v3 Global CREST Parameters — 0.1°, daily, satellite-native

v3: satellite-native global parameters, honestly measured

100% satellite inputs: IMERG V07 P, ERA5-lapse T → Snow-17/Oudin, 22 global covariates, SoilGrids priors. No rain gauges anywhere in the chain.

The training network — now 8,460 basins with the monsoon anchor

Asia goes from empty to anchored: the zero-shot number quantifies the risk the confidence layer predicted; the in-training run will price what one monsoon observation network is worth. Remaining gaps: China, SE Asia, Central Asia, interior Africa.

Holdout KGE, station by station — v3 best

Every dot is a blind prediction (station never in training, window never trained). Large = GRDC yardstick (410; med +0.514; 92% >0, 76% >0.3, 51% >0.5); small = expansion-network holdout (749; med +0.568). The red pockets are physically coherent — arid US Southwest, interior Spain, semi-arid NE Brazil, Western Australia: the dry-regime mode shared by every global model, not random scatter.

The ladder — every step paired, multi-seed

0.343 (v1) → 0.405 → 0.445 → 0.484 → 0.514 (v3). Beyond 480 iters train fit keeps climbing (0.61→0.68) while ungauged stays flat — pure memorization, documented and stopped.

Why IMERG-native is an argued design, not a compromise

The gauge premium exists only where gauges exist — precisely not the deployment target of a global ungauged product. MSWEP twin (0.605) bounds it; Africa flips its sign. Model structure is also not the bottleneck: CREST ≈ HBV dead tie on the identical harness, both objectives × both forcings.

Budyko lets ungauged continents train the model — ET cannot

The law it traces: gain ∝ how badly transfer breaks the water balance — large where β collapses (SA/AF), zero-to-negative where transfer is already water-tight (EU). Placebo controls: a shuffled curve helps nowhere (levels must be right); a global-constant target ties Budyko in mesic SA but is catastrophic in arid AF (−0.31, β>2) — the curve's aridity structure is load-bearing exactly at climate extremes. Satellite-ET supervision: −0.075 (refuted). Monsoon India: the curve itself errs (seasonality) — its known boundary.

The boundary condition: an observation-free, low-dimensional axiom (long-term Budyko water balance) transfers safely to unanchored regions; a high-dimensional dynamic observation with its own errors (satellite monthly ET) corrupts them — its bias gets absorbed wholesale where no discharge anchors the balance. Ablation-clean (prior-reg zero, adaptive weighting negative), monotone dose–response, two continents. In-distribution price −0.01…−0.02 → two fields.

Leave-continent-out map: risk is regime novelty, not distance

CNN head off-continent: −0.49 (spatial texture is a fingerprint that does not transfer) → dual-head rule: CNN where trained, MLP + hardened field where not. Asia is assigned SA-class risk and shipped as labeled extrapolation.

Head-to-head with δHBV2-Globe at 116 common stations

Audited (units forced to m³/s→mm/day; per-station auto-detection bug fixed): at the only symmetric protocol — stations ungauged for BOTH models — we lead, not significantly. Their advantage concentrates entirely at their own training sites. β 0.958 vs 0.988, both unbiased. Their validation excludes Africa and their "Asia" is essentially Japan+Korea; ours keeps Africa and South America with an 8-yr gate — the other end of the coverage-vs-completeness trade-off.

Two fields + a confidence layer

Field	yardstick KGE	use where
A · yardstick-optimal	0.514	gauged continents
B · Budyko-hardened	0.490	data-sparse regions (LRO +0.05…+0.09)

Per-cell confidence = 3-seed dispersion × covariate coverage × continent LRO prior. Blind-flood vignettes: Brazil 33k km² peak +1%; South Africa 221 km² flash flood timing exact.

Physics vs. a pure LSTM under the identical harness

Mechanism, measured: the LSTM's transfer deficit is not timing (r identical to dPL, p=0.25) but variability inflation (α median 1.82; 69% of its error budget). Controlling for the LSTM's own water-balance error, every other predictor - aridity, snow, area, and covariate novelty - loses significance; where the LSTM's β lands in [0.8,1.25] (31% of stations) the two are statistically tied. Physics buys failure avoidance, not a higher ceiling.

An accurate obs-free anchor - the law itself is not the active ingredient

Where must physics live? Loss < architecture < full structure

Three closed verdicts. (1) The in-distribution cost of architectural conservation (-0.11) is capacity-independent (32/64/128 cells: 0.42/0.42/0.42) - an intrinsic tax, not a size problem. (2) Conservation's marginal value decays monotonically with how water-anchored the target region already is, and turns negative in arid intermittent regimes - in both directions of failure. (3) Stacking a Budyko loss anchor on top of the conserving architecture adds nothing abroad (0.29 vs 0.30/0.34) and hurts at home (-0.06): constraint gain = min(channel unanchoredness, reach) - anchor error.

Honesty list and what comes next