Shroedinger — gen4

Falsification-grade research program on cross-scale organization of the atmospheric circulation (ERA5 / MERRA-2). This branch supersedes gen1-gen3 and retracts the central empirical claim of the v1 manuscript (the A15 "Lambda_b ~ Pi_b closure"): see docs/RECONCILIATION.md.

What stands (preregistered, held-out, audited)

• Cross-scale envelope-coupling profile P — a regional invariant of the 850 hPa circulation: a season-, year- and ENSO-stable signature (p = 0.001 on held-out samples), beyond the semi-fractal level features and beyond symmetric cross-scale statistics. Its beyond-spectrum component is physical, not cartographic: the equal-km design control (Phase 18) removed the box-geometry confound by construction and the beyond-spectrum residual clustering survived (p = 0.033 anchored / 0.007 raw), lifting the former conditional verdict.

• The estimator is not a re-labelling of the nearest prior art (AUDIT-1, docs/PROTOCOL_AUDIT1_PRIOR_ART_HEADTOHEAD.md). On the same 902 tiles, anchored P vs the Mathis-Hutchins-Marusic amplitude-modulation coefficient: rho = +0.14 (ESTIMATOR_DISTINCT); the AM form carries almost no reproducible tile-level signal (cross-season reliability 0.26 vs P's 0.77) and does not reproduce the map (LOSO R^2 = 0.06). But P vs its Pearson twin: rho = +0.99 — the rank/copula construction is decoration and is dropped from the papers; the nearest prior art for the FORM is the amplitude-amplitude coupling of cross-frequency analysis, cited as such. The attribution is invariant to the estimator convention (R^2 0.536 vs 0.546, identical loadings). AUDIT-2 (docs/PROTOCOL_AUDIT2_INTERMITTENCY_HEADTOHEAD.md) retires the second claimant: P vs the Kolmogorov-Obukhov cascade prediction rho = -0.42 (CASCADE_DISTINCT) — the cascade prediction has no beyond-spectrum component at all (anchored 0.010 vs P's 0.256) — while the local intermittency parameter is a substantial relative (rho = +0.69) that adds +0.21 LOSO R^2 (AUDIT-2b, split-half decontaminated). AUDIT-2b also corrects the map's reliability ceiling: within-season split-half gives R^2 = 0.914, so the Phase-20 attribution explains 59% of the reproducible variance, not 89% — the global map is NOT nearly saturated. AUDIT-3 (docs/PROTOCOL_AUDIT3_SCALE_YEAR_ROBUSTNESS.md, 12 equal-km boxes x 2 windows, bands to 1600 km) reproduces both verdicts off the tile grid (AM +0.39, cascade +0.04, P_lin +0.98) and carries one open item: the tie to the intermittency parameter strengthens with scale (rho = +0.92 at box scale vs +0.69 at tile scale). AUDIT-4 characterises what is left: after the covariates (59% of the reproducible variance) and the intermittency block (83%), the remainder is itself reproducible (split-half r_full = 0.64), not spectral, and geographically organised on monsoon margins, orography flanks and deep-convective cores. Its drivers are named future work; the analysis programme for the papers closes there.

• P has no accessible dynamics of its own (Phases 14, 15, 19). Fast (~10 h), memoryless relaxation to a static regional value; no regime coupling on either grid (the R7/R5 sign split reproduces on equal-km territory); no scale hierarchy of fluctuation timescales (tau flat 9-11 h over 71-1131 km); the derivative-estimator class is invalid by identity. No ENSO modulation at 30x power over 1979-2024, on both carriers (Phases 16, 17, 19C). One open anomaly: a tropical interannual variance excess (F = 1.5-1.8 in R1/R3/R5), carrier-robust, non-ENSO.

• P's geography is attributable (Phase 20, Arm A). As a 144-tile map, out-of-region R^2 = 0.40 (p = 0.001): convective regime lowers P beyond the spectrum (10/12 regions within-region), storm-track activity raises it through the spectrum (11/12); orography acts on the spectral slope, not on P. P and synoptic activity covary at lag 0 with no lead either way (co-emergence, Phase 19C).

• The global map (Phase 20, Arm B). 936 tiles, 60S-60N: maxima on the Southern Ocean ring and the NH storm tracks, minima on the deep convective cores (Amazon, Congo, Maritime Continent); season-stable, consistent with the box-level results (rho = 0.84), attributed at LOSO R^2 = 0.54 (p = 0.001, non-zonal component certified), and effectively one-dimensional (synoptic activity alone = 85% of skill).

• Theory candidate (v1.4): docs/THEORY_CANDIDATE_QUENCHED_TEXTURE.md — quenched-texture organization (P as a functional of the local invariant measure over a quenched constraint field), postulates QT-1..5, evidence map E1-E15, predictions QT-P1..P6. Score after three rounds (Phases 21-23): P2 SUPPORTED (free-running model reproduces the global map at 97% of the resolution ceiling), P3 PASS (k80 = 1), P4 SUPPORTED (the tropical excess is coherent with the IPO), P5 SUPPORTED (sampling clock); P1 open — the ERA5 drift is detected (p = 0.025, CI excludes zero) but one transient free-running member cannot confirm it (right sign, ~27% magnitude, null-consistent), so the reanalysis-trend caveat stands; P6 (stratigraphic/early-warning form) FAILED — P is an architecture registrar, not a sensitive reorganization indicator (trend SNR ranks last, behind CAPE by 3.6x).

• The observing-network confound is closed (Phase 13). The regional geography of P replicates in a free-running CMIP6 HighResMIP integration that assimilates no atmospheric observations (rho = 0.71 against an ERA5-to-ERA5 across-period ceiling of 0.93). The property is atmospheric, not an artefact of the observing system.

• P measures what it is said to measure (Phase 12). It agrees with an independent rank mutual-information measure of addressability (rho = -0.93) while being nearly independent of band amplitude (+0.20) and of temporal persistence (+0.02).

• A complete catalogue of negative results (flux closure, universal laws, local sources, level invariance, moisture-budget information content, and the three applied predictions of Phases 9-11).

What has been retracted

• The v1 manuscript's central claim (A15 "Lambda_b ~ Pi_b closure"): see docs/RECONCILIATION.md.
• The interpretation of the transfer-asymmetry index A (Phase 12). The index is a reproducible regional statistic — replicated in MERRA-2 (rho = 0.93) and in the free-running model (rho = 0.90) — but it does not measure the irreversibility of generalisation. On synthetic fields where irrecoverability is known and swept it does not respond in either the spatial or the modal reading, while it tracks temporal persistence (Spearman 1.0 synthetic, +0.53 on real domains). A is a persistence statistic, and the cause is methodological: the transfer operators are fitted over a 20-step sliding window.
• The Sect. 6.2 predictability hypothesis (Phase 9) and its level-based reformulation (Phase 10). In all three applied tests, including the mesoscale deficit of AI weather models (Phase 11), plain band variance was a stronger predictor than the descriptors.

Repository map

• docs/RESEARCH_PROGRAM_FULL.csv — all 73 experiments (gen1-2 + gen3) with final reconciliation statuses.
• docs/PROTOCOL_PHASE1..23_*.md — frozen preregistered protocols with deviation logs. docs/PRIOR_ART_AUDIT_P.md + docs/PROTOCOL_AUDIT1_PRIOR_ART_HEADTOHEAD.md — the estimator's prior-art audit and its frozen head-to-head test.
• docs/RECONCILIATION.md — authoritative final scoreboard, audit findings, retractions. docs/PROGRAM_MAP.md — narrative program map (through Phase 23). research_programm_summary.csv — canonical experiment table (TOY_MODEL / ATMOSPHERE_* / CLEAN_PHASES blocks).
• docs/THEORY_CANDIDATE_QUENCHED_TEXTURE.md — theory candidate v1.4 (seed note kept as docs/THEORY_NOTE_QUENCHED_TEXTURE.md).
• clean_experiments/experiment_B*.py — gen3/gen4 experiments (B1-B23); download_b*.py — data downloaders (CDS API, NASA Earthdata, NOAA GEFS on AWS Open Data, WeatherBench 2, ESGF).
• clean_experiments/results/ — per-region-window JSON results, reports, figures (results/figures/).
• run_phase67_pipeline.sh — resumable download+experiment pipeline.
• Legacy gen1-2 scripts (T/A series) are retained for provenance; their statuses are in the CSV.

Reproduction

python -m venv .venv && source .venv/bin/activate
pip install numpy pandas scipy matplotlib xarray netCDF4 h5netcdf earthaccess cdsapi

ERA5 requires ~/.cdsapirc (CDS API); MERRA-2 requires NASA Earthdata credentials. All experiments are resumable via per-region-window caches.

Per-paper reproduction. Each paper of the series has a dedicated route (data -> computations -> artifact check) that names the exact 8-12 files behind its tables and figures, so a reviewer never has to guess which parts of this repository a given paper uses:

• Paper 1 (regional invariant): reproducibility/article1_README.md — one-command orchestrator reproducibility/reproduce_article1.py (--stage download|compute|check), pinned environment reproducibility/requirements_article1.txt, SHA-256 of every expected artifact, and a smoke test that verifies the computational chain on a single region-window without bulk downloads.
• Papers 2-3: routes will be added alongside their submissions.

Raw ERA5 / MERRA-2 / HighResMIP fields are deliberately not stored in the repository (large externally licensed products); the exact download scripts and all derived tables behind the papers' statistics are.

Branches

• gen4 — current line of work (this branch).
• gen3 — frozen at release v4.0; kept for the record. It carries a parallel, squashed import of the B1-B8 programme and does not contain manuscript_v2/ or Phases 9-13.
• gen2, gen1 — superseded.

Provenance

• Current manuscript: manuscript_v2/article_v3.tex.
• v1 manuscript (superseded; central claim retracted by Phase B1): Zenodo 19565805 — main.pdf, main_ru.pdf, manuscript/ are kept for the record.
• Release v4.0 (gen3): Zenodo 21940262.
• Citation metadata: CITATION.cff; Zenodo metadata: .zenodo.json.