The Yang--Mills Mass Gap as an Orbit-Space Curvature Problem in the Information Manifold Model IMM Paper 15 --- Open Series, v3

This paper localizes the forcing half of the Yang--Mills mass gap problem to a single geometric hypothesis and does not solve it: no progress is claimed on the existence half of the Clay problem, and no proof or likelihood claim is made for the central hypothesis. Within the Information Manifold Model (IMM), the physical projection instantiates on Yang--Mills as the gauge quotient : / , and the IMM operator (Paper 0B, P-00-1) becomes the Witten Laplacian of the Yang--Mills measure on orbit space. Under this dictionary (Ansatz A-15-1) and an explicit conditional chain (Proposition P-15-1), a mass gap follows from uniform positivity of the renormalized, measure-weighted Bakry--\'Emery Ricci on the fundamental modular region (hypothesis H2 of Conjecture Cj-15-1 ' ), with scoping hypotheses H1 and H3 derived from known falsifying regimes rather than convenience: the rigorous 3D compact U(1) gap with zero orbit curvature (G"opfert--Mack) kills necessity across dimensions, and conformal non-abelian theories kill group-theoretic sufficiency. A na"ive form of the conjecture is stated, refuted by these regimes, and withdrawn; the refutation produces the live form's hypotheses. Four pre-registered lattice experiments instrument the program: an abelian/non-abelian discrimination test (E-YM-1/1b: two-state collapse at 1.00 for compact U(1) at 5.5 ; (3,3)=0.2019 0.0149 persisting for SU(2) ), a G"opfert--Mack control harness (E-YM-C/C-b: the abelian gap correctly attributed to the monopole channel, =0.41 _m , R^2=0.955 , against the semiclassical exponent 0.5 , with the curvature observable identically zero), and a matched-scale renormalization-group transport measurement of the curvature proxy (E-YM-3: M_2=1.020 0.005 at equal physical scale across a factor-2 cutoff change --- the collapse scenario excluded at this scheme and volume). A publication-grade protocol for the measure-weighted object itself (E-YM-3b) is registered with binding validity gates and pre-classified outcomes, including the outcome that would damage the program; its pilot tier has been executed: the synthetic validity gate first caught a genuine convention error and then passed at relative error 10^ -15 , the abelian kill switch returned exactly zero on every control configuration, the Faddeev--Popov-weighted soft-shell Ricci is positive at 161 -- 608 per point on 12^4 , and the flow classification remains inconclusive exactly as the registered underpowered declaration predicted, with a volume-matching design finding queued for the full tier. Three pre-registered criteria failed during the series (C1b, K1, T3), and a fourth retrospective correction --- the C1a significance quote, demoted to replication-based evidence --- was produced by a hostile self-review; all were instrument calibration or criterion design, repaired by labeled addenda with zero silent threshold moves, and are reported in full. The Millennium Problem remains exactly: existence (OP-15-1) plus H2 plus H3.