Hidden multi-state structure versus the piecewise-Poisson flare rate on 50 years of GOES/XRS solar flares

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-31
DOI
https://doi.org/10.5281/zenodo.22180472
Primary Topic
Solar and Space Plasma Dynamics
Type
preprint
Controls
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preprint

Hidden multi-state structure versus the piecewise-Poisson flare rate on 50 years of GOES/XRS solar flares

Evan Tabak Atlas
Zenodo (CERN European Organization for Nuclear Research)
Solar and Space Plasma Dynamics
preprint

Hidden multi-state structure versus the piecewise-Poisson flare rate on 50 years of GOES/XRS solar flares

Evan Tabak Atlas
preprint en

Abstract

Paper F of the Fenocosm arm of the Feno program. The first estimable hidden-state alternative entered against solar physics' nonstationary-Poisson incumbent, on the full ~50-year GOES/XRS soft-X-ray flare record. Abstract. The statistics of solar flare occurrence have a mature incumbent description: a time-dependent (nonstationary) Poisson process whose rate varies with the solar cycle and with active-region evolution, usually represented by a piecewise-constant rate. No estimable hidden-state alternative — an exact hierarchical regime filter with a likelihood — has been entered against it. We enter one, on 8,393 M1.0+ and 64,996 C1.0+ flares (1975–2025, era-stitched from the NCEI legacy reports and the GOES-R L2 flare summary), and report what it settles and what it does not. (i) Several latent switching layers beat one, decisively and at fixed parameter count: ΔBIC +3,175 (M1.0) and +10,195 (C1.0), and +460 / +1,436 nats out of sample. (ii) Against the piecewise-constant incumbent the cascade wins on parsimony, not on fit: ΔBIC is +3,102 and +6,172, but the Bayesian-blocks partition carries 531 and 1,423 parameters against the cascade's four and fits the record better in raw likelihood, by +1,035 and +3,876 nats — the entire BIC margin is the parameter penalty net of that deficit. (iii) The specific geometric ladder buys no descriptive advantage over a free transition matrix at these sample sizes: the cascade leads the free-transition Poisson HMM at M1.0 by only +119 BIC, of which +117.8 is the parameter penalty and +1.7 is fit, and loses by −1,475 BIC at C1.0; the sealed calibration shows the axis fires +147 BIC on a synthetic no-hierarchy world, so it cannot be read as a hierarchy test. (iv) A causal, filter-only 24-hour M-class now-cast carries real skill from the event record alone (BSS +0.589 against the training-period climatology, +0.338 against the verification period's own). Stated limitations, carried with the deposit. There is not one uncertainty interval on a fitted parameter or a model-comparison margin in this paper. Every fitted ladder, every ΔBIC and every held-out margin is a point estimate from multi-start numerical optimisation. The paper's discipline about bias says nothing about variance, and its most delicate result (+119 BIC, of which +1.7 is fit) is exactly the kind of margin that needs an interval. Profile-likelihood or parametric-bootstrap intervals on the fitted parameters and paired intervals on every margin are named as the first thing a referee should ask for. An uncorrected, same-shape-as-the-signal systematic. Detection completeness against cycle phase is not quantified. The soft-X-ray background rises by more than an order of magnitude from solar minimum to maximum, so above-background flare identification loses small events preferentially near maximum — a cycle-phase dependent multiplicative detection efficiency with the same shape as the latent rate being fitted. At C1.0 (mean 3.56 flares/day, tens per day at maximum) overlapping flares also merge into single catalogued events. Both bite hardest exactly where the paper's largest numbers live. The systematic and its sign are stated; it is not corrected for. The HMM adversary is a two-point grid (J ∈ {2, 4}), so the +119 M1.0 margin is a lead over J ≤ 4, not over the free-transition HMM family; the extended-J re-run is queued. Correction note (2026-08-30) — record v35. §7's estimability discipline was written against record v32, which reported that the event-altitude ladder is never recovered to truth anywhere in the sealed grid ("N*_recovery is above the grid"), and de-biased this paper's fitted multiplier on that basis. That reading was a model-misspecification artifact: v32 re-read fits in which the cascade was given covariate = exposure while the generator built the world on exposure × a hard-gated activity window. Record v35 refits the same sealed seeds with the generator's own covariate and recovers the injected multiplier inside the grid. The paper's N*_recovery statements are withdrawn as artifacts; N*_selection ≈ 800 stands (now quoted with its interval); and §7.2's de-biasing paragraph has been rewritten to use the observation-process-matched calibration, or to rest the floor clearance on N alone. The substantive conclusions (i)–(iv) are unaffected, and the ladder remains a model-selection quantity for the separate reason §6.5 gives. Deposit note. All seven Feno-program repositories are private and remain private, so this deposit is standalone: it carries its own reproduction materials, its metadata contains no repository link, and sibling work is referenced by DOI rather than by repository path. Related Zenodo DOIs cited below are reserved with publication pending. Part of the Feno program. The source repository is private; the reproduction materials for this record are contained in the record itself. Version 2 (2026-09-01): reference-list publication-status notes corrected (the program's reserved DOIs were published 2026-08-31); content otherwise unchanged.

Zenodo (CERN European Organization for Nuclear Research)
Solar and Space Plasma Dynamics
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