Predictions

This page carries six numbered entries, and they are not all the same thing. Two are falsifiable predictions — #5 and #6, the open 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. The distinction is kept explicit because counting six would overstate what is actually at risk. Every value on this page is read directly from the 3D Simulation  using objective measurement functions, not derived from theoretical assumptions (Analysis & Export Tools describes how measurements are taken).

This page establishes:

• #1 is a consequence, not a discriminator: the elements turn where polynomials keep going, in agreement with Laskar, separating only from truncated convenience fits that nobody defends outside their stated range — 1.
• #2 has no observation able to test it yet: the ~100-kyr LOD modulation, against satellite records spanning 50 years; the stack’s century-scale trough (2,205 AD) lies ~180 years ahead — 2.
• #3 is withdrawn by its own pre-registered test (T7) and kept as the record — 3.
• #4 is withdrawn: the lunar-precession track it tested rode a day-length counter the model no longer carries — 4.
• #5 and #6 are the falsifiable predictions: the obliquity band on the precession–s₃ beat, and the deglacial spin-up leading the interglacial optimum — Deep-time predictions.
• The observation that tests each — Verification pathways.

Validated retrodictions are catalogued in Supporting Evidence: the Devonian day count, the Cheng cross-proxy fit (the former Roche-limit genesis claim is withdrawn — Expanding Resonance §3). Resolved questions live on their subject pages — Mercury’s anomaly → General Relativity at Mercury Precession, the Jupiter/Saturn window trends at Supporting Evidence §9.

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; half a perihelion-of-date cycle after the 1246.03 AD alignment with the December solstice, perihelion sits at the June solstice), and the analemma changes shape — width with eccentricity, length with obliquity (22.08°–24.45°).

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 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 the clock T_p(t) — the axial-precession period was ~21,235 yr at the Devonian and rises to ~28,315 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.

Two timescales coexist. At geological timescales (Myr+) the model agrees with standard tidal evolution — LOD monotonically increases per ESSRT Driver 1 (Earth-Moon tidal evolution), the same mechanism standard theory invokes. See Expanding Resonance for the deep-time layer. On top of that monotonic tidal drift, the refined α(t) coupling to the Climate Formula’s L1 orbital layer adds a ~250 ms peak-to-peak Milankovitch oscillation at ~100 kyr timescales — visible as wiggles on the tidal trend, matching known glacial-interglacial cycles. Standard theory’s polynomial extrapolation doesn’t model this Milankovitch oscillation; the model adds it as a specific physical prediction. The disagreement is therefore about the superimposed climate-cycle structure — not about the monotonic deep-time trend.

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 26-event eclipse alignment audit, on documented solar eclipses spanning -762 BCE to 2026 CE. The framework’s umbra reaches the observation site within the ±4-hour scan window on 21 of 26 events, and 5 of those 26 are pure geographic misses.
• The higher-resolution lunar timing test, on 267 primary-source observations. Mean |residual| is 20.2 min, matching NASA within 15 s and beating NASA on 117 of 267 events.
• An out-of-sample comparison against the Bond 2001 IRD drift-ice record, at Pearson r = +0.41 in the 4,000 BC – 1,800 AD window. This is an open correspondence that fails its null tests, and the two eclipse tracks do not depend on it.

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. 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 the withdrawn extrapolation of entry 3). 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 2013  (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. Entries 2 and 3 are the same physical mechanism viewed through two observables (LOD vs δ¹⁸O) — neither counts as a falsifiable prediction: #2 has no observation able to test it, and #3 is withdrawn. See Lunar Eclipse Validation §4 for the derivation.

The same coupling appears 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. The figure overlays the LR04 record itself for direct comparison — inverted δ¹⁸O, the very dataset the L1 layer is fitted against. 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 lands 8.5 kyr later than the ~50 kyr the natural-forcing estimates above cluster on; the wider 50–100 kyr spread in that table comes from CO₂ scenarios rather than from orbital forcing. No observation adjudicates between them — a glaciation date is right or wrong only when it arrives — and none of this is evidence for the formula, which the T7 test withdrew above. 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. The 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”. 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 on a day-length counter — WITHDRAWN

Withdrawn. The track tied the Moon’s apsidal and nodal periods to a day-length counter the model no longer carries, and it held only on that counter’s own definition, not in the Moon’s dynamics — see Earth’s Clock.

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|). Here ψ̇(t) is the composed lunisolar rate — Earth’s spin from the recession history, carrying both torques, with 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). Meanwhile 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 are degenerate at 41.1 vs 41.1 kyr, which is why both have always fit. (That simpler reading is pure precession-scaling.) But they diverge into the Precambrian: at 1.4 Ga 19.1 vs 23.9 kyr, and at 2.46 Ga 14.3 vs 18.9 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.

The prediction is the band — its period and amplitude — and deliberately not the obliquity’s value at a deep epoch: measured on the model’s own integration, the value is linearly sensitive at 450″ per one part in a million of the precession constant at 100 Ma, and the GIA channel’s ice-free baseline is known to the 10⁻⁴ class, so the value beyond ~20 Myr is the integration on its inputs (Obliquity).

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, because the GIA rate term tracks the melting rate. α follows ice volume — more ice means mantle displaced equatorward, so a larger α — which makes dα/dt ∝ d(ice)/dt, so melting drives α down. The rate minimum therefore marks maximum melting speed, and peak interglacial warmth follows ~5–10 kyr later, when melting completes. The derivative leads the integral: LR04’s warm peaks sit at ~121,000 BC and the Holocene plateau. 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

Most predictions on this page can be verified directly using the formulas at Formulas.

← Supporting Evidence