The Markov-switching multifractal as an estimable propagating-fluctuations model

Abstract

Paper A of the Fenocosm arm of the Feno program. A metrology paper for the Markov-switching multifractal (MSM) read as a propagating-fluctuations model of accreting-source variability: which of its correspondences are exact, which are approximate, and where the estimator stops working. Abstract. The MSM cascade reproduces, in closed form, the two marginal-law signatures that motivate propagating-fluctuations models of accretion variability: a lognormal flux marginal and a linear rms–flux relation. This paper derives those correspondences, measures how far each survives the observation process (a binned Cox photon channel), and asks the estimability question directly: at what photon rate does the exact 2k-state filter stop recovering the injected cascade contrast? The answer is a metrology result rather than an astrophysical one. Recovery of the true contrast holds down to ~0.06 counts/bin (~500 photons), well below the rate at which the signal has already vanished from the moments — the closed-form overdispersion available for detection falls under the sampling floor near 0.05 counts/bin — and the failure mode at lower rates is an upward blow-up of the estimate, never a quiet collapse toward a flat cascade. The operational reading: an apparent likelihood collapse on real streams is emission-model misspecification, not photon starvation, and the diagnostic for it is a failed resynthesis (a statistical Turing test), not a flat likelihood. Scope note added 2026-08-30 (§6.1). The "no collapse" result is measured in one arena — a binned Cox channel at fixed length with a correctly specified emission model. It is not a statement about the event-altitude arena (a sparse point process read through an exposure mask and activity window), which has its own floor curve and its own selection-versus-recovery distinction. The paper now carries that cross-reference explicitly, including the 2026-08-30 correction to the program's recovery reading (record v35). 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.