The Projection--Equilibrium Question: A Form-Only Null Hypothesis for the Information Manifold Model IMM Paper 16 --- Open Series, v1

This paper constructs the null hypothesis that the Information Manifold Model's deepest informal claim must beat, and reports that the corpus currently does not beat it. The claim --- that the recurrence of shared mathematical structure across the Riemann (Paper 13), Yang--Mills (Paper 15), and signature-selection (Paper 3) programs indicates a common underlying source --- is given a precise adjudication framework: everything derivable from abstract structural schemas is attributed to shared form and carries no evidence for a source; only cross-schema regularities that the schemas cannot force may count. Two results delimit what form provides. Theorem A (proved): for finite measured quotient systems, projection never destroys a spectral gap --- quotient spectra embed in ambient spectra and gaps are monotone along towers of quotients --- so, within this schema, gaps die only in limits, never under projection; this relocates the corpus's open hardness into uniformity tiers, exactly where its experimental program independently found it. For the continuum schema we state the quotient identity for free isometric circle actions with invariant weight, _ BE (B, )(X,X)= _ BE (M, )( X, X)+2|A_X|^2+ X, ^2 : the identity is due to Lott (2003, Eq. (3.11)), a fact established by this program's own mandatory literature gate after an independent derivation; we present that derivation --- a three-lemma _2 -calculus argument structurally different from Lott's tensor computation --- as an alternative proof, together with three exact validations and two corollaries of interpretive value to Paper 15 (a refined abelian kill switch: connection flatness, not group abelianness; and the Faddeev--Popov channel entering with a nonnegative sign). Proposition C assembles the classical ^1 stability tier of the independent-generator schema, localizing the Riemann-side hardness at the ^2 ^1 boundary where Paper 13 already found it. The decomposition into two inequivalent schemas is itself a finding: no cross-schema identity is forced by form, so the corpus's unique candidate evidence for a common source --- Paper 13's Experiment EH ``structural bridge'' --- was audited under pre-registered criteria. Verdict: artifact. The published exactness ( a=1.0000 , b=1/16 , R^2=1.000 ) reproduces for arbitrary substituted potentials; the bridge is an internal consistency check, and Paper 13's cross-paper language is withdrawn. Conclusion: the corpus presently contains no evidence that shared form cannot explain; the common-source reading remains metaphysics, explicitly labeled, with the exceedance bar now formalized. No claim in this paper advances any Clay problem.