research/docs/PROOF_INDEX.md

Proof index

The numbering is from the distributed manuscript.

Central result	Location	Proof mechanism
Unrestricted linear minimax recovery	Chapter 3	Pseudoinverse upper bound and opposite-state lower witness
Exact common-matrix convexification	Chapter 5	Y=t(CCᵀ)⁻¹; reverse determinant interpolation
Target capacity and budget regimes	Chapter 6	Floored MAXDET feasibility and spectral threshold
Complete noncommuting frontier	Chapter 7	Reflection averaging, scalar determinant envelope, analytic roots
Joint affine continuous design	Chapter 8	Convex joint hypograph
Common-envelope dual certificate	Chapter 9	Log-determinant conjugacy and PSD complementarity
Two-scenario closed form	Chapter 9	Whitening and sign averaging
Tensor envelope composition	Chapter 10	Product primal feasibility and tensorized KKT multipliers
Direct-sum capacity	Chapter 11	Block sign symmetry and log-determinant additivity
Future-universal summary criterion	Chapter 12	Equality of feasible regions; singleton future constraint witness
Dimension-dependent memory bound	Chapter 12	First-order trace inequality and scaling
Exact coordinate schedule realization	Chapter 13	Largest-residual induction
Finite ellipsoid minimax	Chapter 14	Two-resource LP/SDP duality and quadratic completion
Infinite Sobolev-ellipsoid minimax	Chapter 15	Explicit shrinkage rule and two-coordinate witness
Local nonlinear stability	Chapter 16	Integrated Jacobian perturbation bound
Integrability obstruction	Chapter 16	Mixed partial incompatibility
Passive dilation	Chapter 19	Singular value decomposition
Linear-head task certificate	Chapter 20	Pairwise margin and Cauchy–Schwarz

Fourteen theorems, thirteen propositions, three lemmas and two corollaries appear in the main text. Thirty-one explicit proof environments accompany the results; one compatibility proposition is justified in the immediately following prose. These are manuscript proofs, not formal proof-assistant objects.