QICLean paper-gap notes

Mathematical notes recording each discrepancy between a cited source and the formal development: missing hypotheses, scalar corrections, scope restrictions, and replacement proof routes. 61 notes: 12 open (6 high-severity), 3 in progress, 49 resolved or historical. Classified by status; source keys in the legend below. The conventions are stated in the policy note. Cite a note by its permanent URL https://sirui-lu.com/QICLean/paper-gaps/<name>.pdf or via paper-gaps.bib.

Open 9

2026-04-30The Perron–Frobenius Rank-One Step in Cirac–Perez-Garcia–Schuch–Verstraete 2017 Appendix C.2 cpgsv17 false-source · cited ×4 (tex)
2026-08-10Normalization of the tensor printed in CPSV16 Example 4.12 cpsv16 false-source · cited ×1 (tex)
2026-08-24The Spectral-Radius Identification in Wolf Theorem 6.5 wolf open-gap · cited ×1 (tex)
2026-07-16Scalar Normalization in Wolf's Lorentz Normal Form wolf open-gap · cited ×3 (tex)
2026-08-24Scope of Wolf Chapter 5 Operator Convexity and Monotonicity Results wolf scope-restriction · cited ×1 (tex)
2026-08-09Wolf Theorem 8.6 — the Doubly-Substochastic Half of Birkhoff wolf scope-restriction · cited ×3 (tex)
2026-07-18The Abstract Schwarz-Map Hypotheses in Wolf Theorem 6.12 wolf scope-restriction · cited ×1 (tex)
2026-08-09Complete-Positivity Scope of the Peripheral Cyclicity Theorem wolf scope-restriction · cited ×16 (tex)
2026-08-23Wolf Theorem ``Asymptotic Convergence I'' — Jordan-Scaling Qualifications wolf scope-restriction · cited ×1 (tex)

In progress 3

2026-08-24The Minkowski Canonical-Pair Dependency in Four Real Dimensions qiclean open-gap wip (tex)
2026-08-24Implicit Nilpotent-Space Classification in the Low-Dimensional Quantum Wielandt Corollary wolf open-gap wip · cited ×1 (tex)
2026-08-24Scope of Ha's A_\gamma Witness for Choi-Type Maps ha98 scope-restriction wip · cited ×1 (tex)

Resolved and historical 49

2026-07-31The Mutual-Information Bound for Matrix Product Density Operators cpgsv17 false-source resolved · cited ×1 (tex)
2026-08-15The CPSV16 Unit-Weight Convention and Renormalization-Fixed-Point Scale cpsv16 false-source resolved · cited ×3 (tex)
2026-08-04The General Compact-Convex Brouwer Fixed-Point Theorem wolf open-gap resolved · cited ×2 (tex)
2026-08-24The Rotation Sign in Wolf's Spinor Exponential Formula wolf false-source resolved · cited ×4 (tex)
2026-08-24The Nonvanishing Partner in Wolf's Kramers Theorem II wolf false-source resolved · cited ×5 (tex)
2026-08-24Wolf Chapter 5 Special-Function Jensen and Lieb Concavity wolf false-source resolved · cited ×9 (tex)
2026-08-21The Inverse on the Range in the Two-Variable Operator Schwarz Inequality wolf open-gap resolved · cited ×3 (tex)
2026-08-24The Missing Order Hypothesis in Wolf's Unitary Comparison wolf false-source resolved · cited ×2 (tex)
2026-08-23The False Converse in Wolf's Pauli-Block Truncation Proposition wolf false-source resolved · cited ×2 (tex)
2026-08-24Exact-Rank Wording in Wolf's Choi and Witness Criteria wolf false-source resolved · cited ×5 (tex)
2026-08-21Schur Complement TFAE — Missing Left-Support Condition wolf false-source resolved · cited ×5 (tex)
2026-08-24Slater Strong Duality: Finiteness Conditions for Attainment wolf false-source resolved · cited ×2 (tex)
2026-07-19Wolf Theorem 6.14: Fixed-Point Classification Completion Record wolf open-gap resolved · cited ×13 (tex)
2026-08-24Wolf Theorem 6.3: Positive-Map Scope and Boundary Corrections wolf false-source resolved · cited ×8 (tex)
2026-08-24Yamagami Lemma 6: The Strict-Disk Endpoint at Stride One yamagami93 false-source resolved (tex)
2026-08-23The Nonzero-Coefficient Convention for CPSV16 Canonical Forms cpsv16 local-correction resolved · cited ×2 (tex)
2026-07-15The marginal-support expansion in CPSV16 Appendix D.2 cpsv16 local-correction resolved · cited ×2 (tex)
2026-05-30Global and Per-Sector Unit-Weight Witnesses in the CPSV16 BNT Argument cpsv16 scope-restriction resolved · cited ×2 (tex)
2026-07-16Nilpotent Basis Elements in the Simple-Tensor Definition of Cirac–Pérez-García–Schuch–Verstraete cpsv16 local-correction resolved · cited ×1 (tex)
2026-06-08Zero correlation length uses the physical-trace transfer in Cirac–Perez-Garcia–Schuch–Verstraete 2017 cpsv16 local-correction resolved · cited ×1 (tex)
2026-08-08Nil-Matrix Product-Length Bound in the MPU Blocking Argument mpu local-correction resolved · cited ×3 (tex)
2026-08-23Hypothesis Boundaries for the Indecomposability of the Breuer–Hall Map (Wolf Example 3.1) wolf local-correction resolved · cited ×1 (tex)
2026-08-08Wolf's Operator-System Extension: Matrix-Algebra Realization wolf scope-restriction resolved · cited ×6 (tex)
2026-08-08Zero Multiplicities in Wolf's Two-Pure-State Spectrum Shorthand wolf local-correction resolved · cited ×4 (tex)
2026-06-23The Trace Sign in Wolf's Lorentz-Cone Converse wolf local-correction resolved · cited ×2 (tex)
2026-08-16The Phase Index in the Weighted Cesàro Formula, Wolf Equation (6.15) wolf local-correction resolved · cited ×3 (tex)
2026-08-09Wolf Equation (8.103) — Small-Power Exponent Scope wolf scope-restriction resolved · cited ×5 (tex)
2026-08-04The Rectangular Choi–Jamiolkowski Correspondence: Resolution of the Square-Dimensional Scope Restriction wolf scope-restriction resolved · cited ×6 (tex)
2026-07-30Source-General Projected Support Corner Star-Algebra wolf scope-restriction resolved · cited ×1 (tex)
2026-08-24Wolf Corollary 6.7: Source-General Resolution Record wolf scope-restriction resolved · cited ×3 (tex)
2026-08-13Jordan-Block Norm Estimate: the Shift Norm in One Dimension wolf local-correction resolved · cited ×2 (tex)
2026-07-02, revised 2026-08-24Resolution of the Choi-Type Positivity Scope (Wolf Example 3.1) wolf scope-restriction resolved · cited ×7 (tex)
2026-08-24Formalization-Derived Corrections to Wolf's Quantum Channels & Operations wolf local-correction resolved · cited ×2 (tex)
2026-06-24Top-index scope of the maximal-overlap lemma (Wolf Lemma 3.1) wolf scope-restriction resolved (tex)
2026-07-18Wolf Proposition 1.5: Factor and Coordinate Direct-Sum Scope Restrictions wolf scope-restriction resolved · cited ×3 (tex)
2026-06-30, updated 2026-08-04The Square-Dimension Restriction in Wolf's Generic Normal Form (restriction resolved 2026-08-04) wolf scope-restriction resolved · cited ×2 (tex)
2026-08-24Wolf's PPT–Indecomposable Existence Equivalence: Resolution of the Reverse Implication wolf scope-restriction resolved · cited ×1 (tex)
2026-08-23Wolf Proposition 6.1 — The Russo–Dye Factor wolf scope-restriction resolved · cited ×1 (tex)
2026-08-05Wolf Proposition 6.2 — Trivial Jordan Blocks for Peripheral Eigenvalues wolf scope-restriction resolved · cited ×1 (tex)
2026-08-13The Schmidt-rank set in the spectral n-positivity criterion (Wolf Prop. 3.2) wolf scope-restriction resolved · cited ×4 (tex)
2026-06-24Top-index scope of the spectral n-positivity criterion (Wolf Prop. 3.2) wolf scope-restriction resolved · cited ×4 (tex)
2026-08-23The nonempty-family condition in Wolf's Radon–Nikodym theorem wolf local-correction resolved · cited ×1 (tex)
2026-06-24Schmidt-number premise of Wolf's reduction criterion (Wolf eq. (3.18)) wolf scope-restriction resolved · cited ×7 (tex)
2026-08-21SIC–POVM Equality Families: the One-Dimensional Degeneracy wolf local-correction resolved (tex)
2026-06-24Top Schmidt-rank index in the n-positivity threshold of T_η (Wolf Chapter 3) wolf scope-restriction resolved · cited ×7 (tex)
2026-08-24Wolf Theorem 6.16: The Two Schwarz Orientations in the Printed Proof wolf local-correction resolved · cited ×3 (tex)
2026-07-18Wolf Chapter 5: Abstract Multiplicative-Domain Hypotheses wolf clarification resolved (tex)
2026-08-05Wolf Proposition 1.6: Complete Positivity from Positivity, Commutative Side wolf clarification resolved · cited ×1 (tex)
2026-08-24Yamagami's Simultaneous-Singularity Boundary Count yamagami93 clarification resolved · cited ×1 (tex)

Sources legend