A discrimination atlas for Hawkes-versus-Cox model selection: where self-excitation and latent-regime clustering can be told apart

No published power curve exists for the Hawkes-versus-Cox discrimination problem, which is odd given how often the two are raced. This note supplies one: a known-truth atlas over sample size, branching ratio, ladder depth and design, in which every arm generates streams, every arm is refit to every stream, and a cell is called decidable only when the generating arm is recovered in at least 80 per cent of replications, with held-out conditional log-loss reported as a cross-check. The map has three practical consequences. It gives the onset sample size at which each mechanism becomes recoverable; it locates the degenerate cell where a near-critical power-law Hawkes and a multiplicative cascade mutually mimic, and identifies time-asymmetry as the discriminator that survives there; and it shows that panel designs recover a shared regime that no single stream of the same total length can. It is offered as a reusable instrument: cite your cell before your verdict. Amplitude non-comparability (dated note, 2026-08-30). The λ² amplitudes reported for the degenerate-cell atlas use a from-repository stand-in for the canonical finite-depth factor, β = k/(k+1) = 0.750 at k = 3, where the programme's canon measures β(4,2) ≈ 0.90 and has no canonical entry at k = 3 — about 0.83× the canonical factor at the nearest pinned depth. These amplitudes are therefore not comparable with any sibling record's amplitude and must not be pulled into a cross-repository amplitude table without the canonical factor at the matched depth. Comparisons internal to the record are unaffected: the same factor sits on both sides. Programme context. Fenocrisis is the crisis-entanglement repository of the Feno programme. Its discipline is stated once and applies to every record here: a verdict ships only where a decidability atlas computed on known-truth simulation says the design could have seen the effect; every number regenerates bit-for-bit from a pinned seed; the results ledger is append-only; and nothing forecasts, warns, or ranks — every figure is a retrospective model comparison on public, aggregate data. 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. Version 3 (2026-09-15). Carries the Omori corner: Fenocrisis record v13 (10.5281/zenodo.22759715, the T1 seismicity grid at Omori α ≈ 0.1 and the κ-sign non-identifiability), consumed by the atlas after the version-2 deposit, together with the concept-DOI citations of the Feno-program records it reads and record v12's identifier. The deposited copy is rebuilt from the repository source.