@techreport{gap:cpgsv17_bicf_block_separation,
  author      = {The {TNLean} contributors},
  title       = {Sharp Finite-Length Block Separation for Canonical-Form Tensors},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_bicf\_block\_separation},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_bicf_block_separation.pdf},
}

@techreport{gap:cpgsv17_blocked_chi_uniformity,
  author      = {The {TNLean} contributors},
  title       = {CPGSV17 Blocked-Basis Chi Families and Uniform BNT Labels},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_blocked\_chi\_uniformity},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_blocked_chi_uniformity.pdf},
}

@techreport{gap:cpgsv17_mpdo_blocked_rfp_physical_transport,
  author      = {The {TNLean} contributors},
  title       = {Physical-Isometry Transport for the Blocked MPDO Fixed Point},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_mpdo\_blocked\_rfp\_physical\_transport},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_mpdo_blocked_rfp_physical_transport.pdf},
}

@techreport{gap:cpgsv17_mpdo_mutual_information_bound,
  author      = {The {TNLean} contributors},
  title       = {The Mutual-Information Bound for Matrix Product Density Operators},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_mpdo\_mutual\_information\_bound},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_mpdo_mutual_information_bound.pdf},
}

@techreport{gap:cpgsv17_mpdo_s0_trace_subspin_typo,
  author      = {The {TNLean} contributors},
  title       = {The Final Traced Subspin in the Definition of S\_0},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_mpdo\_s0\_trace\_subspin\_typo},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_mpdo_s0_trace_subspin_typo.pdf},
}

@techreport{gap:cpgsv17_mpdo_sal_zcl_eta_local_structure,
  author      = {The {TNLean} contributors},
  title       = {The SAL to Eta-Local Structure Step in Cirac--Perez-Garcia--Schuch--Verstraete 2017 Appendix C.2},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_mpdo\_sal\_zcl\_eta\_local\_structure},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_mpdo_sal_zcl_eta_local_structure.pdf},
}

@techreport{gap:cpgsv17_mpdo_theorem_4_9_implication_label,
  author      = {The {TNLean} contributors},
  title       = {The Implication Label in the Proof of MPDO Theorem 4.9},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_mpdo\_theorem\_4\_9\_implication\_label},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_mpdo_theorem_4_9_implication_label.pdf},
}

@techreport{gap:cpgsv17_mpdo_zero_weight_preparation_completion,
  author      = {The {TNLean} contributors},
  title       = {Zero-Weight Sector Completions in the MPDO Refinement Map},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_mpdo\_zero\_weight\_preparation\_completion},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_mpdo_zero_weight_preparation_completion.pdf},
}

@techreport{gap:cpgsv17_periodic_sector_projector,
  author      = {The {TNLean} contributors},
  title       = {The Periodic-Sector Argument in Proposition 4.13},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_periodic\_sector\_projector},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_periodic_sector_projector.pdf},
}

@techreport{gap:cpgsv17_pf_rank_one,
  author      = {The {TNLean} contributors},
  title       = {The Perron--Frobenius Rank-One Step in Cirac--Perez-Garcia--Schuch--Verstraete 2017 Appendix C.2},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_pf\_rank\_one},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_pf_rank_one.pdf},
}

@techreport{gap:cpgsv17_vertical_cf_grouping,
  author      = {The {TNLean} contributors},
  title       = {Vertical Canonical-Form Grouping in Proposition 4.13},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_vertical\_cf\_grouping},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_vertical_cf_grouping.pdf},
}

@techreport{gap:cpgsv17_vertical_diagonal_restriction,
  author      = {The {TNLean} contributors},
  title       = {Diagonal Restriction and the Vertical Canonical Form in Proposition 4.13},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_vertical\_diagonal\_restriction},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_vertical_diagonal_restriction.pdf},
}

@techreport{gap:cpgsv17_vertical_isometry_zero_sector,
  author      = {The {TNLean} contributors},
  title       = {The Vertical Canonical Form Retains Only the Nonzero Physical Sectors},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_vertical\_isometry\_zero\_sector},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_vertical_isometry_zero_sector.pdf},
}

@techreport{gap:cpgsv17_vertical_tensor_definition,
  author      = {The {TNLean} contributors},
  title       = {The Vertical Direction in Proposition 4.13 Is the Index-Exchanged Tensor},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv17\_vertical\_tensor\_definition},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv17_vertical_tensor_definition.pdf},
}

@techreport{gap:cpgsv21_block_diagonal_parent_ground_space,
  author      = {The {TNLean} contributors},
  title       = {Block-Diagonal Boundary Conditions in the Degenerate Parent-Hamiltonian Ground Space},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv21\_block\_diagonal\_parent\_ground\_space},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv21_block_diagonal_parent_ground_space.pdf},
}

@techreport{gap:cpgsv21_martingale_overlap,
  author      = {The {TNLean} contributors},
  title       = {The Martingale Principal-Angle Estimate for MPS Parent Hamiltonians},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv21\_martingale\_overlap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv21_martingale_overlap.pdf},
}

@techreport{gap:cpgsv21_normal_range_reduction,
  author      = {The {TNLean} contributors},
  title       = {Normal Parent-Hamiltonian Range Reduction in Cirac--Perez-Garcia--Schuch--Verstraete 2021},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpgsv21\_normal\_range\_reduction},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpgsv21_normal_range_reduction.pdf},
}

@techreport{gap:cpsv16_active_physical_support_compression,
  author      = {The {TNLean} contributors},
  title       = {Active physical support compression in the CPSV16 commuting-form argument},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_active\_physical\_support\_compression},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_active_physical_support_compression.pdf},
}

@techreport{gap:cpsv16_blocked_operator_trace_ratio_exponent,
  author      = {The {TNLean} contributors},
  title       = {The Trace-Ratio Exponent in the Blocked Vertical-Operator Formula},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_blocked\_operator\_trace\_ratio\_exponent},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_blocked_operator_trace_ratio_exponent.pdf},
}

@techreport{gap:cpsv16_bnt_characterization_active_blocks,
  author      = {The {TNLean} contributors},
  title       = {Active Canonical-Form Blocks in the BNT Characterization},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_bnt\_characterization\_active\_blocks},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_bnt_characterization_active_blocks.pdf},
}

@techreport{gap:cpsv16_bnt_rate_quantification,
  author      = {The {TNLean} contributors},
  title       = {Historical Note: Rate-Quantified BNT Cross-Overlap Decay for a Retired Projection Argument},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_bnt\_rate\_quantification},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_bnt_rate_quantification.pdf},
}

@techreport{gap:cpsv16_bnt_uniqueness_zero_coefficient,
  author      = {The {TNLean} contributors},
  title       = {BNT Uniqueness and Zero Coefficients in CPSV16},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_bnt\_uniqueness\_zero\_coefficient},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_bnt_uniqueness_zero_coefficient.pdf},
}

@techreport{gap:cpsv16_canonical_form_renormalization_flow_phase_gap,
  author      = {The {TNLean} contributors},
  title       = {A Phase Obstruction to Canonical-Form Renormalization-Flow Convergence},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_canonical\_form\_renormalization\_flow\_phase\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_canonical_form_renormalization_flow_phase_gap.pdf},
}

@techreport{gap:cpsv16_cf_normalization_and_proportional_comparison,
  author      = {The {TNLean} contributors},
  title       = {Canonical-Form Weight Normalization and the Proportional MPV Comparison},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_cf\_normalization\_and\_proportional\_comparison},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_cf_normalization_and_proportional_comparison.pdf},
}

@techreport{gap:cpsv16_commuting_form_to_sal,
  author      = {The {TNLean} contributors},
  title       = {The Commuting-Form-to-SAL Implication for Simple MPDOs},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_commuting\_form\_to\_sal},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_commuting_form_to_sal.pdf},
}

@techreport{gap:cpsv16_decorrelation_slice_expansion_fix,
  author      = {The {TNLean} contributors},
  title       = {The marginal-support expansion in CPSV16 Appendix D.2},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_decorrelation\_slice\_expansion\_fix},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_decorrelation_slice_expansion_fix.pdf},
}

@techreport{gap:cpsv16_equalMPS_gauge_phase_gap,
  author      = {The {TNLean} contributors},
  title       = {CPSV16 Lemma equalMPS Gauge-Phase Components and Resolution},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_equalMPS\_gauge\_phase\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_equalMPS_gauge_phase_gap.pdf},
}

@techreport{gap:cpsv16_exact_arithmetic_scope,
  author      = {The {TNLean} contributors},
  title       = {Exact arithmetic scope for CPSV16 Examples 4.10 and 4.11},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_exact\_arithmetic\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_exact_arithmetic_scope.pdf},
}

@techreport{gap:cpsv16_example_4_12_normalization,
  author      = {The {TNLean} contributors},
  title       = {Normalization of the tensor printed in CPSV16 Example 4.12},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_example\_4\_12\_normalization},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_example_4_12_normalization.pdf},
}

@techreport{gap:cpsv16_examples_4_10_4_11_entropy,
  author      = {The {TNLean} contributors},
  title       = {Finite-Ring Entropy Corrections for CPSV16 Examples 4.10 and 4.11},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_examples\_4\_10\_4\_11\_entropy},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_examples_4_10_4_11_entropy.pdf},
}

@techreport{gap:cpsv16_figure11_fusion_coisometry,
  author      = {The {TNLean} contributors},
  title       = {The Figure 11 Fusion Map Is a Coisometry onto the Active Sectors},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_figure11\_fusion\_coisometry},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_figure11_fusion_coisometry.pdf},
}

@techreport{gap:cpsv16_figure11_per_pair_support,
  author      = {The {TNLean} contributors},
  title       = {Per-Pair Support in the CPSV16 Figure 11 Decomposition},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_figure11\_per\_pair\_support},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_figure11_per_pair_support.pdf},
}

@techreport{gap:cpsv16_fixed_block_cancellation,
  author      = {The {TNLean} contributors},
  title       = {Historical Note: the Fixed-Block Cancellation Step in CPSV16 Theorem II.1},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_fixed\_block\_cancellation},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_fixed_block_cancellation.pdf},
}

@techreport{gap:cpsv16_ft_one_copy_scope_restriction,
  author      = {The {TNLean} contributors},
  title       = {Basis-of-Representatives Scope Restriction in the Fundamental Theorem Formalization},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_ft\_one\_copy\_scope\_restriction},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_ft_one_copy_scope_restriction.pdf},
}

@techreport{gap:cpsv16_global_vs_persector_unit_witness,
  author      = {The {TNLean} contributors},
  title       = {Global and Per-Sector Unit-Weight Witnesses in the CPSV16 BNT Argument},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_global\_vs\_persector\_unit\_witness},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_global_vs_persector_unit_witness.pdf},
}

@techreport{gap:cpsv16_gsnnch_sector_decomposition,
  author      = {The {TNLean} contributors},
  title       = {The Sector Decomposition in the GSNNCH Definition of Cirac--P{\'{e}}rez-Garc{\'{i}}a--Schuch--Verstraete},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_gsnnch\_sector\_decomposition},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_gsnnch_sector_decomposition.pdf},
}

@techreport{gap:cpsv16_nncph_ground_state_scope,
  author      = {The {TNLean} contributors},
  title       = {The NNCPH ground-state clause in Cirac--Perez-Garcia--Schuch--Verstraete 2016},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_nncph\_ground\_state\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_nncph_ground_state_scope.pdf},
}

@techreport{gap:cpsv16_nondominant_per_block_projection,
  author      = {The {TNLean} contributors},
  title       = {Historical Note: Non-Dominant Per-Block Projection in CPSV16 {\S} II Step 1},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_nondominant\_per\_block\_projection},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_nondominant_per_block_projection.pdf},
}

@techreport{gap:cpsv16_nonzero_proportionality_reading,
  author      = {The {TNLean} contributors},
  title       = {Projective Reading of Proportional MPVs in CPSV16},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_nonzero\_proportionality\_reading},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_nonzero_proportionality_reading.pdf},
}

@techreport{gap:cpsv16_parent_commuting_hamiltonian_scope,
  author      = {The {TNLean} contributors},
  title       = {The parent commuting Hamiltonian condition in Cirac--Perez-Garcia--Schuch--Verstraete 2016},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_parent\_commuting\_hamiltonian\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_parent_commuting_hamiltonian_scope.pdf},
}

@techreport{gap:cpsv16_power_sum_alternative_route,
  author      = {The {TNLean} contributors},
  title       = {Power Sums in the BNT Weight Comparison},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_power\_sum\_alternative\_route},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_power_sum_alternative_route.pdf},
}

@techreport{gap:cpsv16_projector_closure_canonical_form,
  author      = {The {TNLean} contributors},
  title       = {The Projector-Closure Sufficient Condition for Canonical Form},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_projector\_closure\_canonical\_form},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_projector_closure_canonical_form.pdf},
}

@techreport{gap:cpsv16_proportional_length_scalar_gap,
  author      = {The {TNLean} contributors},
  title       = {Length-Dependent Scalars Do Not Determine Copy Weights in the Proportional BNT Theorem},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_proportional\_length\_scalar\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_proportional_length_scalar_gap.pdf},
}

@techreport{gap:cpsv16_pure_zcl_adjacent_gap_cid_scope,
  author      = {The {TNLean} contributors},
  title       = {Adjacent regions obstruct the unrestricted CID forward implication in Cirac--Perez-Garcia--Schuch--Verstraete 2017},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_pure\_zcl\_adjacent\_gap\_cid\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_pure_zcl_adjacent_gap_cid_scope.pdf},
}

@techreport{gap:cpsv16_pure_zcl_local_orthogonality_scope,
  author      = {The {TNLean} contributors},
  title       = {Pure zero correlation length and local orthogonality in Cirac--Perez-Garcia--Schuch--Verstraete 2017},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_pure\_zcl\_local\_orthogonality\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_pure_zcl_local_orthogonality_scope.pdf},
}

@techreport{gap:cpsv16_pure_zcl_raw_weight_counterexample,
  author      = {The {TNLean} contributors},
  title       = {A raw-weight counterexample to the pure-state ZCL equivalence in Cirac--Perez-Garcia--Schuch--Verstraete 2017},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_pure\_zcl\_raw\_weight\_counterexample},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_pure_zcl_raw_weight_counterexample.pdf},
}

@techreport{gap:cpsv16_purification_rfp_definition,
  author      = {The {TNLean} contributors},
  title       = {Purification RFP in Cirac--Perez-Garcia--Schuch--Verstraete 2017},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_purification\_rfp\_definition},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_purification_rfp_definition.pdf},
}

@techreport{gap:cpsv16_renormalization_flow_index_typo,
  author      = {The {TNLean} contributors},
  title       = {The Index Typo in the Pure-State Renormalization-Flow Equation},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_renormalization\_flow\_index\_typo},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_renormalization_flow_index_typo.pdf},
}

@techreport{gap:cpsv16_rfp_gauge_pure_equivalence_false,
  author      = {The {TNLean} contributors},
  title       = {The Pure-State Blocking-up-to-Gauge Equivalence Is False},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_rfp\_gauge\_pure\_equivalence\_false},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_rfp_gauge_pure_equivalence_false.pdf},
}

@techreport{gap:cpsv16_rfp_isometry_scope,
  author      = {The {TNLean} contributors},
  title       = {Per-block RFP Isometry Form and the Source Isometry Condition in CPSV16},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_rfp\_isometry\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_rfp_isometry_scope.pdf},
}

@techreport{gap:cpsv16_rfp_sal_data_processing,
  author      = {The {TNLean} contributors},
  title       = {Closure record for saturation of the area law from MPDO renormalization fixed points},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_rfp\_sal\_data\_processing},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_rfp_sal_data_processing.pdf},
}

@techreport{gap:cpsv16_sector_relabeling_hypothesis,
  author      = {The {TNLean} contributors},
  title       = {Common Sector Relabeling as an Unconditional Identity},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_sector\_relabeling\_hypothesis},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_sector_relabeling_hypothesis.pdf},
}

@techreport{gap:cpsv16_simple_tensor_nilpotency,
  author      = {The {TNLean} contributors},
  title       = {Nilpotent Basis Elements in the Simple-Tensor Definition of Cirac--P{\'{e}}rez-Garc{\'{i}}a--Schuch--Verstraete},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_simple\_tensor\_nilpotency},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_simple_tensor_nilpotency.pdf},
}

@techreport{gap:cpsv16_ssa_equality_hayashi_markov,
  author      = {The {TNLean} contributors},
  title       = {Closure Record for the Strong-Subadditivity Equality Characterization and Hayashi--Markov Decomposition},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_ssa\_equality\_hayashi\_markov},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_ssa_equality_hayashi_markov.pdf},
}

@techreport{gap:cpsv16_ssa_from_lieb_route,
  author      = {The {TNLean} contributors},
  title       = {Strong Subadditivity as a Standalone Axiom and Its Lieb-Concavity Elimination Route},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_ssa\_from\_lieb\_route},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_ssa_from_lieb_route.pdf},
}

@techreport{gap:cpsv16_topological_gibbs_length_one,
  author      = {The {TNLean} contributors},
  title       = {The Domain Boundary of the Topological Gibbs Decomposition},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_topological\_gibbs\_length\_one},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_topological_gibbs_length_one.pdf},
}

@techreport{gap:cpsv16_topological_gibbs_physical_complement,
  author      = {The {TNLean} contributors},
  title       = {The Physical Complement in the Topological Gibbs Decomposition},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_topological\_gibbs\_physical\_complement},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_topological_gibbs_physical_complement.pdf},
}

@techreport{gap:cpsv16_topological_projector_recursion,
  author      = {The {TNLean} contributors},
  title       = {The Arbitrary-Chain Topological Projector Recursion},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_topological\_projector\_recursion},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_topological_projector_recursion.pdf},
}

@techreport{gap:cpsv16_two_layer_sector_refinement,
  author      = {The {TNLean} contributors},
  title       = {Historical Note: Two-Layer Sector Refinement of CPSV16 eq:II\_ABasicTensors},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_two\_layer\_sector\_refinement},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_two_layer_sector_refinement.pdf},
}

@techreport{gap:cpsv16_two_site_sector_unitary_gauge_gap,
  author      = {The {TNLean} contributors},
  title       = {A Mixed-Prefix Repair of the Two-Site Sector Comparison},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_two\_site\_sector\_unitary\_gauge\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_two_site_sector_unitary_gauge_gap.pdf},
}

@techreport{gap:cpsv16_unit_weight_rfp_scale_tension,
  author      = {The {TNLean} contributors},
  title       = {The CPSV16 Unit-Weight Convention and Renormalization-Fixed-Point Scale},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_unit\_weight\_rfp\_scale\_tension},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_unit_weight_rfp_scale_tension.pdf},
}

@techreport{gap:cpsv16_vertical_sector_invertibility,
  author      = {The {TNLean} contributors},
  title       = {CPSV16 Vertical-Sector Invertibility and Sector Relabelling},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_vertical\_sector\_invertibility},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_vertical_sector_invertibility.pdf},
}

@techreport{gap:cpsv16_zcl_canonical_form_normalization,
  author      = {The {TNLean} contributors},
  title       = {Zero correlation length uses the physical-trace transfer in Cirac--Perez-Garcia--Schuch--Verstraete 2017},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_zcl\_canonical\_form\_normalization},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_zcl_canonical_form_normalization.pdf},
}

@techreport{gap:cpsv16_zero_tail_length_zero_decomposition,
  author      = {The {TNLean} contributors},
  title       = {Removing Length-Zero Bookkeeping from the Blocked Canonical-Form Decomposition},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv16\_zero\_tail\_length\_zero\_decomposition},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv16_zero_tail_length_zero_decomposition.pdf},
}

@techreport{gap:cpsv17_transfer_trace_power,
  author      = {The {TNLean} contributors},
  title       = {Shifted Trace Powers and the Exact MPU Transfer Spectrum},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {cpsv17\_transfer\_trace\_power},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/cpsv17_transfer_trace_power.pdf},
}

@techreport{gap:dccsp17_normal_canonical_irreducible_form_weights,
  author      = {The {TNLean} contributors},
  title       = {Phase-Normalized Weights in the Normal-Canonical Implication to Irreducible Form},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {dccsp17\_normal\_canonical\_irreducible\_form\_weights},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/dccsp17_normal_canonical_irreducible_form_weights.pdf},
}

@techreport{gap:dccsp17_periodic_overlap_route_alignment,
  author      = {The {TNLean} contributors},
  title       = {Proof-Route Alignment for the Periodic Overlap Dichotomy (de las Cuevas--Cirac--Schuch--P{\'{e}}rez-Garc{\'{i}}a)},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {dccsp17\_periodic\_overlap\_route\_alignment},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/dccsp17_periodic_overlap_route_alignment.pdf},
}

@techreport{gap:dccsp17_root_kraus_rank_thm41,
  author      = {The {TNLean} contributors},
  title       = {The Root-Channel Kraus-Rank Step in Theorem 4.1},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {dccsp17\_root\_kraus\_rank\_thm41},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/dccsp17_root_kraus_rank_thm41.pdf},
}

@techreport{gap:hjpw04_petz_factorization_maximally_mixed_scope,
  author      = {The {TNLean} contributors},
  title       = {Support scope of the HJPW product-reference Petz factorization},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {hjpw04\_petz\_factorization\_maximally\_mixed\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/hjpw04_petz_factorization_maximally_mixed_scope.pdf},
}

@techreport{gap:hjpw04_ssa_product_marginal_reference,
  author      = {The {TNLean} contributors},
  title       = {The Product-Marginal Reference in the Relative-Entropy Form of Strong Subadditivity},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {hjpw04\_ssa\_product\_marginal\_reference},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/hjpw04_ssa_product_marginal_reference.pdf},
}

@techreport{gap:knabe88_finite_range_coefficient,
  author      = {The {TNLean} contributors},
  title       = {The Finite-Range Cyclic Knabe Coefficient},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {knabe88\_finite\_range\_coefficient},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/knabe88_finite_range_coefficient.pdf},
}

@techreport{gap:mpu_blocking_rank_product_exponent,
  author      = {The {TNLean} contributors},
  title       = {The Endpoint Rank-Product Exponent in MPU Index Well-Definedness},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_blocking\_rank\_product\_exponent},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_blocking_rank_product_exponent.pdf},
}

@techreport{gap:mpu_canonical_form_full_support,
  author      = {The {TNLean} contributors},
  title       = {Full Support in MPU Normality and Theorem III.8},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_canonical\_form\_full\_support},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_canonical_form_full_support.pdf},
}

@techreport{gap:mpu_equivalence_fixed_bond,
  author      = {The {TNLean} contributors},
  title       = {Fixed Virtual Bond Dimension in MPU Tensor Equivalence},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_equivalence\_fixed\_bond},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_equivalence_fixed_bond.pdf},
}

@techreport{gap:mpu_nil_matrix_bound,
  author      = {The {TNLean} contributors},
  title       = {Nil-Matrix Product-Length Bound in the MPU Blocking Argument},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_nil\_matrix\_bound},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_nil_matrix_bound.pdf},
}

@techreport{gap:mpu_one_letter_mixed_residual_trace,
  author      = {The {TNLean} contributors},
  title       = {MPU One-Letter Mixed Residual Trace: Resolved Local Correction},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_one\_letter\_mixed\_residual\_trace},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_one_letter_mixed_residual_trace.pdf},
}

@techreport{gap:mpu_reduced_representative_supplied_fixed_pair,
  author      = {The {TNLean} contributors},
  title       = {The Supplied Fixed Pair in the Reduced-Representative Step of Proposition IV.5},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_reduced\_representative\_supplied\_fixed\_pair},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_reduced_representative_supplied_fixed_pair.pdf},
}

@techreport{gap:mpu_sourceu_range_restriction,
  author      = {The {TNLean} contributors},
  title       = {The Hidden Range Restriction in the Source-u Contraction},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_sourceu\_range\_restriction},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_sourceu_range_restriction.pdf},
}

@techreport{gap:mpu_two_projection_projector_typo,
  author      = {The {TNLean} contributors},
  title       = {Two-Projection Decomposition: Repeated-Projector Typo},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {mpu\_two\_projection\_projector\_typo},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/mpu_two_projection_projector_typo.pdf},
}

@techreport{gap:peps_gaugeConsistency_connectivity_gap,
  author      = {The {TNLean} contributors},
  title       = {Injective PEPS Gauge Consistency Needs a Connectivity Hypothesis},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {peps\_gaugeConsistency\_connectivity\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/peps_gaugeConsistency_connectivity_gap.pdf},
}

@techreport{gap:peps_gauge_edge_scalars,
  author      = {The {TNLean} contributors},
  title       = {PEPS Gauge Uniqueness and Balanced Edge Scalars},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {peps\_gauge\_edge\_scalars},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/peps_gauge_edge_scalars.pdf},
}

@techreport{gap:peps_injective_ft_section3_route,
  author      = {The {TNLean} contributors},
  title       = {Injective PEPS Fundamental Theorem: Section 3 Route},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {peps\_injective\_ft\_section3\_route},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/peps_injective_ft_section3_route.pdf},
}

@techreport{gap:peps_normal_ft_2d_overlap,
  author      = {The {TNLean} contributors},
  title       = {The Two-Dimensional Overlapping-Window Strengthening of the Normal PEPS Fundamental Theorem},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {peps\_normal\_ft\_2d\_overlap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/peps_normal_ft_2d_overlap.pdf},
}

@techreport{gap:peps_normal_ft_section3_route,
  author      = {The {TNLean} contributors},
  title       = {Normal PEPS Fundamental Theorem: Section 3 Route},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {peps\_normal\_ft\_section3\_route},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/peps_normal_ft_section3_route.pdf},
}

@techreport{gap:pgvwc07_common_identity_coefficients,
  author      = {The {TNLean} contributors},
  title       = {Common Identity Coefficients in the Block Ground-Space Intersection},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgvwc07\_common\_identity\_coefficients},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgvwc07_common_identity_coefficients.pdf},
}

@techreport{gap:pgvwc07_direct_sum_input,
  author      = {The {TNLean} contributors},
  title       = {The Direct-Sum Input from the Older MPS Representation Paper},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgvwc07\_direct\_sum\_input},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgvwc07_direct_sum_input.pdf},
}

@techreport{gap:pgvwc07_intertwiner_chain_off_by_one,
  author      = {The {TNLean} contributors},
  title       = {The Intertwiner Count in the Quadratic Reconstruction Argument},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgvwc07\_intertwiner\_chain\_off\_by\_one},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgvwc07_intertwiner_chain_off_by_one.pdf},
}

@techreport{gap:pgvwc07_periodic_decomposition_scope,
  author      = {The {TNLean} contributors},
  title       = {Scope of the Formal Periodic Decomposition Relative to PGVWC07},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgvwc07\_periodic\_decomposition\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgvwc07_periodic_decomposition_scope.pdf},
}

@techreport{gap:pgvwc07_site_independent_scope,
  author      = {The {TNLean} contributors},
  title       = {Scope of the Formal Site-Independent Construction Relative to PGVWC07},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgvwc07\_site\_independent\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgvwc07_site_independent_scope.pdf},
}

@techreport{gap:pgvwc07_ti_canonical_form_scope,
  author      = {The {TNLean} contributors},
  title       = {Scope of the Formal Canonical-Form Reductions Relative to PGVWC07},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgvwc07\_ti\_canonical\_form\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgvwc07_ti_canonical_form_scope.pdf},
}

@techreport{gap:pgvwc07_ti_uniqueness_scope,
  author      = {The {TNLean} contributors},
  title       = {Scope of the Formal Block-Separation Lemmas Relative to PGVWC07 Uniqueness},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgvwc07\_ti\_uniqueness\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgvwc07_ti_uniqueness_scope.pdf},
}

@techreport{gap:pgwsvc08_string_order_virtual_boundary,
  author      = {The {TNLean} contributors},
  title       = {PGWSVC08 Physical String Order versus Virtual-Boundary Nondecay},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {pgwsvc08\_string\_order\_virtual\_boundary},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/pgwsvc08_string_order_virtual_boundary.pdf},
}

@techreport{gap:rmp_aklt_continuous_rotation_gap,
  author      = {The {TNLean} contributors},
  title       = {Scope Note: The AKLT On-Site SO(3) Symmetry Is Formalized; Its Cohomological Classification Is Not},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {rmp\_aklt\_continuous\_rotation\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/rmp_aklt_continuous_rotation_gap.pdf},
}

@techreport{gap:rmp_common_blocking_span_equality,
  author      = {The {TNLean} contributors},
  title       = {Common Blocking and Span Equality in the Non-periodic MPS Fundamental Theorem},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {rmp\_common\_blocking\_span\_equality},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/rmp_common_blocking_span_equality.pdf},
}

@techreport{gap:rmp_conditional_after_blocking_ft_statement,
  author      = {The {TNLean} contributors},
  title       = {Conditional After-Blocking Fundamental Theorem versus the CPSV Statement},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {rmp\_conditional\_after\_blocking\_ft\_statement},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/rmp_conditional_after_blocking_ft_statement.pdf},
}

@techreport{gap:rmp_example_parent_hamiltonian_scope,
  author      = {The {TNLean} contributors},
  title       = {Example Parent Hamiltonians in Cirac--Perez-Garcia--Schuch--Verstraete 2021},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {rmp\_example\_parent\_hamiltonian\_scope},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/rmp_example_parent_hamiltonian_scope.pdf},
}

@techreport{gap:rmp_majumdar_ghosh_tensor_gap,
  author      = {The {TNLean} contributors},
  title       = {Source-Notation Gap: The Majumdar--Ghosh Example Tensor},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {rmp\_majumdar\_ghosh\_tensor\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/rmp_majumdar_ghosh_tensor_gap.pdf},
}

@techreport{gap:rmp_nonperiodic_bnt_comparison_inputs,
  author      = {The {TNLean} contributors},
  title       = {Paper Comparison for BNT Inputs in the Non-periodic MPS Fundamental Theorem},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {rmp\_nonperiodic\_bnt\_comparison\_inputs},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/rmp_nonperiodic_bnt_comparison_inputs.pdf},
}

@techreport{gap:rmp_w_state_ti_bound,
  author      = {The {TNLean} contributors},
  title       = {Deferred Result: The Translation-Invariant Bond-Dimension Lower Bound for the W State},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {rmp\_w\_state\_ti\_bound},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/rmp_w_state_ti_bound.pdf},
}

@techreport{gap:spc11_spt_interpolation_upper_range,
  author      = {The {TNLean} contributors},
  title       = {Schuch--P{\'{e}}rez-Garc{\'{i}}a--Cirac SPT Interpolation: Upper-Range Correction},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {spc11\_spt\_interpolation\_upper\_range},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/spc11_spt_interpolation_upper_range.pdf},
}

@techreport{gap:spwc10_wielandt_one_step_subspace,
  author      = {The {TNLean} contributors},
  title       = {The One-Step Subspace in the Quantum Wielandt Inequality},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {spwc10\_wielandt\_one\_step\_subspace},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/spwc10_wielandt_one_step_subspace.pdf},
}

@techreport{gap:tnlean_algebraic_ft_same_state_combined_mpv_gap,
  author      = {The {TNLean} contributors},
  title       = {Fixed-Length Chain Equality Does Not Imply Combined-Tensor MPV Equality},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {tnlean\_algebraic\_ft\_same\_state\_combined\_mpv\_gap},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/tnlean_algebraic_ft_same_state_combined_mpv_gap.pdf},
}

@techreport{gap:tnlean_bnt_ft_theorem_surface,
  author      = {The {TNLean} contributors},
  title       = {Theorem Surface Audit for Canonical Form, BNT, and the Non-periodic MPS Fundamental Theorem},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {tnlean\_bnt\_ft\_theorem\_surface},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/tnlean_bnt_ft_theorem_surface.pdf},
}

@techreport{gap:tnlean_ft_dependency_audit,
  author      = {The {TNLean} contributors},
  title       = {Dependency Audit for the Non-periodic MPS Fundamental Theorem Blueprint},
  institution = {TNLean},
  type        = {Paper-gap note},
  number      = {tnlean\_ft\_dependency\_audit},
  year        = {2026},
  url         = {https://sirui-lu.com/TNLean/paper-gaps/tnlean_ft_dependency_audit.pdf},
}