Abstract

Simulation results here are held-out climate-model evidence (E2-SIM), PB-1's selection is observed-validation evidence (E3-VAL), and the final result is the project's pristine sealed-test evidence (E4a-TEST). We test whether supervised forecast-task pretraining on CMIP6 historical simulations can overcome the observed transfer gap documented in Report 3. Eleven CMIP6 source models train a coefficient-native persistence-residual Earthformer on the exact 12-to-14-month forecast task (21,505 balanced windows); three whole source models (GFDL-ESM4, MCM-UA-1-0, MRI-ESM2-0) are held out for all checkpoint selection. Exact-continuation training to 30k steps (v1$\to$v2$\to$v3) shows an early held-out primary peak, late selector divergence, and broad late held-out overfit — grounds to stop simulation training. The predeclared PB-1 consultation then compares two transfers of the selected v3 backbone against the fixed V6 reference under the frozen Phase A protocol: the features-only zero-output transfer wins with the project's first resolvable observed primary improvement (Niño-3.4 correlation delta $+0.489$, 90% CI $[+0.256,+0.857]$; validation RMSE $0.5407$, ACC $+0.3579$, Niño-3.4 correlation $+0.6157$). After Phases C and D were evaluated and rejected on validation, a written protocol froze PB-1 as the single final model and authorized exactly one hash-gated evaluation of the sealed 2016–2020 split. That evaluation returned pooled field RMSE $0.5406$ versus persistence $0.6591$ and zero anomaly $0.6200$ (paired delta $-0.1185$, 90% CI $[-0.1561,-0.0858]$); $35/35$ windows beating persistence and $14/14$ leads beating zero; field ACC $+0.2553$; Niño-3.4 correlation $+0.3432$; and amplitude ratios $0.408/0.398/0.411$ — confirmed pattern and phase skill with persistent amplitude damping.

Study ID R4 / Phase B. Incoming state: the frozen Phase A transfer protocol and the V6 reference from Report 3. Changed factor: supervised forecast-task exposure at simulation scale. Evidence tiers: E2-SIM pretraining and budget study; E3-VAL predeclared transfer consultation; E4a-TEST final result. Outgoing baseline: immutable PB-1 (checkpoint SHA-256 c6b49723…) for Reports 5–8. Timeline note: reading order is thematic — the Phase C and Phase D studies of Reports 5–6 were executed after PB-1 selection but before this report's test section, and Phase E onward came after it. Phase B itself spans 2026-07-03 to 2026-07-05; the test read is 2026-07-06.

Report 3 ended with a measured negative: masked reconstruction, even with regional auxiliaries, improved representation diagnostics without improving forecasts. The natural alternative inverts the pretext: train on the target task itself — 12 months in, 14 months out, persistence-residual, same loss — using the only source of abundant tropical-Pacific trajectories available: coupled climate simulations. The sim-to-real hypothesis is that model trajectories, despite simulation bias, teach forecastable ENSO evolution, provided checkpoint selection stays on held-out source models and the observed transfer is governed as tightly as Phase A prescribed. Precedent exists at the index level [1] and for medium-range fields [2]; the contribution here is the field-level, coefficient-native instance with explicit statistical governance and a sealed confirmatory endpoint.

Climate-simulation pretraining entered ENSO deep learning with [1], which trained a CNN on CMIP historical simulations and SODA-era reanalysis before fine-tuning; [2] showed the same lever for gridded medium-range prediction; and transformer-based Earth system models routinely assume large training corpora [3]. Three practices distinguish this study. Source-model holdout: selection uses whole held-out models — generalization across model physics, not across windows of one model. Exact continuation: v1$\to$v2$\to$v3 resume model, optimizer, sampler position, and RNG state bit-exactly, making the 10k/20k/30k budget study a single controlled trajectory. Residual initialization and sealed evaluation: the zero-output transfer preserves exact persistence at step 0 on observations, and the endpoint is a one-shot, hash-gated test governed by a frozen written protocol [5]. The study is a task-alignment and evidence-governance experiment, not a comprehensive ENSO benchmark.

Observed: $24\times48$ tropical Pacific ($30^{\circ}$S–$30^{\circ}$N, $120^{\circ}$E–$280^{\circ}$E); 12 context / 14 target months; train 1981–2010; validation 2011–2015 (35 windows); sealed test 2016–2020 (35 windows); cosine-weighted Niño-3.4 box, leads-3–14 summary; persistence and zero-anomaly baselines. CMIP uses analogous geometry but realization-local detrending, climatology, and normalization; simulation scores are therefore not absolute counterparts of ERA5 scores, and the CMIP selector's Niño-3.4 correlation (flattening windows and leads) is not numerically identical to the observed D4 statistic.

Discovery against the public Pangeo CMIP6 catalog (CMIP/historical/Omon/tos/r1i1p1f1) on 2026-07-03 returned 57 candidate datasets across 50 source models; metadata inspection rejected curvilinear and unstructured grids, incomplete 1850–2014 coverage, and unit problems, leaving 14 complete rectilinear stores [4]. Each realization is processed independently: longitude normalization; selection of $30^{\circ}$S–$30^{\circ}$N, $120^{\circ}$E–$280^{\circ}$E with an interpolation halo; regrid to $24\times48$; Celsius conversion; cell-wise linear detrending fit over 1850–2014 with calendar-month fixed effects, applied before climatology; subtraction of a 1900–1999 realization-local monthly climatology; three-level DTCWT packing; and store-local per-channel normalization. Every store spans 1,980 months with coefficient geometry $[1980,24,48,37]$, carries allowed_use: pretrain_forecast and simulation_calendar: true, and is rejected by observed supervised loaders. Training balances windows by source_id (equal 1,955-window quotas), giving 21,505 train and 5,865 held-out windows.

Eleven source models train: CESM2, CESM2-FV2, CESM2-WACCM, CESM2-WACCM-FV2, E3SM-1-0, E3SM-1-1, E3SM-1-1-ECA, GFDL-CM4, GISS-E2-1-G, GISS-E2-1-G-CC, GISS-E2-1-H. Three are held out whole: GFDL-ESM4, MCM-UA-1-0, and MRI-ESM2-0 — MRI and MCM are family-unique in the compatible set, and GFDL supplies a third institution (its relation to GFDL-CM4 is the documented compromise required for a three-model holdout). Whole-source holdout matters because windows within one realization are highly dependent; aggregation weights models equally so no source dominates silently. All Phase B checkpoint decisions use these three models only, consuming zero observed-validation consultations (Table 1).

Role	Source models (historical r1i1p1f1, one per source)	Windows
Training (11)	CESM2, CESM2-FV2, CESM2-WACCM, CESM2-WACCM-FV2; E3SM-1-0, E3SM-1-1, E3SM-1-1-ECA; GFDL-CM4; GISS-E2-1-G, GISS-E2-1-G-CC, GISS-E2-1-H	21,505
Held out (3)	GFDL-ESM4 (shares an institution with GFDL-CM4 — the documented compromise); MCM-UA-1-0 and MRI-ESM2-0 (family-unique)	5,865

The model, target, and loss are exactly Report 2's supervised configuration — coefficient-native Earthformer $[12,24,48,37]\to[14,24,48,37]$, persistence-residual target, unweighted residual_skill_v0 — with one difference declared in advance: all 166 optimizable tensors train in simulation (pretraining does not authorize observed full-backbone unfreezing; the observed transfer retains the frozen Phase A boundary). AdamW at $10^{-4}$, batch 1, balanced source sampling. Stage continuations resume last.pt exactly — model, optimizer, deterministic sampler position, and Python/NumPy/CPU/CUDA RNG state — so v1 (0–10k), v2 (10k–20k), and v3 (20k–30k) form one uninterrupted optimization trajectory with recorded stage hashes.

A six-train/two-holdout real pilot (1,000 CUDA steps) validated ingestion, dataset, shape, and checkpoint paths (selected checkpoint held-out Niño-3.4 correlation $0.509$). The expanded v1 trained 10,000 steps on the 11/3 split: selected step 5,000 with aggregate coefficient RMSE $1.1739$, field RMSE $0.6579$, field ACC $0.2730$, Niño-3.4 correlation $0.5644$ — against held-out persistence field RMSE $0.7418$ (correlation $0.3183$) and zero-anomaly $0.6364$. Variability ratios $0.828/0.771/0.742$: simulation training preserves far more amplitude than any observed fine-tune of Reports 2–3.

V2 selected stage step 1,000 (global 11,000): Niño-3.4 correlation $0.5854$ ($+0.0211$ over v1), field RMSE $0.6442$ ($-0.0137$), ACC $0.2965$ ($+0.0236$), variability $0.829/0.838/0.816$. The primary then oscillated, ending at $0.5728$ at global 20,000 — an early-peak/late-regression warning, but not broad degradation (end-stage RMSE and ACC improved).

V3 retained global step 21,000 (SHA-256 2247c1f9…): Niño-3.4 correlation $0.5835$ ($-0.0019$ vs v2 — the primary has stopped improving), coefficient RMSE $1.1112$, field RMSE $0.6214$ (crossing below the zero baseline by $0.0149$ for the first time), ACC $0.3015$, but variability ratios worsened to $0.765/0.777/0.752$. Selector divergence appeared: the composite-loss and field-RMSE selectors both chose global 24,000 (RMSE $0.6187$, correlation $0.5720$), while the global-30,000 endpoint's primary fell to $0.5355$ — broad late held-out overfit relative to the early peak (Fig. 1). Per-model v3 primaries: GFDL-ESM4 $0.574$, MCM-UA-1-0 $0.465$, MRI-ESM2-0 $0.668$. Decision: stop simulation training; proceed to the predeclared observed consultation from the v3 selected state.

The consultation was predeclared in the ledger before any candidate ran: two transfers of v3's selected backbone against the fixed V6 pretrained reference, both under the frozen Phase A protocol (decoder_last_block, $10^{-4}/5\times10^{-6}$, epoch cadence, unweighted loss, guarded selection). The candidates differ only in residual-head handling: head-preserving (none: the pretrained residual head transfers, so no step-zero persistence equivalence, recorded as not applicable) and features-only (zero_output: the residual head is re-zeroed, exact persistence at step 0). Adoption rule: primary CI $>0$ with delta $\ge +0.02$, no resolvable pooled-RMSE regression $\ge +0.005\,{}^{\circ}\mathrm{C}$, no resolvable mean-window-ACC regression $\le -0.01$; branches for unresolved and resolvably-worse outcomes were declared with it. Bootstrap: paired moving blocks of 6, 10,000 resamples, 90%, seed 20260703.

Both 1,000-step CUDA fine-tunes completed; for the first time the selection metric did not saturate at the first epoch boundary (zero_output peaked at step 670; none improved through step 1,000). Selected zero_output validation: RMSE $0.540731$, mean field ACC $+0.357874$, Niño-3.4 correlation $+0.615723$. Paired against V6: primary $\mathbf{+0.488977}$, CI $[+0.256068,+0.857422]$ — the first resolvable observed primary improvement in the project record; RMSE $-0.002497$ $[-0.020406,+0.012208]$ unresolved; mean-window ACC $+0.041523$ $[+0.009528,+0.087033]$ resolvably better (Fig. 2). The none candidate also passed the rule (primary $+0.313891$ $[+0.136393,+0.749443]$) but is dominated on primary and both guards. Declared diagnostics: the full-field amplitude ratio resolvably decreased ($-0.1009$) while the Niño-3.4 ratio resolvably increased ($+0.1090$); the 2015 case remained worse than persistence ($0.7922$ vs $0.7420$, case-study-only). Decision: adopt the features-only transfer as PB-1 (best_skill.pt, step 670, SHA-256 c6b49723…); the second Phase B consultation was not consumed.

Between PB-1's adoption and the test read, two further phases ran to completion on validation and were rejected: Phase C (OHC300 input; Report 5) and Phase D (per-coefficient Gaussian heads; Report 6, first half). Both consumed their predeclared consultations; PB-1 remained the single surviving model. On 2026-07-06 — before any 2016–2020 month was materialized — the final protocol was frozen in writing: exactly one evaluation of exactly one model (PB-1, named by full checkpoint SHA-256), plus persistence and zero-anomaly baselines (which consume no budget); the complete metric list with bootstrap settings; the rule that everything is reported favorable or not and that no test number ever selects, tunes, or gates anything; and a recorded honest expectation (“comparable modest skill”). The evaluator itself is fail-closed: it refuses to materialize test months unless the protocol file exists and its declared SHA-256 matches the checkpoint under evaluation.

The single authorized evaluation ran on 2026-07-06 (35 windows):

Metric (2016–2020, 35 windows)	PB-1	Persistence	Zero anomaly
Pooled field RMSE (${}^{\circ}\mathrm{C}$)	0.5406	0.6591	0.6200
Paired $\Delta$ vs persistence	$-0.1185$, 90% CI $[-0.1561,-0.0858]$ (resolvable)
Windows beating persistence	35 / 35	—	—
Leads beating zero anomaly	14 / 14	—	—
Mean field ACC	$\mathbf{+0.2553}$	$+0.2292$	undefined
Niño-3.4 correlation, leads 3–14	$\mathbf{+0.3432}$	$-0.015$	undefined
Amplitude ratios (full/eq/Niño-3.4)	0.408/0.398/0.411	$\approx1$	0

Leadwise structure appears in Fig. 3: PB-1 trails persistence only at lead 1 (where persistence is nearly perfect by construction), beats it at every later lead, and holds positive Niño-3.4 correlation through lead 14.

The positive field ACC and Niño-3.4 correlation are what make Table 2 more than a climatology-like win: Report 2 documented models that beat both baselines on RMSE with zero pattern correlation, and PB-1 is not that. Simultaneously, the amplitude ratios ($\approx0.41$) record the persistent damping the deterministic frame imposes — the exact limitation the probabilistic program (Reports 6–8) subsequently attacks. Event-specific test behavior is reported descriptively only, and nothing in the test result was used to select or tune anything afterward.

The three evidence blocks are kept separate. E2-SIM: v1/v2/v3 selected rows (field RMSE $0.6579/0.6442/0.6214$; Niño-3.4 correlation $0.5644/0.5854/0.5835$; variability $0.83/0.83/0.76$ full-field), with persistence $0.7418$ and zero $0.6364$ on the same holdout. E3-VAL: PB-1 selected validation row (RMSE $0.5407$, ACC $+0.3579$, Niño-3.4 $+0.6157$) with the paired deltas of Fig. 2. E4a-TEST: Table 2, where the CI attaches to RMSE versus persistence only — other test CIs would require documented recomputation from the preserved per-window records. X4: v1 selected 10d8319b…; v2 3c822401…; v3 2247c1f9… (plus guardrail 36550518…/a4034ad5…); PB-1 c6b49723…; stage runtimes 4,944/4,767/5,464 s; exact 177-state reloads at every stage; test_data_read: false in every artifact before the authorized read.

Why did supervised task alignment transfer where reconstruction did not? The pretraining gradient now points at the downstream object itself — the conditional distribution of a 14-month future given a 12-month past — so the representation is organized around forecastable evolution rather than interpolation. Simulation scale (21,505 windows versus 335) provides the event diversity the observed record cannot.

Why did features-only transfer dominate head preservation? The pretrained residual head encodes CMIP-calibrated correction magnitudes in store-local normalized units; zeroing it lets observed fine-tuning rebuild the output map from exact persistence while keeping the pretrained features — initialization bias where it helps, none where it binds.

Why did simulation selectors diverge late? Long training overfits the held-out models unevenly across metrics: coefficient/field losses keep improving while the cross-window index correlation — the quantity closest to the observed primary — peaks early. Treating the primary's early peak as the selection signal, with RMSE/ACC as guards, is what the frozen policy prescribed, and the observed transfer result vindicates it.

What does the sealed test establish? That the core hypothesis — forecasting complete complex-wavelet coefficient maps with an Earthformer backbone yields real tropical-Pacific SST skill — holds on truly sealed data, with effect size comparable to its validation estimate (RMSE $0.5407$ validation vs $0.5406$ test against a harder persistence baseline).

Climate-model dependence and shared CMIP biases; only three held-out source models (one sharing an institution with a training model); simulation metrics aggregated differently from observed metrics (flattened correlation; realization-local normalization); ERA5 as the observational target rather than independent in-situ products; a modest baseline suite; persistent amplitude damping; a single five-year test period; and no authorization to reuse the test result for later probabilistic selection. A separately predeclared bounded amendment was later exercised once by G2-long (Report 8); it did not alter PB-1's result and fully spent the split.

Supervised CMIP6 forecast-task pretraining produced the project's strongest pristine sealed result: resolvable held-out field skill with positive pattern and phase correlation, from a training recipe whose every selection decision is documented and whose test access was governed by a written one-shot gate. PB-1 is hereafter immutable — the SST-only deterministic mean reference for every subsequent report. Two questions leave this report open: whether subsurface predictors can add transferable information (Report 5, answered in the negative), and whether the damped amplitude can be cured probabilistically (Reports 6–8). Neither question carries test authority; Report 8 documents the separate second and final amended consultation.