observation able to test it yet — satellite records span ~50 years against a ~100-kyr band. The distinction is kept explicit because counting six would overstate what is actually at risk. The former Planet Nine and KBO-obliquity items rested on the retired eccentricity-amplitude relation and are withdrawn with it. Validated retrodictions (the Earth-Moon genesis at the Roche limit, the Devonian day count, the Cheng cross-proxy fit) are catalogued in Supporting Evidence; resolved questions (Mercury’s anomaly → General Relativity, the Jupiter/Saturn window trends) live on their subject pages — Mercury Precession and Supporting Evidence §9 — and earlier versions of this page remain available in the project’s git history.

Medium- and long-term predictions (centuries to millennia)

1. The elements turn where standard polynomials keep going

Every orbital element the model bounds reverses — reaches a minimum (or maximum) and comes back — where the standard polynomial extrapolations continue monotonically past their fit windows. One claim, one table:

The model agrees with the standard curves throughout the fitted windows (obliquity through ~13,700 AD, perihelion through ~3000 AD); the discriminator is always what happens next. Two visible consequences ride along: the Gregorian calendar drifts against the real solar year (June solstice on June 17 by 6486 AD; by ~11,725 AD perihelion sits at the June solstice), and the analemma changes shape — width with eccentricity, length with obliquity (22.21°–24.72°).

The same turning read off the sky. Each panel is the Sun’s position at a fixed clock time through one year of its epoch; the perihelion marker walks once around the figure-eight as the perihelion-of-date completes its circuit, starting from the 1246.03 AD perihelion–solstice alignment the anchor was fitted on. The equation-of-time envelope narrows as eccentricity falls. Anyone can check a panel against their own epoch’s almanac.

At geological timescales the means themselves drift with H(t) — the axial-precession period was ~21,699 yr at the Devonian and rises to ~28,208 yr at +200 Myr (~6 yr per Myr today, in principle observable in high-precision IAU precession-rate series over decades). Framework: Expanding Resonance.

2. Earth rotation / LOD / Delta-T

Standard theory: Earth’s rotation is monotonically slowing due to tidal friction. The empirical Stephenson polynomial encodes a Munk-MacDonald-scale (~5-6 ms/cy) non-tidal Earth-rotation speedup component on top, attributing the apparent gap to glacial isostatic adjustment + core-mantle coupling. The model predicts LOD monotonically increases under Driver 1 (Earth-Moon tidal recession) at a modern rate of ~1.7 ms/century, with a ~250 ms peak-to-peak Milankovitch oscillation superimposed from the refined α(t) coupling to the Climate Formula’s L1 orbital layer (see below). Short-term fluctuations (like the 2020–present speedup) sit on top of this trend. Both sidereal day and stellar day follow the same tidal-recession + Milankovitch pattern.

The model’s ΔT formula has been tested against the historical record on two independent eclipse tracks, with a third, weaker comparison against a paleoclimate proxy: (a) a 26-event eclipse alignment audit on documented solar eclipses spanning -762 BCE to 2026 CE (21/26 events with framework umbra reaching the observation site within the ±4-hour scan window; 5/26 pure geographic misses); (b) the higher-resolution lunar timing test on 267 primary-source observations (20.2-min mean |residual|, matching NASA within 12 s and beating NASA on 121/267 events); and (c) an out-of-sample comparison against the Bond 2001 IRD drift-ice record at Pearson r = +0.43 in the 4,000 BC – 1,800 AD window — an open correspondence that fails its null tests, and which the two eclipse tracks do not depend on. The full Munk-MacDonald postulate (~5-6 ms/cy) is rejected by the historical record; a smooth GIA-scale channel (dLOD/dt = -0.35 ms/cy at J2000, Cox & Chao 2002 satellite anchor with Peltier ICE-6G factor-2.0) is included via the L1-orbital-coupled α(t) correction, and an era-localized fractional non-tidal channel (~0.5 ms/cy window-average) is carried by the Core-mantle swing — see Lunar Eclipse Validation §1 for the quantitative statement and §6 for the three-component decomposition of the medieval residual. Canonical: Timekeeping; empirical validation: Solar Eclipse Validation and Lunar Eclipse Validation.

LOD is coupled to the same orbital forcing that drives climate. The L1-orbital-coupled α(t) correction above uses the same L1 orbital layer that fits the LR04 δ¹⁸O record in the Climate Formula — one mechanism, two observables. Ice sheets grow and retreat under Milankovitch orbital forcing on ~100 kyr timescales; that ice-mass redistribution modulates Earth’s polar moment α on the same timescale; and α modulates LOD. The model predicts that length-of-day carries a ~250 ms peak-to-peak Milankovitch oscillation in phase with the glacial cycle, superimposed on the smooth tidal-recession trend. LOD peaks (α max) fall at glacial extrema — MIS 6 (~140 ka BP), MIS 2 / LGM (~22 ka BP), and the projected next-glacial (~60,500 AD, matching Prediction 3) — and LOD troughs (α min) fall at interglacial extrema — MIS 7e (~215 ka BP), MIS 5e Eemian (~125 ka BP), and today’s Holocene. The underlying “ice → J₂ → α → LOD” mechanism is confirmed on decadal timescales by Cheng, Tapley & Ries 2011  (LAGEOS satellite J₂ shifting from linear GIA-driven decrease to acceleration around 1998, attributed to polar ice-mass loss). The 100-kyr extrapolation follows from the same physics but is not yet directly observable — modern satellite records span only ~50 years. The unifying claim: planetary gravity, climate, and Earth’s rotation are one system, connected by ice mass as the mediator. Predictions 2 and 3 are the same physical mechanism viewed through two observables (LOD vs δ¹⁸O). See Lunar Eclipse Validation §4 for the derivation.

The same coupling in the rate domain: over the last two glacial cycles the Tidal + GIA baseline rides above the tidal line through ice-sheet growth and dips sharply at the two deglaciations — with the LR04 record itself (inverted δ¹⁸O, the very dataset the L1 layer is fitted against) overlaid for direct comparison. The deepest negative-rate excursions land at Termination II (→ Eemian) and Termination I (→ Holocene).

Climate prediction

3. Next natural glaciation peak at ~60,500 AD — WITHDRAWN as a prediction (T7)

The canonical 3-layer Climate Formula extrapolated forward from t ≈ 2000 AD identified the following glacial maxima and interglacial peaks:

The signal C(t) is the normalised δ¹⁸O proxy from the post-MPT regime fit (negative = warmer/interglacial; positive = colder/glacial). The Holocene is correctly identified as interglacial; MIS 6 is placed within ~2 kyr; the LGM is predicted within ~9 kyr (the expected ice-sheet response lag).

Comparison with established forecasts:

The extrapolated ~58.5 kyr (~60,500 AD) figure sits in the consensus range and matches Berger & Loutre 2002 within ~16%. What distinguishes it is the mechanism: standard frameworks attribute the 100-kyr cycle to direct eccentricity forcing; the formula carries the band as the planets’ eccentricity beats read from the model’s own modes (94.9 / 98.8 / 110.0 kyr), not Earth’s own apsidal cycle. Full comparison and mechanistic distinction: Climate Formula.

The pacing departs from the post-MPT 100-kyr regime: two strong glaciations at ~58.5 kyr and ~196.5 kyr from now (138 kyr apart, not the regular ~100-kyr drumbeat), with mostly weak intermediate wiggles. The L1 orbital component is a sum of the engine’s beat lines at fixed periods (a property of the L1 fit — see Climate Formula) and within that stated precision matches the late-Pliocene “41-kyr world” 8H ago. Physical interpretation and three climate-response scenarios: Climate Formula §Pacing shift.

Deep-time predictions

These predictions extend the model’s testable claims across geological time. They follow from the proper-physics two-layer LOD formula (Driver 1 — Earth-Moon tidal evolution) combined with the adiabatic invariant a × M_☉ = const (Driver 2 — solar mass loss). Framework: Expanding Resonance — which also carries the model’s validated deep-time retrodictions (the Earth-Moon genesis at the Roche limit at ~4.5 Ga, the Devonian day count matching Wells 1963, the Cheng cross-proxy fit): those are banked evidence, catalogued in Supporting Evidence, not open predictions.

4. Lunar precession scales as (U/U₀)² on the era-clock counter across geological time

The Lunar Precession Invariant — the Moon’s apsidal period times the era-clock counter U, where U(t) = U₀ · LOD(t)/LOD₀ is the frozen era clock’s named convention (pure spin scaling) — is held at 2,966,728 yr² (year-units, equinox-of-date frame) at every epoch by the (U/U₀)² scaling, with the analogous nodal invariant 6,241,369 yr². The Moon’s apsidal period was ~9.69 yr at the Devonian and ~17.15 yr at −2.5 Gyr (J2000 anchor: 8.848 yr); the nodal period was ~20.38 yr at Devonian (J2000 anchor: 18.613 yr). The squared-counter form matches the leading m² order of Brown’s lunar perturbation theory (the historical Newton–Clairaut problem); the framework anchors the J2000 magnitude from observation and adopts the (U/U₀)² scaling for deep-time evolution, with no polynomial corrections.

Independent deep-time reconstructions of the lunar apsidal period — via spectral analysis of tidal rhythmites, cyclostratigraphic records sensitive to perigean modulation, or future high-precision paleo-tidal sediment studies — should reproduce the U₀²/U(t) track within ~1%. A Phanerozoic apsidal period substantially off this track would falsify the invariant. Full derivation: Expanding Resonance §6: The Lunar Precession Invariant.

5. The deep-time obliquity band follows the beat, not pure precession-scaling

The obliquity cycle is physically the beat of Earth’s spin precession against the strongest nodal mode: period = 2π/(ψ̇(t) − |s₃|), with ψ̇(t) the composed lunisolar rate — Earth’s spin from the recession history carrying both torques, the lunar torque growing as (a₀/a_M)³ (the two-engine table, matched by the Precambrian precession constants at 1.4 and 2.46 Ga) — while s₃ stays at its dynamical value under the measured solar-mass history (μ(2.48 Ga) = 1.00 ± 0.07). Today this beat and the simpler “obliquity period ∝ T_p” reading (pure precession-scaling; historically “H/8 scales with H”) are degenerate — 41.2 vs 41.2 kyr, which is why both have always fit — but they diverge into the Precambrian: at 1.4 Ga 19.1 vs 23.9 kyr, and at 2.46 Ga 15.1 vs 19.8 kyr (roughly a factor two) — a split cyclostratigraphy can resolve. The model pre-registers the beat form (it is what the derived obliquity dynamics produce — Supporting Evidence §15); the existing 1.4/2.46-Ga confirmations constrain the precession/LOD side only, so the deep obliquity period is an open, discriminating test. A precisely dated Precambrian obliquity band at the precession-scaled period rather than the beat period would falsify this form — and vice versa.

6. Deglacial spin-up leads the interglacial optimum

Sustained negative dLOD/dt occurs nowhere in the framework’s 200-kyr record except during the two major deglaciations — GIA-channel rate minima of ~−1.2 ms/cy at ~10,600 BC (Termination I) and ~127,800 BC (Termination II). The mechanism makes this a leading indicator by construction: the GIA rate term tracks the melting rate — α follows ice volume (more ice ⇒ mantle displaced equatorward ⇒ larger α), so dα/dt ∝ d(ice)/dt and melting drives α down — so the rate minimum marks maximum melting speed, and peak interglacial warmth follows ~5–10 kyr later, when melting completes (LR04 warm peaks at ~121,000 BC and the Holocene plateau — the derivative leads the integral). See the 200-kyr chart in Prediction 2 and Timekeeping §When the day got shorter.

Falsifiable test: any eclipse-independent paleo-rotation record should show the spin-up episode preceding the Holocene Climatic Optimum and the Eemian peak by several kyr. A rotation record showing the spin-up concurrent with or after peak warmth would falsify the α(t) coupling’s phase structure.

Scope caveat: causality runs climate → rotation (ice → J₂ → α → LOD); the rotational signature indicates warming already in progress — a leading indicator of peak warmth, not a driver of warming. At millennial scale the stack channel follows the concurrent sign rule on the accumulated offset — warm ↔ Σ_stack > 0, i.e. a longer day — not on its rate; the lagged relationship is specific to the deglacial GIA channel, whose sign is the opposite (see Timekeeping §Two channels).

Verification pathways

The quickest test:

1. BepiColombo (April 2027) — the Mercury consistency check the model shares with General Relativity (resolved to GR), plus the sharper solar-J₂ separation.

← Supporting Evidence