The Solar-Flare Activation Level: Deterministic, Data-Direct Early Warning from Photospheric Mode Decomposition, with a Size-Scaled Lead Time

HELIOGRAPH is a deterministic, training-free instrument that reads solar-flare hazard directly from the observed photospheric magnetic field, with no field extrapolation and no learned parameters. Operational flare forecasting is dominated by machine-learning systems that issue a probabilistic occurrence forecast over a roughly 24-hour window; the principal deterministic alternative (Kusano et al. 2020) computes a magnetohydrodynamic instability threshold from an extrapolated coronal field. HELIOGRAPH instead applies a proper orthogonal decomposition (POD) to the time-evolving SHARP radial-field (B_r) maps, isolating the dominant evolving spatial mode of the field change. The amplitude of this mode is an integrate-and-fire "parasitic energy" that loads, crosses a near-constant activation level, and then saturates as the region becomes flare-critical and holds. On a blind, apples-to-apples held-out set of solar-cycle-25 X-class flares — each active region compared against its own non-flaring window — the activation level is reproducible (coefficient of variation 0.29) and separates the pre-flare state from the region's quiet baseline at AUC 0.75; the loaded energy sets the eruption's field-reorganization rate (r = +0.81). The central result is a size-scaled lead time: the moment the parasitic energy crosses the activation level advances with the loaded energy (r = +0.96), so larger events announce themselves earlier — a relationship the one prior timing method (Korsós et al. 2019) explicitly reports it could not find. A two-tier alarm gives a broad loading watch (median 13.8 hours, 9 of 10 events) and a high-confidence major-flare warning at the activation crossing (median 12.1 hours, 6 of 10 events). The 2024-10-03 X9.0, the largest flare of solar cycle 25 to date, crossed its activation level about 17 hours before onset. The scope is stated plainly. The instrument reads field-energy magnitude, not GOES soft-X-ray class directly; about 25% of loaded quiet windows cross the threshold without producing a flare in the test window; and the firing time within an open window is consistent with the established stochastic / self-organized-critical picture and is not forecast. HELIOGRAPH is offered as a deterministic, auditable, mode-decomposition complement to the trained, probabilistic forecasters that define the operational standard — not a replacement for them, and not a claim to predict the minute a flare fires.