A Semi-Analytic Torque Framework for Early Black-Hole Fuel Supply

This paper formulates a semi-analytic model for gas supply to early black holes through gravitationally-driven torques, and tests it against 12 real, published black-hole mass measurements using a single fiducial normalization (not tuned per object). At fiducial parameters, the model under-produces most observed masses by up to ~2 dex — a negative result, stated plainly rather than hidden. Three independently reproducible tests A single-epoch supply-vs-Eddington diagnostic across 12 objects A full trajectory integration using a published halo-accretion history (Fakhouri, Ma & Boylan-Kolchin 2010) for 5 objects A 100,000-realization Monte Carlo ensemble exploring the model's parameter space, independently re-executed and verified byte-for-byte against the supplied code All source code, data, and figures are included in the upload. Scope of the claim The paper states one falsifiable prediction for future high-redshift discoveries, derived entirely from already-published objects. It does not claim to establish or confirm a physical formation mechanism — several parameters (notably the gas-fraction normalization) are explicitly degenerate, and this is discussed in the text. Note on v1.0 The previous version reported a 31-object, 28/31 match that could not be independently reproduced and has been withdrawn from this version. It has been replaced by the three tests above, all with source code and verification included. This is independent, exploratory theoretical work and has not undergone peer review.