TNLean 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. 241 notes: 79 open (19 high-severity), 6 in progress, 162 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/TNLean/paper-gaps/<name>.pdf or via paper-gaps.bib.

Open 73

2026-05-10Canonical-Form Weight Normalization and the Proportional MPV Comparison cpsv16 unfaithful · cited ×4 (tex)
2026-08-31The Missing Algebraic Specification of the PEPS Boundary-RFP Diagrams cpsv16 open-gap · cited ×3 (tex)
2026-07-31Per-block RFP Isometry Form and the Source Isometry Condition in CPSV16 cpsv16 open-gap · cited ×34 (tex)
2026-04-30; revised 2026-09-26The Root-Channel Kraus-Rank Step in Theorem 4.1 dccsp17 unfaithful · cited ×9 (tex)
2026-08-29Source Boundary for the MPU Gauss Laws and Their Commuting Projectors fbc25 open-gap (tex)
2026-08-29Source Boundary for MPU Action Tensors and Stabilizer Data fbc25 open-gap · cited ×2 (tex)
2026-10-02The Truncated-Symmetry Detector Depends on the Endpoints gs24 false-source · cited ×4 (tex)
2026-09-26The unblocked parity reading of the Fundamental Theorem of matrix product unitaries mpu false-source · cited ×7 (tex)
2026-08-28Global Phase Freedom in the PGVWC07 Quadratic Reconstruction System pgvwc07 false-source · cited ×6 (tex)
2026-10-04Pure-Exponential Correlator Expansion and Jordan Blocks in CPGSV21 rmp false-source · cited ×12 (tex)
2026-06-04The Martingale Principal-Angle Estimate for MPS Parent Hamiltonians rmp false-source · cited ×18 (tex)
2026-05-01Conditional After-Blocking Fundamental Theorem versus the CPSV Statement rmp open-gap (tex)
2026-05-06Paper Comparison for BNT Inputs in the Non-periodic MPS Fundamental Theorem rmp open-gap · cited ×2 (tex)
2026-09-26The CZX Tensor: Orientation of the Bond Labels rmp false-source · cited ×5 (tex)
2026-06-17, revised 2026-09-28Deferred Result: The Translation-Invariant Bond-Dimension Lower Bound for the W State rmp open-gap · cited ×9 (tex)
2026-10-11The Scanner Estimate from the Conclusions of Its Inputs arealaw2d scope-restriction · cited ×9 (tex)
2026-10-04The Finite Periodic One-Species PVBS Gap bn12 scope-restriction · cited ×3 (tex)
2026-07-30Active physical support compression in the CPSV16 commuting-form argument cpsv16 scope-restriction · cited ×16 (tex)
2026-06-12The NNCPH ground-state clause in Cirac–Perez-Garcia–Schuch–Verstraete 2016 cpsv16 scope-restriction · cited ×56 (tex)
2026-06-15The parent commuting Hamiltonian condition in Cirac–Perez-Garcia–Schuch–Verstraete 2016 cpsv16 scope-restriction · cited ×4 (tex)
2026-06-10Pure zero correlation length and local orthogonality in Cirac–Perez-Garcia–Schuch–Verstraete 2017 cpsv16 scope-restriction · cited ×26 (tex)
2026-06-04; revised 2026-08-02Proof-Route Alignment for the Periodic Overlap Dichotomy (de las Cuevas–Cirac–Schuch–Pérez-García) dccsp17 scope-restriction · cited ×19 (tex)
2026-09-03Defect Covariance in State-Level Gauging fbc25 scope-restriction · cited ×2 (tex)
2026-09-06Endpoint-Coordinate Scope of Truncated-Symmetry Unitarity fbc25 scope-restriction · cited ×2 (tex)
2026-10-01Klein Three-Cocycles: Circle and Nonzero-Complex Coefficients glm23 scope-restriction · cited ×1 (tex)
2026-10-05Matrix Product Operator Symmetric States:\newline Formalized Layers and Remaining Scope glm23 scope-restriction · cited ×11 (tex)
2026-09-27The Rep(S_3) and su(2)_4 Phases: Completeness of the Lists glm23 scope-restriction · cited ×1 (tex)
2026-10-05Weak-Hopf Parent Terms: Support Averaging and Ambient Completion glm23 scope-restriction · cited ×13 (tex)
2026-09-01Single-Block Scope for the Schumacher–Werner Commuting-Algebra Proposition gnvw12 scope-restriction · cited ×1 (tex)
2026-08-24Homogeneous-Chain Scope for the GNVW Support Algebras, Adjacent Generation, and Index gnvw12 scope-restriction · cited ×2 (tex)
2026-08-24Full-Matrix Scope for the GNVW Support-Algebra Formalization gnvw12 scope-restriction · cited ×6 (tex)
2026-10-01Exchange of Domain-Wall Endpoints on Glued Half-Chains gs24 scope-restriction · cited ×1 (tex)
2026-09-03Full Support in MPU Normality and Theorem III.8 mpu scope-restriction · cited ×64 (tex)
2026-08-16The Supplied Fixed Pair in the Reduced-Representative Step of Proposition IV.5 mpu scope-restriction · cited ×7 (tex)
2026-10-01Supplied Two-Site Decompositions of the Shift Matrix Product Unitaries mpu scope-restriction · cited ×1 (tex)
2026-08-29Identity-Ancilla Transport of MPU Symmetries mpu scope-restriction · cited ×6 (tex)
2026-09-26GHZ Form of the Fixed-Point State: Local Orthogonality as a Hypothesis mswc24 scope-restriction · cited ×1 (tex)
2026-10-02Inhomogeneous Matrix Product States: Block Length mswc24 scope-restriction · cited ×26 (tex)
2026-10-03Polynomial Approximation Accuracy at Positive Correlation Length mswc24 scope-restriction · cited ×2 (tex)
2026-10-01Circuits Between States in the Same Phase: the Normal Case mswc24 scope-restriction · cited ×1 (tex)
2026-10-05Compatible Coherent Seeds and Non-Normal State Conversion mswc24 scope-restriction · cited ×1 (tex)
2026-09-26Sequential Factorization of the Blocked Isometry: Positive Block Length mswc24 scope-restriction · cited ×1 (tex)
2026-10-01; chain length resolved 2026-10-02; canonical extension 2026-10-05The Tree Circuit with Measurements: Rounds, Registers, and Chain Length mswc24 scope-restriction · cited ×1 (tex)
2026-05-06Normal PEPS Fundamental Theorem: Section 3 Route peps scope-restriction · cited ×103 (tex)
2026-05-05The Direct-Sum Input from the Older MPS Representation Paper pgvwc07 scope-restriction · cited ×8 (tex)
2026-10-04Half-Chain Spectrum: Canonical Orientation, Normalization, and Decay pgvwc07 scope-restriction · cited ×2 (tex)
2026-08-22The Intertwiner Count in the Quadratic Reconstruction Argument pgvwc07 local-correction · cited ×5 (tex)
2026-08-12Scope of the Formal Site-Independent Construction Relative to PGVWC07 pgvwc07 scope-restriction · cited ×2 (tex)
2026-10-06PGWSVC08 Physical String Order versus Virtual-Boundary Nondecay pgwsvc08 scope-restriction · cited ×24 (tex)
2026-10-13Product-Reference Estimates and a Column on the Open Square polypeps scope-restriction · cited ×2 (tex)
2026-10-08Party-Network Bounds in the Dyadic Routing Lemma polypeps scope-restriction · cited ×3 (tex)
2026-10-04Finite Adaptive Local Channels and Source Protocol Blocks psc21 scope-restriction · cited ×2 (tex)
2026-10-04Asymptotic Local Channel Conversion without Classical Feedforward psc21 scope-restriction · cited ×13 (tex)
2026-10-03Translation-Invariant MPS and the Trivial Phase under Circuits with Measurements: One Direction psc21 scope-restriction · cited ×2 (tex)
2026-10-04Physical-Port Simulation of Bounded Register Channels psc21 scope-restriction · cited ×5 (tex)
2026-09-23Scope of the Physical-Deformation Ground-Space Correspondence Relative to CPGSV21 rmp scope-restriction (tex)
2026-06-04Scope Note: The AKLT On-Site SO(3) Symmetry Is Formalized; Its Cohomological Classification Is Not rmp scope-restriction · cited ×3 (tex)
2026-06-04Example Parent Hamiltonians in Cirac–Perez-Garcia–Schuch–Verstraete 2021 rmp scope-restriction · cited ×3 (tex)
2026-09-25Kitaev Chain: the Bosonic Contraction of the Fixed-Point Matrices rmp scope-restriction · cited ×1 (tex)
2026-10-04The CZX PEPS: Actual Rectangle Boundaries and Their Symmetry rmp scope-restriction · cited ×5 (tex)
2026-09-26Two-Dimensional PEPS Examples: Tori of Width Two rmp scope-restriction · cited ×19 (tex)
2026-10-03Quantum-Double PEPS: Normalization, Representations and Scope rmp scope-restriction · cited ×179 (tex)
2026-10-05Finite dual-path deformation of regular PEPS flux strings scp10 scope-restriction · cited ×11 (tex)
2026-10-05Commuting Parent Hamiltonians of G-Isometric Tensors: the Projector and the Scope scp10 scope-restriction · cited ×4 (tex)
2026-10-05Physical bond separation and the remaining regular PEPS blocking step scp10 scope-restriction · cited ×3 (tex)
2026-10-05Uniform native-closure regular PEPS renormalization scp10 scope-restriction · cited ×3 (tex)
2026-10-05Two-by-two regular PEPS renormalization with the original tensor scp10 scope-restriction · cited ×1 (tex)
2026-08-22The One-Step Subspace in the Quantum Wielandt Inequality spwc10 scope-restriction · cited ×1 (tex)
2026-10-02Bond Dimensions of the Successive Decompositions and Minimal Resources ssvcw05 scope-restriction · cited ×1 (tex)
2026-09-03One-Dimensional Scope of Schumacher–Werner Support-Algebra Covariance sw04 scope-restriction (tex)
2026-10-02The Three-Object Ising Twist: Channels and Formal Scope tnlean scope-restriction · cited ×3 (tex)
2026-05-05Theorem Surface Audit for Canonical Form, BNT, and the Non-periodic MPS Fundamental Theorem tnlean clarification · cited ×1 (tex)
2026-05-08Dependency Audit for the Non-periodic MPS Fundamental Theorem Blueprint tnlean clarification (tex)

In progress 6

2026-09-04Trace Preservation in the Forward Direction of Theorem 4.1 (de las Cuevas–Cirac–Schuch–Pérez-García) dccsp17 false-source wip · cited ×19 (tex)
2026-09-06Compatibility of CZX Fusion and Action Coordinates fbc25 open-gap wip · cited ×1 (tex)
2026-10-02The Positive Part of a Blocked Tensor with Overlapping Blocks mswc24 false-source wip · cited ×48 (tex)
2026-10-02Ground-Space Subtraction in the Infinite-Volume Gap Argument nachtergaele96 open-gap wip · cited ×52 (tex)
2026-10-05Typed Multiplicity Indices for the Coupled Pentagon glm23 local-correction wip · cited ×13 (tex)
2026-09-30The Anomaly Class of the Two-Qubit Z_2\timesZ_2 Tensors: From Detector Values to the Class glm23 scope-restriction wip · cited ×1 (tex)

Resolved and historical 162

2026-09-25Simultaneous Left Inverse of Injective Operator Blocks bmwshv17 false-source resolved · cited ×6 (tex)
2026-07-11The SAL to Eta-Local Structure Step in Cirac–Perez-Garcia–Schuch–Verstraete 2017 Appendix C.2 cpsv16 open-gap resolved · cited ×86 (tex)
2026-08-30The Perron–Frobenius Rank-One Step in Cirac–Perez-Garcia–Schuch–Verstraete 2017 Appendix C.2 cpsv16 false-source resolved · cited ×10 (tex)
2026-07-11Diagonal Restriction and the Vertical Canonical Form in Proposition 4.13 cpsv16 unfaithful resolved · cited ×3 (tex)
2026-07-11The Vertical Direction in Proposition 4.13 Is the Index-Exchanged Tensor cpsv16 unfaithful resolved (tex)
2026-05-13Historical Note: Rate-Quantified BNT Cross-Overlap Decay for a Retired Projection Argument cpsv16 unfaithful historical · cited ×3 (tex)
2026-07-30A Phase Obstruction to Canonical-Form Renormalization-Flow Convergence cpsv16 false-source resolved · cited ×8 (tex)
2026-05-10CPSV16 Lemma equalMPS Gauge-Phase Components and Resolution cpsv16 unfaithful resolved · cited ×4 (tex)
2026-08-12Finite-Ring Entropy Corrections for CPSV16 Examples 4.10 and 4.11 cpsv16 false-source resolved · cited ×44 (tex)
2026-05-11Historical Note: the Fixed-Block Cancellation Step in CPSV16 Theorem II.1 cpsv16 unfaithful historical · cited ×6 (tex)
2026-05-13Historical Note: Non-Dominant Per-Block Projection in CPSV16 § II Step 1 cpsv16 unfaithful historical · cited ×2 (tex)
2026-08-31The SAL–ZCL Blocking-Channel Conclusion of CPSV16 Proposition C.15 Is False cpsv16 false-source resolved · cited ×10 (tex)
2026-07-25Adjacent regions obstruct the unrestricted CID forward implication in Cirac–Perez-Garcia–Schuch–Verstraete 2017 cpsv16 false-source resolved · cited ×5 (tex)
2026-07-14A raw-weight counterexample to the pure-state ZCL equivalence in Cirac–Perez-Garcia–Schuch–Verstraete 2017 cpsv16 false-source resolved · cited ×4 (tex)
2026-08-10The Pure-State Blocking-up-to-Gauge Equivalence Is False cpsv16 false-source resolved · cited ×5 (tex)
2026-07-28Closure Record for the Strong-Subadditivity Equality Characterization and Hayashi–Markov Decomposition cpsv16 open-gap resolved · cited ×1 (tex)
2026-06-22Strong Subadditivity as a Standalone Axiom and Its Lieb-Concavity Elimination Route cpsv16 open-gap resolved (tex)
2026-07-23The Physical Complement in the Topological Gibbs Decomposition cpsv16 open-gap resolved · cited ×36 (tex)
2026-07-23The Arbitrary-Chain Topological Projector Recursion cpsv16 open-gap resolved · cited ×5 (tex)
2026-10-13Corrections to matrix product density operator fixed-point statements cpsv17 false-source resolved · cited ×1 (tex)
2026-08-09Shifted Trace Powers and the Exact MPU Transfer Spectrum cpsv17 open-gap resolved · cited ×1 (tex)
2026-09-05The Empty Interior Word in the Printed CZX Action Pair fbc25 false-source resolved · cited ×2 (tex)
2026-10-05The Fibonacci Module: Direct-Sum Classification glm23 false-source resolved · cited ×4 (tex)
2026-09-27The \mathbb Z_3 Phase of Rep(S_3): the Printed Action of \psi glm23 false-source resolved · cited ×1 (tex)
2026-09-27The Unbroken Subgroup Is the Stabilizer of a Block gs24 false-source resolved · cited ×1 (tex)
2 October 2026CZY fusion: associativity on the physical image lmsvkl25 false-source resolved · cited ×6 (tex)
2026-08-30The Proportionality Scalar in the MPS Reduction Theorem mgsc18 false-source resolved · cited ×7 (tex)
2026-08-29The Empty-Word Summation Error in the MPS Residual Expansion mgsc18 false-source resolved · cited ×11 (tex)
2026-08-30Orientation of the Three-Swap Ancilla Circuit mpu false-source resolved · cited ×1 (tex)
2026-09-04; updated 2026-09-27CZX: Normalization and the Physical Z Gates mpu false-source resolved · cited ×11 (tex)
2026-09-26Decaying Correlations: Windows of Separations and the Connected Correlator mswc24 false-source resolved · cited ×5 (tex)
2026-10-04The Full-Input Pseudoinverse Obstruction and Its Support Correction mswc24 false-source resolved · cited ×8 (tex)
2026-10-02The Fixed-Point State of a Tensor with Repeated Blocks mswc24 false-source resolved · cited ×8 (tex)
2026-09-04The Lower Endpoint of Nachtergaele's Theorem 2.1(i) nachtergaele96 false-source resolved · cited ×7 (tex)
2026-08-31A Two-Site Counterexample to Cyclic MPS Bond Uniformity peps false-source resolved · cited ×1 (tex)
2026-06-06Injective PEPS Gauge Consistency Needs a Connectivity Hypothesis peps false-source resolved · cited ×16 (tex)
2026-04-30PEPS Gauge Uniqueness and Balanced Edge Scalars peps false-source resolved · cited ×19 (tex)
2026-10-02The Two-Dimensional Overlapping-Window Strengthening of the Normal PEPS Fundamental Theorem peps open-gap resolved · cited ×188 (tex)
2026-10-05Scalar Phases in the Physical String-Order Criterion pgwsvc08 false-source resolved (tex)
2026-06-11Block-Diagonal Boundary Conditions in the Degenerate Parent-Hamiltonian Ground Space rmp open-gap resolved · cited ×25 (tex)
2026-10-04Critical Parameters and Boundary Localization in the One-Species PVBS Chain rmp false-source resolved · cited ×3 (tex)
2026-10-02A Gapless Short-Range Parent Hamiltonian of a Canonical MPS rmp false-source resolved · cited ×12 (tex)
2026-09-27SPT Fixed Points: The Printed Tensor Is Not Normal rmp false-source resolved · cited ×5 (tex)
2026-07-20Fixed-Length Chain Equality Does Not Imply Combined-Tensor MPV Equality tnlean unfaithful resolved (tex)
2026-10-08Nondegenerate Rectangles and Triangles in Area-Law Templates arealaw2d local-correction resolved · cited ×1 (tex)
2026-09-24Fibonacci String-Net: Entries of the Two Operator Blocks bmwshv17 local-correction resolved · cited ×11 (tex)
2026-09-25Fibonacci String-Net: the Projector Identity at Positive Length bmwshv17 local-correction resolved · cited ×4 (tex)
2026-09-24, updated 2026-09-27Ising String-Net Operators: the Normalization of the \sigma Tensor bmwshv17 local-correction resolved · cited ×8 (tex)
2026-07-15Sharp Finite-Length Block Separation for Canonical-Form Tensors cpsv16 scope-restriction resolved · cited ×16 (tex)
2026-07-09CPGSV17 Blocked-Basis Chi Families and Uniform BNT Labels cpsv16 scope-restriction resolved · cited ×30 (tex)
2026-07-12Physical-Isometry Transport for the Blocked MPDO Fixed Point cpsv16 scope-restriction resolved · cited ×4 (tex)
2026-07-12The Final Traced Subspin in the Definition of S_0 cpsv16 local-correction resolved · cited ×7 (tex)
2026-07-12The Implication Label in the Proof of MPDO Theorem 4.9 cpsv16 local-correction resolved · cited ×8 (tex)
2026-07-12Zero-Weight Sector Completions in the MPDO Refinement Map cpsv16 local-correction resolved · cited ×24 (tex)
2026-07-13The Periodic-Sector Argument in Proposition 4.13 cpsv16 local-correction resolved · cited ×13 (tex)
2026-07-13The Vertical Canonical Form Retains Only the Nonzero Physical Sectors cpsv16 local-correction resolved · cited ×26 (tex)
2026-07-21The Trace-Ratio Exponent in the Blocked Vertical-Operator Formula cpsv16 local-correction resolved · cited ×1 (tex)
2026-07-31The Commuting-Form-to-SAL Implication for Simple MPDOs cpsv16 scope-restriction resolved · cited ×200 (tex)
2026-08-12Exact arithmetic scope for CPSV16 Examples 4.10 and 4.11 cpsv16 scope-restriction resolved · cited ×1 (tex)
2026-07-20The Figure 11 Fusion Map Is a Coisometry onto the Active Sectors cpsv16 local-correction resolved · cited ×22 (tex)
2026-05-10Basis-of-Representatives Scope Restriction in the Fundamental Theorem Formalization cpsv16 scope-restriction resolved · cited ×18 (tex)
2026-07-15The Sector Decomposition in the GSNNCH Definition of Cirac–Pérez-García–Schuch–Verstraete cpsv16 local-correction resolved · cited ×12 (tex)
2026-08-29The Positive-Gap Boundary for Distance- and Length-Independent MPDO Correlations cpsv16 scope-restriction resolved · cited ×7 (tex)
2026-08-31Blocking and the Parent-Hamiltonian Range in CPSV16 cpsv16 local-correction resolved · cited ×2 (tex)
2026-08-28Purification RFP in Cirac–Perez-Garcia–Schuch–Verstraete 2017 cpsv16 local-correction resolved · cited ×8 (tex)
2026-07-30The Index Typo in the Pure-State Renormalization-Flow Equation cpsv16 local-correction resolved · cited ×3 (tex)
2026-07-23The Domain Boundary of the Topological Gibbs Decomposition cpsv16 local-correction resolved · cited ×16 (tex)
2026-05-13Historical Note: Two-Layer Sector Refinement of CPSV16 eq:II_ABasicTensors cpsv16 scope-restriction historical · cited ×2 (tex)
2026-08-02A Mixed-Prefix Repair of the Two-Site Sector Comparison cpsv16 local-correction resolved · cited ×21 (tex)
2026-07-19CPSV16 Vertical-Sector Invertibility and Sector Relabelling cpsv16 scope-restriction resolved · cited ×5 (tex)
2026-09-30Peripheral Roots after Blocking a Periodic Tensor dccsp17 local-correction resolved · cited ×9 (tex)
2026-10-01Wraparound in the Orbit-Phase Telescoping Product dccsp17 local-correction resolved · cited ×2 (tex)
2026-08-30Nondegeneracy in the Alternating-Network Proportionality Lemma fbc25 local-correction resolved · cited ×1 (tex)
2026-08-29Reciprocal Factors in the Block-Independence Argument fbc25 local-correction resolved · cited ×4 (tex)
2026-08-29The Repeated Determinant Factor in the Generalized-Cocycle Lemma fbc25 local-correction resolved · cited ×2 (tex)
2026-09-07The Comparison Matrix Between the Two First-Cut Factorizations fbc25 scope-restriction resolved · cited ×2 (tex)
2026-09-06The Missing Tilde in the Inverse-Compatible Gate Argument fbc25 local-correction resolved · cited ×3 (tex)
2026-08-29The Block Index in the Positive Generalized-Cocycle Corollary fbc25 local-correction resolved · cited ×2 (tex)
2026-08-29The Positive Primitive in the Generalized-Cocycle Corollary fbc25 local-correction resolved · cited ×2 (tex)
2026-09-03The Representative Index in the First Stabilizer Factor fbc25 local-correction resolved · cited ×3 (tex)
2026-08-28The Repeated Case in the Scalar Three-Cocycle Normalization fbc25 local-correction resolved · cited ×2 (tex)
2026-08-29The Final Index in the Block-Dependent Two-Cochain Coboundary fbc25 local-correction resolved · cited ×4 (tex)
2026-09-26The Fusion Gauge of the Stabilizer Reconstruction Formula glm23 local-correction resolved · cited ×5 (tex)
2026-10-10The Printed One-Qubit Z_2\timesZ_2 Symmetry: Diagonal Values of the Anomaly glm23 local-correction resolved · cited ×1 (tex)
2026-09-24One Left Shift per Site in the Periodic Group Operators glm23 local-correction resolved · cited ×2 (tex)
2026-09-26The L-Symbol Relation Imposed by Time Reversal glm23 local-correction resolved · cited ×3 (tex)
2026-08-24Outer-Factor Basis Correction in the Support-Algebra Commutation Lemma gnvw12 local-correction resolved · cited ×1 (tex)
2026-08-24Star-Closure Correction for the GNVW Support-Algebra Lemma gnvw12 local-correction resolved · cited ×5 (tex)
2026-09-25The Left Action Vectors of the CZX Product States gs24 local-correction resolved · cited ×5 (tex)
2026-09-27Domain Walls: Nonzero Tensors, Phases and Blocked Local Actions gs24 local-correction resolved · cited ×9 (tex)
2026-07-28Support scope of the HJPW product-reference Petz factorization hjpw04 scope-restriction resolved (tex)
2026-08-12The Endpoint Rank-Product Exponent in MPU Index Well-Definedness mpu local-correction resolved · cited ×10 (tex)
2026-08-10, revised 2026-10-06Virtual Bond Dimension in MPU Tensor Equivalence mpu local-correction resolved · cited ×5 (tex)
2026-08-09MPU One-Letter Mixed Residual Trace: Resolved Local Correction mpu local-correction resolved · cited ×5 (tex)
2026-08-30Specified-Tensor Shift Values and the Public MPU Index mpu scope-restriction resolved · cited ×7 (tex)
2026-09-01The First MPU Source Cut and the Orientation of the Source Gates mpu local-correction resolved · cited ×12 (tex)
2026-10-03, revised 2026-10-09One-Sided Swap Transformation of MPU Symmetries mpu local-correction resolved · cited ×2 (tex)
2026-08-12Two-Projection Decomposition: Repeated-Projector Typo mpu local-correction resolved · cited ×2 (tex)
2026-10-05Coherent Canonical Sector Encoders mswc24 scope-restriction resolved (tex)
2026-10-03The Constant in the Depth Lower Bound mswc24 local-correction resolved · cited ×3 (tex)
2026-09-26The Depth Lower Bound in the Gauge of a Normal Tensor mswc24 scope-restriction resolved · cited ×2 (tex)
2026-09-27; resolved 2026-09-28Preparation in Logarithmic Depth: Chain Lengths Divisible by the Block Length mswc24 scope-restriction resolved · cited ×1 (tex)
2026-09-28Preparation in Logarithmic Depth: the Periodic State Must Not Vanish mswc24 local-correction resolved · cited ×8 (tex)
2026-10-05Long-Range Matrix Product States with Measurements: Scope of the Formal Statement mswc24 scope-restriction resolved · cited ×9 (tex)
2026-10-02A Corrected Approximating State for a Tensor with Repeated Blocks mswc24 local-correction resolved · cited ×22 (tex)
2026-10-02Repeated Overlapping Blocks with a Small Weight Sum mswc24 scope-restriction resolved · cited ×1 (tex)
2026-09-30; chain-length restriction resolved 2026-10-04The Tree Circuit as a Multiscale Network: Two-Site Injectivity and Chain Length mswc24 scope-restriction resolved · cited ×3 (tex)
2026-10-03Exact Preparation at a Zero Subleading Transfer Spectrum mswc24 local-correction resolved · cited ×2 (tex)
2026-10-07; resolved 2026-10-08; interface labels, sampled guides and one ratio for all generic displacements 2026-10-08Guide Properties in the Angular Separation of Dyadic Repaintings openai26 scope-restriction resolved (tex)
2026-07-30Common Identity Coefficients in the Block Ground-Space Intersection pgvwc07 scope-restriction resolved · cited ×2 (tex)
2026-10-04Scope of the Formal Periodic Decomposition Relative to PGVWC07 pgvwc07 scope-restriction resolved · cited ×3 (tex)
2026-09-26Sequential Generation Without an Ancilla Needs Two Sites pgvwc07 local-correction resolved · cited ×3 (tex)
2026-10-02Sequential Generation With an Ancilla: Nonempty Chains and Ancillas pgvwc07 local-correction resolved · cited ×2 (tex)
2026-09-05Positive Block Dimensions in the PGVWC07 Canonical Form pgvwc07 local-correction resolved · cited ×1 (tex)
2026-05-12Scope of the Formal Canonical-Form Reductions Relative to PGVWC07 pgvwc07 scope-restriction resolved · cited ×15 (tex)
2026-05-12, updated 2026-09-05Scope of the Formal Block-Separation Lemmas Relative to PGVWC07 Uniqueness pgvwc07 scope-restriction resolved · cited ×5 (tex)
2026-10-08Nonempty parties in distributed density compression polypeps local-correction resolved · cited ×1 (tex)
2026-10-08Bounded-Change Expansions of Births, Deaths and Exchanges polypeps scope-restriction resolved (tex)
2026-10-07Party Ownership in the Elimination of Normalized Pair Effects polypeps scope-restriction resolved · cited ×1 (tex)
2026-10-09The Polynomial Count of the Small-Patch Rewrite polypeps scope-restriction resolved · cited ×1 (tex)
2026-09-26The Interaction Range in the Block-Injective Parent-Hamiltonian Gap rmp scope-restriction resolved · cited ×15 (tex)
2026-10-02Injective PEPS Parent Interactions: the Physical Reconstruction Condition rmp local-correction resolved · cited ×4 (tex)
2026-04-30Normal Parent-Hamiltonian Range Reduction in Cirac–Perez-Garcia–Schuch–Verstraete 2021 rmp scope-restriction resolved · cited ×17 (tex)
2026-09-25The Sign of \sigma_y in the Pauli Form of the AKLT Tensor rmp local-correction resolved · cited ×1 (tex)
2026-09-25Source-Notation Gap: The Majumdar–Ghosh Example Tensor rmp local-correction resolved · cited ×2 (tex)
2026-09-26The RVB Tensor: the Singlet Matrix on the Vacuum rmp local-correction resolved · cited ×1 (tex)
2026-10-04SPT Fixed Points with Time Reversal and Reflection rmp scope-restriction resolved · cited ×1 (tex)
2026-10-03SPT Fixed Points from a Supplied Projective Representation rmp scope-restriction resolved · cited ×1 (tex)
2026-10-03SPT Fixed Points with a Nontrivial Character rmp scope-restriction resolved · cited ×11 (tex)
2026-10-02Finite-Group Commutants: The Unital Qualification scp10 local-correction resolved · cited ×2 (tex)
2026-10-05Quantum-double Hamiltonian terms: normalization and local scope scp10 local-correction resolved · cited ×5 (tex)
2026-10-10The Virtual Unitary in the Symmetric Isometric Deformation spc11 scope-restriction resolved · cited ×3 (tex)
2026-07-26Schuch–Pérez-García–Cirac SPT Interpolation: Upper-Range Correction spc11 local-correction resolved · cited ×36 (tex)
2026-10-02Uniform Parent-Hamiltonian Gaps for Compact Normal Families spc11 scope-restriction resolved · cited ×18 (tex)
2026-10-02Strong and Weak Symmetries of Matrix Product Density Operators: Arbitrary Commuting Boundaries sun25 scope-restriction resolved · cited ×2 (tex)
2026-08-25The Mutual-Information Bound for Matrix Product Density Operators cpsv16 clarification resolved · cited ×4 (tex)
2026-07-27Vertical Canonical-Form Grouping in Proposition 4.13 cpsv16 clarification resolved · cited ×14 (tex)
2026-08-25The Nonzero-Coefficient Convention for CPSV16 Canonical Forms cpsv16 clarification resolved · cited ×27 (tex)
2026-08-25The marginal-support expansion in CPSV16 Appendix D.2 cpsv16 clarification resolved · cited ×2 (tex)
2026-08-25Normalization of the tensor printed in CPSV16 Example 4.12 cpsv16 clarification resolved · cited ×3 (tex)
2026-07-21Per-Pair Support in the CPSV16 Figure 11 Decomposition cpsv16 clarification resolved · cited ×11 (tex)
2026-08-25Global and Per-Sector Unit-Weight Witnesses in the CPSV16 BNT Argument cpsv16 clarification resolved · cited ×7 (tex)
2026-05-11Projective Reading of Proportional MPVs in CPSV16 cpsv16 clarification resolved · cited ×5 (tex)
2026-05-08Power Sums in the BNT Weight Comparison cpsv16 clarification historical · cited ×5 (tex)
2026-07-10The Projector-Closure Sufficient Condition for Canonical Form cpsv16 clarification resolved · cited ×5 (tex)
2026-07-26Length-Dependent Scalars Do Not Determine Copy Weights in the Proportional BNT Theorem cpsv16 clarification resolved · cited ×2 (tex)
2026-07-15Closure record for saturation of the area law from MPDO renormalization fixed points cpsv16 clarification resolved · cited ×6 (tex)
2026-05-10Common Sector Relabeling as an Unconditional Identity cpsv16 clarification resolved (tex)
2026-08-25Nilpotent Basis Elements in the Simple-Tensor Definition of Cirac–Pérez-García–Schuch–Verstraete cpsv16 clarification resolved · cited ×2 (tex)
2026-08-25The CPSV16 Unit-Weight Convention and Renormalization-Fixed-Point Scale cpsv16 clarification resolved · cited ×3 (tex)
2026-08-25Zero correlation length uses the physical-trace transfer in Cirac–Perez-Garcia–Schuch–Verstraete 2017 cpsv16 clarification resolved · cited ×4 (tex)
2026-05-30Removing Length-Zero Bookkeeping from the Blocked Canonical-Form Decomposition cpsv16 clarification resolved · cited ×3 (tex)
2026-06-17Phase-Normalized Weights in the Normal-Canonical Implication to Irreducible Form dccsp17 clarification resolved · cited ×1 (tex)
2026-08-29Circle and Nonzero-Complex Coefficients in Degree-Two Cohomology fbc25 clarification resolved · cited ×2 (tex)
2026-09-04CZX Defect Domains from the Source Diagrams fbc25 clarification resolved · cited ×18 (tex)
2026-07-18The Product-Marginal Reference in the Relative-Entropy Form of Strong Subadditivity hjpw04 clarification resolved (tex)
2026-10-02Finite-Range Knabe Coefficients for Cyclic and Open Chains knabe88 clarification resolved · cited ×22 (tex)
2026-09-03Nilpotency Length One after Blocking: A Terminology Offset mgsc18 clarification resolved · cited ×3 (tex)
2026-09-26Nonzero Weights in the MPU Canonical Form mpu clarification resolved · cited ×4 (tex)
2026-08-25Nil-Matrix Product-Length Bound in the MPU Blocking Argument mpu clarification resolved (tex)
2026-05-06Injective PEPS Fundamental Theorem: Section 3 Route peps clarification resolved · cited ×63 (tex)
2026-04-30Common Blocking and Span Equality in the Non-periodic MPS Fundamental Theorem rmp clarification resolved (tex)

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