Instance #20 — Younger Dryas paleoclimate (Layer-C primitive)
Datasets: NGRIP δ¹⁸O 50-yr resolution (Andersen et al. 2004, 4918 pts), GISP2 reconstructed temperature (Alley 2000, 1632 pts), GRIP δ¹⁸O (Johnsen et al., 5425 pts) — three independent Greenland ice cores.
Sign-aligned cross-shadow median β trajectory:
| Window | β | Sign agreement |
|---|---|---|
| pre-YD | −0.46 | 3/3 unanimous negative |
| onset | +0.09 | 2/3 positive sign-flip |
| YD-active | −0.05 | — |
| termination | −0.27 | 3/3 unanimous |
| post-YD | −0.27 | — |
Layer-C primitive identified: brake-p magnitude σ_cross stays 0.3–1.8 across windows (precision-floor-bound). δ¹⁸O log-range is narrow even at paleoclimate scale, so Theorem 3 still binds. The cross-shadow SIGN-of-β primitive carries the regime-change signal where magnitude does not. This is a third framework primitive, distinct from Layer-A (β magnitude) and Layer-B (direction-and-rate-sign of dΦ/dt).
Honest correction (numerical-tools update): PELT recovers YD onset within ±450 yr and termination within ±400 yr in all 3 cores without being told. Sign-flip lands AT or slightly AFTER YD onset (Δ = −299 yr), NOT strictly before. Verdict downgraded from Outcome A (precursor) to B+ (at-onset).
Instance #21 — Heinrich events cross-proxy
Datasets: NGRIP δ¹⁸O, NGRIP Ca²⁺ (Rasmussen et al. 2008, H1–H3), DSDP609 IRD lithics (Bond et al. 1992), Hulu Cave δ¹⁸O (Wang et al. 2001), Botuverá Cave δ¹⁸O. Five proxies × six events.
Class split:
- Greenland atmosphere shadows (NGRIP δ¹⁸O, Ca²⁺): σ_event = 0.16 / 0.026 — single-class across H1–H6 in the high-latitude atmosphere.
- Tropical/marine shadows (DSDP609, Hulu, Botuverá): σ_event = 0.53 / 0.75 / 0.75 — events differ event-by-event.
Tropical/Greenland σ_event ratio = 3.83×. Framework reads the high-latitude AMOC-coupled cascade as one Heinrich class across H1–H6; tropical/marine cascades carry event-specific information. Supports the Hemming 2004 / Rohling et al. 2017 heterogeneous-trigger picture.
PELT independently rediscovers H1–H6 ages within ±1.5 kyr (NGRIP) / ±1–3 kyr (DSDP609) without imported event dates.
Instance #22 — Mid-Pleistocene Transition (resonance shift)
Datasets: LR04 benthic δ¹⁸O stack, ODP 1123, ODP 982 — three benthic δ¹⁸O records spanning ~5 Ma.
Outcome B (resonance shift): brake-p R² = 0.03–0.05 in every (record, sub-window) — Law V fires, brake does not cleanly apply. Spectral primitive cleanly confirms 41 kyr → 100 kyr periodicity shift (cross-shadow median dom_period: 41.7 → 42.1 → 109.3 kyr).
The framework reads MPT as a resonance reorganisation, not a cascade-class change. Dominant frequency reorganised from obliquity (41 kyr) to eccentricity-modulated (100 kyr), but the brake-rate scaling did not. Theorem 13 anchor: excluding frequency-reparametrisation from the spectral primitive's gauge group is what preserves the 41-kyr-vs-100-kyr distinction.
PELT independently rediscovers MPT date — 2/3 records inside literature 700–1200 kyr band (ODP1123 at 932 kyr, ODP982 at 972 kyr); mean of in-band hits = 952 kyr, matching canonical ~900 kyr to ±50 kyr without imported regime windows.