{
  "schema_version": "1.0.0",
  "artifact_id": "qft.artifact.supersymmetry-duality.duality.global-form-lines-anomalies-map",
  "artifact_class": "three-panel integral charge-lattice, background-anomaly, and duality-wall map",
  "title": "Global form, line lattices, anomalies, and the S-duality wall",
  "evidence_date": "2026-08-24",
  "lifecycle_status": "materialized governed artifact; registry lifecycle and owner integration are recorded in provenance rather than inferred from file existence",
  "reader_question": "How do finite center-charge choices, active electromagnetic transport, continuous one-form backgrounds, and an S-duality wall fit together without conflating their scopes?",
  "dominant_point": "For su(2), the three maximal-isotropic center-charge subgroups form a closed S/T orbit of complete global theories; the same integral symplectic logic transports source-free Maxwell backgrounds and the mixed anomaly, while the S wall is invertible only after the complete flux, line, background, anomaly, and fusion data match.",
  "scope_separation": {
    "finite_center_panel": {
      "scope_id": "finite_Z2_center",
      "theory": "four-dimensional adjoint su(2) gauge theory after root and coroot screening",
      "group": "finite center-charge group Z_2 times Z_2",
      "objects": "center classes of Wilson-'t Hooft lines and maximal-isotropic genuine-line subgroups",
      "limitations": "The finite quotient omits the full weight and coweight labels, spins, monopole bubbling, and non-spin refinements."
    },
    "continuous_maxwell_panel": {
      "scope_id": "continuous_U1_maxwell",
      "theory": "compact source-free U(1) Maxwell theory with no dynamical electric or magnetic charges",
      "group": "continuous U(1) electric and magnetic one-form symmetries",
      "objects": "conserved two-form currents, compact two-form backgrounds, the mixed anomaly class, and the Lorentzian S wall",
      "limitations": "Dynamical charges break one or both continuous one-form symmetries, and global backgrounds require differential-cohomology data beyond local forms."
    },
    "shared_formalism": "Both scopes use an antisymmetric integral pairing and the same displayed S matrix after their ordered doublets are declared.",
    "prohibited_identification": "The continuous backgrounds (B_m,B_e) must not be identified with the finite Z_2 center-charge vectors; no cross-scope map is asserted."
  },
  "conventions": {
    "spacetime": "oriented four-dimensional Lorentzian spacetime with QFT.org metric (+---); on two-forms star squared equals -1",
    "finite_charge_order": "gamma_bar=(p_m,q_e)^T, magnetic first and electric second",
    "integral_charge_order": "gamma=(p_m,q_e)^T in Z^2",
    "period_order": "Pi=(a_D,a)^T",
    "central_charge": "Z_gamma=gamma^T Pi=p_m a_D+q_e a",
    "pairing_matrix": [
      [
        0,
        1
      ],
      [
        -1,
        0
      ]
    ],
    "dirac_pairing": "<gamma,gamma_prime>=p_m q_e_prime-q_e p_m_prime",
    "active_map": "An active matrix moves a physical charge column: gamma maps to M_gamma gamma.",
    "passive_map": "A passive matrix relabels the charge components under a basis or theory-label change and is the inverse of the corresponding active charge motion after the component order is matched.",
    "period_charge_relation": "Simultaneous transport preserving Z_gamma uses Pi maps to M_Pi Pi and gamma maps to M_gamma gamma with M_gamma=M_Pi^{-T}.",
    "background_order": "(B_m,B_e)^T, magnetic background first and electric background second",
    "field_strength_order": "(F,G)^T, with F magnetic-current numerator and G electric-current numerator",
    "maxwell_dual_field_strength": "G=(2 pi/e^2) star F-(theta/2 pi) F in the owner-page unit-flux normalization",
    "wall_orientation": "W=boundary(M_L)=-boundary(M_R), directed from the left theory to the right theory",
    "anomaly_representative": "I_5=2 pi i integral (B_e/2 pi) wedge d(B_m/2 pi); equality under S is equality of the closed-five-manifold class up to an exact form"
  },
  "finite_center_panel": {
    "algebra": "su(2)",
    "quotient_after_screening": "Z_2^2",
    "charge_class_order": [
      "su2",
      "so3_plus",
      "so3_minus"
    ],
    "charge_class_table": [
      {
        "id": "su2",
        "display_name": "SU(2)",
        "scope": "finite_Z2_center",
        "representative_charge_vector_pm_qe": [
          0,
          1
        ],
        "screened_charge_group": "Z_2 magnetic center class times Z_2 electric center class",
        "screening_rule": "Adjoint dynamical fields screen root and coroot charges but carry no center charge, leaving gamma_bar=(p_m,q_e) in Z_2^2.",
        "genuine_lines_mod_2": [
          [
            0,
            0
          ],
          [
            0,
            1
          ]
        ],
        "allowed_line_condition": "p_m congruent to 0 modulo 2",
        "global_form": "SU(2), the simply connected global form",
        "discrete_theta": "Unique simply connected choice; the SO(3) discrete-theta label does not apply.",
        "nonzero_line_interpretation": "fundamental center Wilson class",
        "mutual_locality_status": "pairing vanishes on the two-element subgroup",
        "maximal_isotropic_status": "L equals L-perpendicular and has order 2"
      },
      {
        "id": "so3_plus",
        "display_name": "SO(3)_+",
        "scope": "finite_Z2_center",
        "representative_charge_vector_pm_qe": [
          1,
          0
        ],
        "screened_charge_group": "Z_2 magnetic center class times Z_2 electric center class",
        "screening_rule": "Adjoint dynamical fields screen root and coroot charges but carry no center charge, leaving gamma_bar=(p_m,q_e) in Z_2^2.",
        "genuine_lines_mod_2": [
          [
            0,
            0
          ],
          [
            1,
            0
          ]
        ],
        "allowed_line_condition": "q_e congruent to 0 modulo 2",
        "global_form": "SO(3)=SU(2)/Z_2",
        "discrete_theta": "n=0, conventionally denoted SO(3)_+",
        "nonzero_line_interpretation": "pure magnetic center class",
        "mutual_locality_status": "pairing vanishes on the two-element subgroup",
        "maximal_isotropic_status": "L equals L-perpendicular and has order 2"
      },
      {
        "id": "so3_minus",
        "display_name": "SO(3)_-",
        "scope": "finite_Z2_center",
        "representative_charge_vector_pm_qe": [
          1,
          1
        ],
        "screened_charge_group": "Z_2 magnetic center class times Z_2 electric center class",
        "screening_rule": "Adjoint dynamical fields screen root and coroot charges but carry no center charge, leaving gamma_bar=(p_m,q_e) in Z_2^2.",
        "genuine_lines_mod_2": [
          [
            0,
            0
          ],
          [
            1,
            1
          ]
        ],
        "allowed_line_condition": "p_m congruent to q_e modulo 2",
        "global_form": "SO(3)=SU(2)/Z_2",
        "discrete_theta": "n=1, conventionally denoted SO(3)_-",
        "nonzero_line_interpretation": "dyonic center class",
        "mutual_locality_status": "pairing vanishes on the two-element subgroup",
        "maximal_isotropic_status": "L equals L-perpendicular and has order 2"
      }
    ],
    "pairing_table": {
      "representative_order": [
        "su2",
        "so3_plus",
        "so3_minus"
      ],
      "integer_pairing_matrix": [
        [
          0,
          -1,
          -1
        ],
        [
          1,
          0,
          1
        ],
        [
          1,
          -1,
          0
        ]
      ],
      "modulo_2_pairing_matrix": [
        [
          0,
          1,
          1
        ],
        [
          1,
          0,
          1
        ],
        [
          1,
          1,
          0
        ]
      ],
      "interpretation": "Each two-element genuine subgroup contains zero and one representative, so its internal pairing vanishes; any distinct nonzero class pairs nontrivially and cannot be added."
    },
    "maximal_isotropic_conditions": {
      "mutual_locality": "<L,L>=0 modulo 2",
      "cardinality": "|L|=2=sqrt(|Z_2^2|)",
      "perpendicular_test": "L=L-perpendicular under J",
      "completeness": "No additional independent center-charge class may be made genuine without violating mutual locality."
    },
    "action_table": [
      {
        "source": "su2",
        "S_target": "so3_plus",
        "T_target": "su2"
      },
      {
        "source": "so3_plus",
        "S_target": "su2",
        "T_target": "so3_minus"
      },
      {
        "source": "so3_minus",
        "S_target": "so3_minus",
        "T_target": "so3_plus"
      }
    ],
    "orbit_representatives": {
      "generated_by": [
        "S_gamma modulo 2",
        "T_gamma modulo 2"
      ],
      "representative": "su2",
      "closed_orbit": [
        "su2",
        "so3_plus",
        "so3_minus"
      ],
      "global_theory_status": "The orbit is an orbit of global theories with specified genuine lines and discrete theta data, not a self-duality orbit of the Lie algebra alone."
    }
  },
  "active_charge_and_period_panel": {
    "symplectic_generators": {
      "S": {
        "active_charge_matrix_pm_qe": [
          [
            0,
            1
          ],
          [
            -1,
            0
          ]
        ],
        "active_charge_rule": "(p_m,q_e) maps to (q_e,-p_m)",
        "period_matrix_aD_a": [
          [
            0,
            1
          ],
          [
            -1,
            0
          ]
        ],
        "period_rule": "(a_D,a) maps to (a,-a_D), hence tau maps to -1/tau",
        "inverse_transpose_check": "S_gamma=S_Pi^{-T}",
        "pairing_check": "S_gamma^T J S_gamma=J"
      },
      "T": {
        "active_charge_matrix_pm_qe": [
          [
            1,
            0
          ],
          [
            1,
            1
          ]
        ],
        "active_charge_rule": "(p_m,q_e) maps to (p_m,q_e+p_m)",
        "period_matrix_aD_a": [
          [
            1,
            -1
          ],
          [
            0,
            1
          ]
        ],
        "period_rule": "(a_D,a) maps to (a_D-a,a), hence tau maps to tau-1",
        "inverse_transpose_check": "T_gamma=T_Pi^{-T}",
        "pairing_check": "T_gamma^T J T_gamma=J"
      }
    },
    "active_passive_derivation_from_local_source": {
      "source_path": "src/content/docs/supersymmetry-duality/n4-s-duality-higher-dimensional/line-operators-global-forms-discrete-theta.md",
      "source_lines": "71-129",
      "source_component_order": "(q_e,p_m), written there as (e,m)",
      "source_passive_S_matrix_qe_pm": [
        [
          0,
          1
        ],
        [
          -1,
          0
        ]
      ],
      "source_passive_T_matrix_qe_pm": [
        [
          1,
          -1
        ],
        [
          0,
          1
        ]
      ],
      "reorder_matrix_from_qe_pm_to_pm_qe": [
        [
          0,
          1
        ],
        [
          1,
          0
        ]
      ],
      "reordered_passive_S_matrix_pm_qe": [
        [
          0,
          -1
        ],
        [
          1,
          0
        ]
      ],
      "reordered_passive_T_matrix_pm_qe": [
        [
          1,
          0
        ],
        [
          -1,
          1
        ]
      ],
      "active_S_is_inverse_of_reordered_passive_S": [
        [
          0,
          1
        ],
        [
          -1,
          0
        ]
      ],
      "active_T_is_inverse_of_reordered_passive_T": [
        [
          1,
          0
        ],
        [
          1,
          1
        ]
      ],
      "sign_explanation": "The local N=4 page explicitly calls its T charge rule passive. After reordering from (q_e,p_m) to (p_m,q_e), the active physical-line motion is the inverse, so q_e shifts by +p_m. Its compatible active period matrix shifts tau by -1; the inverse period map is the usual passive tau to tau+1 label change."
    }
  },
  "continuous_maxwell_panel": {
    "scope": "continuous_U1_maxwell",
    "regime": "source-free compact U(1) Maxwell theory, with no dynamical electrically or magnetically charged matter",
    "currents": {
      "magnetic_two_form_current": "j_m^(2)=F/(2 pi)",
      "electric_two_form_current": "j_e^(2)=G/(2 pi)",
      "conservation": [
        "dF=0",
        "dG=0"
      ],
      "symmetry_status": "Both continuous one-form symmetries exist only in the source-free regime; dynamical charges break the corresponding factors."
    },
    "background_map": {
      "ordered_column": "(B_m,B_e)^T",
      "active_S_matrix": [
        [
          0,
          1
        ],
        [
          -1,
          0
        ]
      ],
      "rule": "(B_m,B_e) maps to (B_e,-B_m)",
      "compact_normalization": "B_m/(2 pi) and B_e/(2 pi) are normalized compact two-form backgrounds; their global meaning is differential-cohomological."
    },
    "anomaly_class": {
      "five_manifold": "oriented Y_5 with boundary Y_5=M_4 when descent is retained",
      "representative": "I_5=2 pi i integral_Y5 (B_e/2 pi) wedge d(B_m/2 pi)",
      "transformed_representative": "I_5 maps to -2 pi i integral_Y5 (B_m/2 pi) wedge d(B_e/2 pi)",
      "closed_manifold_equivalence": "-integral B_m wedge dB_e equals integral B_e wedge dB_m on closed Y_5",
      "exact_difference": "The transformed and original representatives differ by -d(B_m wedge B_e), including the same 2 pi normalization factors.",
      "transport_status": "The mixed anomaly class is preserved by S on closed Y_5; with a boundary, the exact difference is interface descent data.",
      "global_refinement": "The differential-form representative does not by itself encode torsion sectors or the full compact differential-cohomology class.",
      "coefficient_check": {
        "basis": [
          "B_e wedge dB_m",
          "B_m wedge dB_e"
        ],
        "original_coefficients": [
          1,
          0
        ],
        "transformed_coefficients": [
          0,
          -1
        ],
        "closed_manifold_relation": "B_m wedge dB_e is equivalent to -B_e wedge dB_m",
        "reduced_transformed_coefficients": [
          1,
          0
        ]
      }
    },
    "S_wall": {
      "signature": "Lorentzian",
      "orientation": "W=boundary(M_L)=-boundary(M_R)",
      "action": "S_W=(1/2 pi) integral_W A_L wedge dA_R",
      "large_gauge_status": "coefficient is integrally normalized for compact U(1) connections",
      "matching_equations": [
        "F_R=G_L",
        "G_R=-F_L"
      ],
      "field_strength_matrix": [
        [
          0,
          1
        ],
        [
          -1,
          0
        ]
      ],
      "field_strength_rule": "(F_R,G_R)^T=S_gamma (F_L,G_L)^T",
      "line_transport_rule": "(p_m,q_e)^T maps actively by S_gamma",
      "wall_status": "The coupling realizes the local S matching conditions and is topological only after the complete quantum boundary problem is well defined.",
      "fusion_status": "Two equally oriented S walls implement S_gamma^2=-I, namely charge conjugation C; the reverse-oriented wall carries S_gamma^{-1}.",
      "invertibility_status": "Invertible only between complete theories whose flux sectors, genuine-line lattices, backgrounds, anomaly classes, zero modes, and counterterms are mapped; local equations alone are insufficient."
    }
  },
  "semantic_tables": {
    "charge_vectors_and_allowed_lines": "finite_center_panel.charge_class_table includes charge vectors, screening, allowed-line conditions, global form, discrete theta, mutual locality, and maximal-isotropic status",
    "pairing_table": "finite_center_panel.pairing_table gives the integer and modulo-two Dirac pairings in Chapter 9 order",
    "orbit_table": "finite_center_panel.action_table and orbit_representatives give every S and T image and the closed orbit",
    "background_anomaly_table": "continuous_maxwell_panel.background_map and anomaly_class give normalized background and anomaly transport",
    "wall_and_fusion_table": "continuous_maxwell_panel.S_wall gives action, matching equations, line map, wall status, fusion, and invertibility condition"
  },
  "text_graph": {
    "node_scope_rule": "Every node belongs either to finite_Z2_center or continuous_U1_maxwell; no node represents an identification between the two scopes.",
    "nodes": [
      {
        "id": "finite_su2",
        "scope": "finite_Z2_center",
        "label": "SU(2) line subgroup generated by (0,1)"
      },
      {
        "id": "finite_so3_plus",
        "scope": "finite_Z2_center",
        "label": "SO(3)_+ line subgroup generated by (1,0)"
      },
      {
        "id": "finite_so3_minus",
        "scope": "finite_Z2_center",
        "label": "SO(3)_- line subgroup generated by (1,1)"
      },
      {
        "id": "maxwell_left_fields",
        "scope": "continuous_U1_maxwell",
        "label": "left source-free field-strength doublet (F_L,G_L)"
      },
      {
        "id": "maxwell_right_fields",
        "scope": "continuous_U1_maxwell",
        "label": "right source-free field-strength doublet (F_R,G_R)"
      },
      {
        "id": "maxwell_left_backgrounds",
        "scope": "continuous_U1_maxwell",
        "label": "left compact background doublet (B_m,B_e)"
      },
      {
        "id": "maxwell_right_backgrounds",
        "scope": "continuous_U1_maxwell",
        "label": "S-transported compact background doublet (B_e,-B_m)"
      },
      {
        "id": "maxwell_anomaly_before",
        "scope": "continuous_U1_maxwell",
        "label": "mixed anomaly representative B_e wedge dB_m"
      },
      {
        "id": "maxwell_anomaly_after",
        "scope": "continuous_U1_maxwell",
        "label": "S image -B_m wedge dB_e in the same closed-manifold class"
      },
      {
        "id": "maxwell_S_wall",
        "scope": "continuous_U1_maxwell",
        "label": "integrally normalized Lorentzian S wall"
      },
      {
        "id": "maxwell_charge_conjugation",
        "scope": "continuous_U1_maxwell",
        "label": "fusion result C from S squared"
      }
    ],
    "edges": [
      {
        "id": "finite_S_swap",
        "scope": "finite_Z2_center",
        "type": "S action",
        "source": "finite_su2",
        "target": "finite_so3_plus",
        "label": "bidirectional S exchange modulo 2",
        "status": "pairing-preserving global-theory map"
      },
      {
        "id": "finite_S_fix",
        "scope": "finite_Z2_center",
        "type": "S action",
        "source": "finite_so3_minus",
        "target": "finite_so3_minus",
        "label": "S fixes the dyonic subgroup modulo 2",
        "status": "closed orbit edge"
      },
      {
        "id": "finite_T_fix",
        "scope": "finite_Z2_center",
        "type": "T action",
        "source": "finite_su2",
        "target": "finite_su2",
        "label": "active T fixes the Wilson subgroup modulo 2",
        "status": "closed orbit edge"
      },
      {
        "id": "finite_T_swap",
        "scope": "finite_Z2_center",
        "type": "T action",
        "source": "finite_so3_plus",
        "target": "finite_so3_minus",
        "label": "bidirectional T exchange modulo 2",
        "status": "discrete-theta-changing global-theory map"
      },
      {
        "id": "maxwell_wall_transport",
        "scope": "continuous_U1_maxwell",
        "type": "wall map",
        "source": "maxwell_left_fields",
        "target": "maxwell_right_fields",
        "label": "F_R=G_L and G_R=-F_L",
        "status": "local S matching equations"
      },
      {
        "id": "maxwell_background_transport",
        "scope": "continuous_U1_maxwell",
        "type": "background map",
        "source": "maxwell_left_backgrounds",
        "target": "maxwell_right_backgrounds",
        "label": "(B_m,B_e) maps to (B_e,-B_m)",
        "status": "active S transport"
      },
      {
        "id": "maxwell_anomaly_transport",
        "scope": "continuous_U1_maxwell",
        "type": "anomaly map",
        "source": "maxwell_anomaly_before",
        "target": "maxwell_anomaly_after",
        "label": "representatives differ by an exact form",
        "status": "same anomaly class on closed Y_5"
      },
      {
        "id": "maxwell_wall_realization",
        "scope": "continuous_U1_maxwell",
        "type": "realizes",
        "source": "maxwell_S_wall",
        "target": "maxwell_right_fields",
        "label": "wall variation imposes the S field-strength map",
        "status": "necessary local realization"
      },
      {
        "id": "maxwell_wall_fusion",
        "scope": "continuous_U1_maxwell",
        "type": "fusion",
        "source": "maxwell_S_wall",
        "target": "maxwell_charge_conjugation",
        "label": "two S walls give S squared equals C",
        "status": "invertibility remains conditional on complete global data"
      }
    ],
    "cross_scope_edges": "none"
  },
  "scientific_sources": [
    {
      "id": "aharony-seiberg-tachikawa-2013-v5",
      "authors": "Ofer Aharony, Nathan Seiberg, and Yuji Tachikawa",
      "year": 2013,
      "title": "Reading between the lines of four-dimensional gauge theories",
      "publication": "Journal of High Energy Physics 08 (2013) 115",
      "doi": "10.1007/JHEP08(2013)115",
      "arxiv": "1305.0318v5",
      "url": "https://arxiv.org/abs/1305.0318",
      "locator": "arXiv v5, section 1.2, with the SU(N)/Z_k line data developed in section 2",
      "use": "Global form, mutually local Wilson-'t Hooft line sets, discrete theta data, and the distinction between theories sharing one Lie algebra."
    },
    {
      "id": "gaiotto-kapustin-seiberg-willett-2015",
      "authors": "Davide Gaiotto, Anton Kapustin, Nathan Seiberg, and Brian Willett",
      "year": 2015,
      "title": "Generalized Global Symmetries",
      "publication": "Journal of High Energy Physics 02 (2015) 172",
      "doi": "10.1007/JHEP02(2015)172",
      "arxiv": "1412.5148v2",
      "url": "https://arxiv.org/abs/1412.5148",
      "locator": "sections 3-4 and Appendix F",
      "use": "Continuous electric and magnetic one-form symmetries, their compact backgrounds, and the mixed-anomaly inflow class."
    },
    {
      "id": "kapustin-tikhonov-2009",
      "authors": "Anton Kapustin and Mikhail Tikhonov",
      "year": 2009,
      "title": "Abelian duality, walls and boundary conditions in diverse dimensions",
      "publication": "Journal of High Energy Physics 11 (2009) 006",
      "doi": "10.1088/1126-6708/2009/11/006",
      "arxiv": "0904.0840v2",
      "url": "https://arxiv.org/abs/0904.0840",
      "locator": "section 2.2",
      "use": "Integral Abelian duality-wall coupling, topological matching conditions, orientation reversal, and the action of S on boundary data."
    }
  ],
  "independent_checks": [
    "All displayed charge vectors and matrix entries are integral.",
    "Each finite genuine-line subgroup is mutually local modulo 2 and equals its symplectic perpendicular.",
    "S_gamma and T_gamma have determinant one and obey M^T J M=J over the integers.",
    "The S and T actions close on all three finite global-theory classes modulo 2.",
    "Each active charge matrix equals the inverse transpose of its displayed period matrix.",
    "Reordering and inverting the verified N=4 passive matrices yields the displayed active matrices.",
    "The Maxwell background map is the same declared S matrix in the (B_m,B_e) order.",
    "The transformed anomaly representative reduces to the original one on a closed five-manifold by integration by parts.",
    "The wall equations equal the S action on the ordered (F,G) doublet, and S squared is minus the identity.",
    "The text graph contains no edge between the finite-center and continuous-Maxwell scopes."
  ],
  "accessibility": {
    "embedded_title": "Global form, line lattices, anomalies, and the S-duality wall",
    "embedded_description": "Three stacked black-and-gray panels separate finite and continuous data. The first lists the su(2) center-charge representatives gamma=(p_m,q_e): SU(2)=(0,1), SO(3) plus=(1,0), and SO(3) minus=(1,1), with their genuine-line conditions, maximal-isotropic test, and S and T orbits. The second distinguishes active charge matrices from period matrices: S_gamma is the antisymmetric matrix with rows (0,1) and (-1,0), while active T_gamma has rows (1,0) and (1,1); each equals the inverse transpose of its displayed period matrix, and the passive N=4 T map is identified as the inverse charge matrix. The third, explicitly separate from the finite center data, shows source-free Maxwell currents, the background map (B_m,B_e) to (B_e,-B_m), preservation of the mixed five-dimensional anomaly class, and the Lorentzian S-wall equations F_R=G_L and G_R=-F_L. It states that two S walls fuse to charge conjugation and that local wall equations alone do not establish invertibility.",
    "visual_panels": [
      "finite su(2) center-charge classes and modular orbit",
      "active charge matrices versus inverse-transpose period matrices",
      "separate continuous source-free Maxwell background, anomaly, wall, and fusion data"
    ],
    "color_independence": "Black outlines, white and gray fills, direct labels, matrix equations, and explicit fixed, exchanged, preserved, and conditional status words encode every distinction without color.",
    "structured_equivalent": "/figures/supersymmetry-duality/global-form-lines-anomalies-map.json",
    "responsive_strategy": "The panels are stacked in reading order and the lossless SVG scales without clipping; the structured JSON preserves full-size access to every table and graph edge at 320 pixels and 200-percent zoom.",
    "white_canvas": "explicit white rectangle behind all marks",
    "path_based_text": "dvisvgm converts every visible glyph to an SVG path",
    "motion": "static artifact with no animation or script"
  },
  "limitations": [
    "The finite panel is a center-charge quotient after adjoint screening, not a complete classification of individual Wilson-'t Hooft operators.",
    "The displayed SO(3) discrete-theta labels use the spin-theory convention; non-spin refinements and line spins require additional data.",
    "The continuous Maxwell anomaly formula is a differential-form representative and does not replace its global differential-cohomology refinement.",
    "The Abelian BF wall equations do not by themselves establish an invertible quantum interface on every manifold or for every global form.",
    "File materialization alone neither promotes the registry nor proves owner integration; current lifecycle and integration bindings are recorded separately in provenance."
  ]
}