Quiver Lab — standalone edition

What the drawing means

The editor accepts up to 128 nodes and 512 edges and trifundamentals together. Drawing or importing a large quiver does not bypass the calculation's time, work, memory or mathematical checks. Use Coulomb to run that branch alone; Cancel retains completed coefficients.

Circles are gauge groups; squares are flavour groups. Select a node to choose U(n), SU(n), SO(N), O(N), USp(n), G₂, F₄, E₆, E₇, E₈, or a finite Zq gauge factor. For USp, enter the even defining dimension n; for SO/O, enter vector dimension N. USp(n) shows n inside the node. Existing JSON continues to store its Cartan rank n/2. Exceptional nodes display their group name and have fixed Cartan rank; ordinary edges use their minimal representations of dimensions 7, 26, 27, 56 and 248 respectively. SU(n) has Cartan rank n−1; Zq has Cartan rank zero. SO gauge nodes offer SO, Spin or the even-dimensional PSO global form, and O gauge nodes offer O+, O− or Pin+. Odd-dimensional O nodes also expose the source-prescribed charge-conjugation parameter δ. O+ remains the default. Plain edges are full hypers; dashed edges are half hypers. Auto chooses half hypers for SO/O–USp and full hypers otherwise. Multiplicity counts repeated hypers or copies of a bond. Add adjoint, symmetric or antisymmetric full-hyper loops by connecting a gauge node to itself, or through its inspector. The default symmetric/antisymmetric tensor includes any invariant singlet; the Traceless option removes it for SO/O symmetric and USp antisymmetric tensors. Explicit half hypers also support SO/O–SU(2), G₂/F₄/E₈–USp and SO/G₂/F₄/E₈–E₇; the engine checks gauge consistency. Other pairs and spinor matter are unsupported. Neutral ordinary hypermultiplets are retained separately on the canvas and in JSON. Their Coulomb factor is 1; finite unrefined Higgs calculations multiply by (1−t)^(−2h). Their refinement, Higgs rational modes and Higgs-union composition are explicitly unavailable. U flavour nodes may have dimension up to 1000; gauge limits remain unchanged. A determinant full-hyper loop on U(n) has weight sum_i m_i and central charge n; its unrefined Coulomb calculation is supported, while Higgs, refinement and decay reject it explicitly. Coupled determinant-one U-node pairs are preserved as trace constraints, drawn as dashed annotated links. Their unrefined finite Coulomb sum imposes each paired trace equation and removes one central Casimir per equation. Compatible constrained pairs are joined before tree gluing to reduce intermediate storage; unavailable operations reject explicitly. Charged matter is edited within the Bifundamental inspector. The endpoint coefficients specify qₛwₛ − qₜwₜ; negative unit coefficients select conjugate U/SU representations. Nonunit charges apply to U(1), SO(2) and Zq endpoints. For SO(2), choose explicitly between its two-weight vector and a one-weight character. Exceptional higher representations are additional hypers selected by Dynkin label in the node inspector; their calculation support is reported by the engine.

Non-simply-laced bonds support U/SU–U/SU and SO–USp in either direction, with integer lacing ℓ from 2 to 30. They are distinct from repeated bifundamental hypers. The arrow points from the scaled long source to the short target. A U–U bond contributes Σᵢⱼ|ℓ m_source,i − m_target,j| to 2Δ per copy. An SO–USp bond uses Fig. 1 of Folding Orthosymplectic Quivers (arXiv:2107.00754): Σᵢⱼ(|ℓ m_source,i − m_target,j| + |ℓ m_source,i + m_target,j|). If SO is odd-dimensional, add Σᵢ|ℓ m_source,i| when USp is the source, or Σⱼ|m_target,j| when USp is the target. Multiply the entire contribution by the copy count. A flavour endpoint has zero magnetic charge. The paper’s orthogonal nodes are SO groups; O+–USp non-simply-laced bonds are not supported. Reverse direction in the edge inspector. These bonds do not specify a full or half hypermultiplet representation: Higgs computation is unavailable even with flatness checking off. Hasse computation supports unitary quivers with full adjoint loops, ordinary and non-simply-laced bonds; other tensor loops and orthosymplectic bonds remain outside its domain.

Choose Trifundamental and click three distinct nodes to add one three-legged tensor-product hypermultiplet. All-flavour trifundamentals are free matter with a point Coulomb branch. The default is a full hyper with all U legs fundamental. Select the diamond junction to edit copies, full/half matter, and each U leg’s fundamental or antifundamental sign. SO/O/USp legs are self-dual. Half trifundamentals use real SO/O and pseudoreal USp or SU(2) legs, with an odd number of pseudoreal legs; additional consistency checks apply in the engines. Deleting a node removes its attached trifundamentals. Ordinary common-shift diagonal U(1) removal is disabled when a trifundamental is present. Use Quotient continuous centre kernel to remove every trivially acting U(1) direction determined by the complete matter-charge matrix; this preserves the selected lattice convention reported by the engine.

The main Higgs and Coulomb tabs are unrefined. The Refined Hilbert series tab retains flavour weights for supported unitary quivers, with selectable order, an irreducible-representation view and a refined plethystic logarithm. Hypermultiplet coordinates have degree t; vector-multiplet complex scalars have degree t²; a monopole of conformal dimension Δ contributes t²Δ. “Through tⁿ” means coefficients through degree n inclusive, with remainder O(tⁿ⁺¹). These are truncated graded expansions, not a coupling expansion.

Exceptional groups

G₂, F₄, E₆, E₇ and E₈ can be drawn, edited, imported and exported with their defining matter and supported additional Dynkin representations. E₆ and E₇ use the simply connected global form; G₂, F₄ and E₈ are centreless. Additional full-hyper entries are independent of the matter on drawn edges. Calculation support is narrower than editing support: the engine checks the representation, magnetic lattice, convergence and resource bounds before returning coefficients. Exceptional quotients, exceptional trifundamentals and unsupported tensor representations are rejected explicitly. Checked Higgs mode does not supply a flatness certificate for exceptional gauge groups. With the flatness check off, a supported Molien–Weyl calculation is a formal Koszul Euler series, not a certified Higgs Hilbert series. Refined and decay tools retain their stated unitary scope.

Higgs branch

A truncated Molien–Weyl constant term is evaluated with exact integer arithmetic. By default, moment-map subtraction is certified by a flatness check. Turn off Check moment-map flatness to bypass this test and evaluate the formal Molien–Weyl / Koszul Euler series, including negative coefficients if present. Unchecked results and their plethystic logarithms are labelled explicitly and are not certified Higgs Hilbert series. Higgs calculations build completed prefixes through increasing orders and retain the last completed prefix when cancelled or stopped by a resource limit. Checked results retain their certificate; unchecked results remain exact coefficients of a formal Molien–Weyl / Koszul Euler series, including any negative coefficients. Patient attempts the supported general methods within its longer work allowance and preserves the selected flatness-check setting. Resource limits still apply.

For classical groups, Higgs Haar integration includes both connected components of every O gauge factor. Checked mode has a rank-stratum regularity certificate for a single continuous SO/O or USp gauge factor with defining matter. A single active U(1) factor with full hypermultiplets also has a direct regularity certificate when its moment-map polynomial is nonzero, including a symmetric charge-2 loop. Neutral U(1) adjoint loops are free hypers. General mixed components and other tensor loops currently require unchecked mode; the unitary flatness theorem is not applied to them.

For trifundamentals, the Higgs engine uses tensor-product matter weights in the Molien–Weyl integral. Full-hyper inputs with only U(1) gauge factors have an effective abelian regularity certificate. Trifundamentals with just one gauge leg reduce exactly to defining matter, allowing the corresponding supported certificates and formulas. Genuine multi-gauge nonabelian cases generally require the explicitly unchecked mode. Ineffective moment-map equations are removed automatically; the Coulomb centre-quotient toggle does not change Higgs invariants.

Simple unframed unitary trees use exact character contraction for the finite Higgs integral, avoiding the explicit torus-variable cap. A separate fundamental-region theorem checks flatness for supported ordinary dimension vectors; other cases use the bounded decomposition test. Turning flatness checking off still gives an unchecked formal series.

Exact rational Higgs calculations also try direct contour residues for U, SU, SO, USp and disconnected O groups with supported full/half defining hypers and tensor loops. For every O gauge node, both determinant components are integrated and averaged; multiple O nodes include every combination. Symplectic SQCD with enough fundamentals uses an exact character resummation at general rank, including both cones in very-even cases. This evaluates the rational Molien–Weyl integral without fitting a series. Unsupported poles or representations and calculations that exceed the symbolic allowance use the existing finite-series fallback. A dashed SO(2F) flavour edge supplies F full symplectic flavours. The exact attempt receives 80% of the Higgs time allowance, with the remainder available for a finite fallback. Identical disconnected sectors share an integral, retaining every sector’s averaging weight. Square monomial poles are factored exactly when needed. An exact formal integral still requires the separate flatness check to be identified as a Higgs Hilbert series.

Independent component quotients

The component controls specify each matter-connected gauge component separately. Shared flavour nodes do not join gauge components. Independent finite quotients have independent magnetic sectors; a single whole-quiver diagonal quotient is different. Finite and exact Coulomb and Higgs calculations multiply the constituent series with their individual lattice prescriptions. Refined, decay and Higgs-union calculations with explicit component settings are not yet supported. Changing the diagram can invalidate a component prescription; the settings remain visible until corrected or reset.

Refined series and flavour symmetry

The refined tab evaluates both branches through selectable orders t⁴, t⁶, t⁸ and t¹⁰, with t⁴ as the default. Completed orders are retained while higher orders are attempted. Higgs fugacities resolve hypermultiplet multiplicity spaces; gauge-equivalent central rotations remain as a documented covering torus. Coulomb fugacities resolve topological monopole charges, with explicit relations and rescalings for gauge quotients. Setting every fugacity to one is checked against the unrefined expansion. Degree-two current weights are checked as a finite root system before naming a Lie algebra; unresolved enhancement is labelled. Known faithful global forms are stated separately using all-orders charge information, not inferred solely from a finite refined expansion. Irrep decompositions use exact character reconstruction and display Dynkin labels and abelian charges. If an enhanced symmetry is unresolved, a manifest-group or topological-torus character expansion is identified as such. The refined PL applies Adams substitutions to both t and every flavour fugacity. Resource stops preserve completed HS, PL and irrep prefixes independently. For total unitary gauge rank at most 15, the refined PL also supplies named conjectured generators and their representations. Leading positive terms suggest generators; later terms can include syzygies. This does not establish a complete generator list. Unchecked formal Higgs output is excluded from operator conjectures.

Direct perturbative cross-check

The Don’t believe me? tab runs the finite monopole sum and the finite plethystic Molien–Weyl integral on the drawn input, bypassing exact formulas, rational reconstruction and quiver reductions. Weyl chambers, residual Casimirs, full disconnected O integration and the selected magnetic lattice remain part of the formulas. Local constant-term contraction may be used for integration. Proven magnetic bounds are required before Coulomb coefficients are certified. The same order, time, work, memory and flatness controls apply. Completed prefixes survive cancellation or resource limits. Coefficient agreement is a finite-order cross-check, not an independent implementation or an all-orders proof. Supplied Higgs branch decompositions must be disabled for a direct Higgs integral.

Coulomb branch

The monopole formula sums dominant integral magnetic charges and their residual-gauge-group dressing factors. Supported ordinary quivers use a finite magnetic-layer test to certify a charge bound for the requested degree; trifundamental quivers use the exact positivity certificates described below. Bad UV gradings and unremoved continuous gauge kernels are flagged. For an unframed component, the optional diagonal quotient is (∏ U(nᵢ))/U(1), with the corresponding scalar dressing removed. For eligible non-simply-laced U components, this uses the weighted central embedding mᵢ → mᵢ + sᵢc, with ℓs_source = s_target along each directed bond; the engine reports its primitive weights and lattice convention.

Classical Coulomb sums use the integral cocharacters of U, SO and USp, with the SO(even) sign distinction and residual classical Casimir degrees. O+ projections include adjacent-flux charge-conjugation phases from arXiv:2505.03875, using δ=0 by default. On odd-dimensional O nodes the explicit δ=1 prescription omits the adjacent-flux phase. Imported O(1) projection metadata and its source citation are preserved. For ordinary eligible unframed U/SO(even)/USp components, Diagonal Z₂ adds simultaneous half-integral sectors. For eligible folded SO–USp components, it selects the correlated magnetic coset of arXiv:2107.00754 Eqs. (2.4)–(2.5): even lacing has half-integral long-node charges and integral short-node charges; odd lacing has half-integral charges on both sides. The implemented folded quotient requires one common lacing and two long/short scale levels; mixed-lacing or multilevel quotients are rejected. With the option off, only the integral lattice is summed. The engine checks consistency across ordinary and folded bonds and reports the lattice. This is distinct from diagonal U(1) removal. Spin restricts the integral magnetic lattice to even total flux; Pin+ combines this restriction with the O+ projection. O− uses the appropriate flux-dependent discrete phase. PSO admits integral and simultaneous half-integral charges and requires centre-neutral matter. Explicit Spin/Pin+ diagonal quotients are validated against their chosen lift; unsupported combinations are rejected. Vector-matter Higgs invariants are unchanged by replacing SO with Spin, or O+ with O−/Pin+. O gauge tensor loops have Higgs integration, but their Coulomb discrete-phase convention is not implemented.

Unframed U(1) quivers with a connected ordinary graph and one full trifundamental use an exact subset-chain sum that preserves the integral magnetic lattice and any finite kernel. It supports leg signs and matter multiplicities. Other unitary trifundamentals first use a convex-dual positivity certificate and verifies every accepted bound with exact integer arithmetic. Other cases use the exact hyperplane fan of matter weights, roots, coordinate walls and Weyl walls. Either method certifies a complete finite charge bound before enumeration. Ordered-charge pruning and shared dressing calculations reduce the summation work. There is no fixed Cartan-rank cutoff; larger components are attempted within the certificate, enumeration and time budgets. Integral U/SO/USp magnetic charges are supported, with the separate continuous-centre quotient where supported. Disconnected O gauge trifundamentals, combinations of non-simply-laced bonds with trifundamentals, and diagonal Z₂ quotients with trifundamentals are outside the implemented Coulomb domain.

Eligible ordinary orthosymplectic quivers use exact node-by-node magnetic-charge gluing. Tree calculations sum from leaves inward and reuse each boundary-charge series. Quivers with loops use an elimination-order heuristic to keep the intermediate boundary small; this is not a claim of a globally optimal order. Exact conditional magnetic-layer bounds discard local charge sectors that cannot contribute through the requested degree. These calculations preserve the input magnetic lattice and residual-gauge dressing factors, and do not use stored literature coefficients. Unsupported projection conventions retain their dedicated checks and evaluation paths.

Large ordinary unitary trees use exact tree dynamic programming to certify monopole degrees. If an unframed component has a rank-one gauge leaf and the diagonal U(1) quotient is enabled, the engine can fix that leaf’s magnetic charge to zero, remove its degree-two Casimir and evaluate the remaining tree with the induced fundamental matter. This is an integral section of the same magnetic quotient; the drawing and exported quiver stay unchanged. Boundary-charge series are glued along the tree. Simultaneous charge inversion reuses equal intermediate values while retaining both magnetic orbits and their multiplicities. Other eligible components use a shared magnetic-layer recurrence. Exact rational mode falls back to a finite calculation when no scalable all-orders method applies. Time, work and retained-memory allowances still apply.

Large ordinary unitary quivers, including cycles and full adjoint loops, can use certified finite-order calculations without enumerating the full Cartesian convergence certificate. Rank alone does not determine feasibility: the requested order and number of contributing magnetic layers also matter. Exact rational mode may fall back to a finite expansion; rational search preserves the selected completed prefix if a higher-order attempt stops.

Finite Coulomb calculations build certified prefixes through increasing orders. Each completed prefix is displayed while the next order is attempted and retained if the calculation is cancelled, reaches a time or work allowance, or its worker stops. The result reports the actual completed order separately from the requested order; partial magnetic sums are never labelled as complete coefficients. Recognized structures still use their faster exact methods.

Exact rational series & plethystic logarithms

Exact rational mode computes an all-orders numerator and denominator using a finite resummation or a supported closed formula. It never certifies a rational function merely by fitting a finite expansion. Coulomb resummation uses strict magnetic-layer chains and geometric series. Connected classical Coulomb groups also support exact strict-layer resummation. O+, O−, Spin and Pin+ use parity-aware exact resummation for supported ordinary vector matter. Non-simply-laced bonds currently use a finite monopole sum, with exact mode falling back to that expansion. Tensor-loop exact support is reported by each engine. For the supported abelian single-trifundamental family, exact mode proves a common denominator and a numerator-degree bound from all strict subset chains, then determines the rational function exactly. Other trifundamental Coulomb inputs fall back to the certified finite sum. Genuine multi-gauge trifundamental Higgs inputs generally fall back to the finite integral; one-gauge-leg reductions can use supported exact Higgs formulas. Classical Higgs exact support currently includes USp(2) SQCD; other families fall back to the finite integral. Higgs exact support is reported with the result; unsupported cases fall back to the ordinary expansion when the time budget permits.

The Hilbert series / Plethystic log control is independent for each branch. The displayed PL is computed as ∑ μ(k)/k log H(tᵏ), with exact rational arithmetic, through the chosen order. Its leading terms can reveal generators and relations; later coefficients also contain syzygy information. A displayed finite truncation does not certify that the full PL terminates.

Higgs rational evaluation & search

Select Exact rational to try a supported all-orders Higgs formula or exact Molien–Weyl calculation. Rational search · Higgs first tries an exact method, then seeks a rational function from longer finite integral expansions using exact arithmetic and withheld coefficient checks. The search uses the Higgs term and memory limits and the shared search order cap. Each candidate remains conjectural, even when extra coefficients agree. It does not impose Coulomb dimension or reciprocity assumptions on the Higgs series. With flatness checking off, both exact evaluation and reconstruction concern the formal Molien–Weyl / Koszul Euler series F(t), including negative coefficients. An exact formal rational identity alone does not establish a Higgs Hilbert-series interpretation.

Coulomb rational search

Rational search · Coulomb first tries a supported all-orders method using at most 20% of the time budget (capped at two seconds). Otherwise it computes successively longer certified finite monopole sums and seeks P(t)/Q(t). With D = twice the effective gauge rank, it tests uniform denominators (1 − tᵏ)ᴰ and bounded mixed-degree denominators, and solves Padé systems using exact integer/rational arithmetic. The denominator search assumes a palindromic numerator of degree deg(Q) − D and infers its second half; this symmetry is part of the fit, not independent evidence. Fits are formed from a training prefix; at least four coefficient positions in the observed t or t² grading are withheld. When budget and order cap permit, eight additional degrees are evaluated after fitting. Candidates must have pole order D at t=1, symplectic reciprocity H(1/t)=tᴰH(t), cyclotomic denominator factors of index at most 64, and nonnegative integral predicted coefficients. The dimension test and reciprocity are structural search assumptions, not a proof for arbitrary generalized magnetic data. A matching finite prefix, a palindromic numerator, and successful extra checks do not establish an all-orders identity. Such outputs are labelled CONJECTURED; only independently certified formulas use the Exact label. If refinement fails, only the last fully computed finite expansion is retained. The search is bounded and can miss rational forms requiring higher degrees or other denominators.

Decay & fission

The Hasse diagram concerns the Coulomb branch of the drawn 3d quiver. For a magnetic quiver, this is the Higgs branch of the theory it represents. The engine enumerates supported good unitary rank-vector multisets and their cover relations, including directed non-simply-laced bonds. Each adjoint contributes +2 to the adjacency diagonal, A_ii = 2g_i − 2. Decay lowers ranks while preserving loops. U(n) with one adjoint is a SYM constituent and can split off in fission; isolated U(1) loop factors are omitted by the published P₁ rule. Transverse slices for multiple adjoint loops are left unnamed. For one U(n) node with one adjoint and one fundamental, the smooth centre-of-mass C² is removed from the residual quivers and retained in the leaf dimensions. Its directed balance and ungauging checks are reported with the result; the primitive weighted quotient and supported long-node ungauging are accepted, while short-node ungauging requires a different rule. Charge and global-form extensions are excluded. Its reported scope and exclusions accompany each result. It does not determine every transverse slice geometry.

Two-step decay exploration

Decay candidates draws the input and its next two decay steps for supported ordinary or non-simply-laced unitary quivers and supported trifundamentals. Residual drawings preserve adjoint loops and the direction, lacing and copy count of every bond. Select a residual quiver and choose Show next two decays to continue from it; Back to input restores the start. Ordinary fissions retain every residual factor. The full ordinary Hasse diagram remains in its own tab, with leaf dimensions and its original edge orientation.

Conjectural trifundamental decay

Use Decay or the button in Decay candidates to run this explorer independently of the Hilbert series. The default view draws the input and two successive decay layers; the complete candidate poset is computed internally to determine its cover relations and is retained in the result export. The checkbox includes this calculation first when running Compute geometry. This explorer supports connected gauge support with all-U nodes, full trifundamentals and ordinary loopless full bifundamentals. Tensor loops and non-simply-laced bonds are excluded in this first version. For each surviving gauge node it requires the proposed local rule e_i(k) = Σ_j m_ijk_j + Σ_{i,j,l} h_ijlk_jk_l − 2k_i ≥ 0, with flavour ranks held fixed. The source and every candidate have their entire ineffective continuous centre recomputed and removed, regardless of the main Coulomb quotient setting. Every nonempty candidate must also pass the exact strictly-positive monopole-grading certificate; local balance alone is insufficient. The displayed graph is a combinatorial rank-decay poset, not a verified symplectic-leaf Hasse diagram. Node labels report residual effective gauge rank, not leaf dimension. No fission rule or transverse-slice identification is asserted. An incomplete search does not return a complete graph.

Charges, global forms & Higgs unions

Set source and target electric charges on ordinary full bifundamental edges. Nonunit charges require a U(1) or finite Zq endpoint; they are independent of multiplicity and NSL lacing. Finite gauge factors are summed by a modular Higgs projection and carry no Coulomb magnetic flux. Mixed U/SU nodes use trace-zero SU cocharacters and SU Haar integration. A central Zk quotient specifies one common order and an integer phase at each U/SU gauge factor; the engines check matter neutrality and admissible central phases. For unframed unitary quivers, a long-node anchor fixes one magnetic charge at any rank; a rank-one short anchor retains its source magnetic sublattice. The separate source fixed-charge mode fixes the last ordered charge and removes one degree-two Casimir without asserting a diagonal kernel. It requires an explicit anchor and a supported unitary tree. Higher-rank short-node results are labelled source-prescribed monopole series; their physical Coulomb-branch interpretation is not certified.

The Higgs cone/intersection editor stores a separate quiver for every signed term. Choose its Coulomb series when using a magnetic quiver, its Higgs series for a direct constituent, or the point series. Signed multiplicities implement inclusion–exclusion. Each constituent series must be certified, and the summed coefficients are exact arithmetic; the geometric decomposition is an explicit user assumption. If a later order stops, only the last common completed order is retained. This option does not infer intersections from the canvas.

Resources & reproducibility

The Higgs term limit controls the number of simultaneously retained terms in a sparse expansion, not a number of bytes or a detected amount of free RAM. Choices range from 180,000 to 20,000,000, with 1,000,000 selected by default. Higher limits can cause substantial temporary allocations; a worker timeout cannot guarantee prevention of a browser memory termination. Exact Higgs character enumeration and Hasse-state limits are separate.

Normal calculation preserves the standard work limits. Large calculation allows up to 100 million magnetic points, 20 million monopole sectors and 2 million trifundamental fan intersections, including finite sums and rational-search fallback. For abelian subset sums, Large raises the coefficient-work limit from 20 to 100 million additions and storage from 1 to 2 million coefficient cells. Patient calculation tries fast structural methods before general attempts on both branches. Its Coulomb allowances include up to 1 billion magnetic points, 100 million monopole sectors and 20 million fan intersections. The Higgs sparse-term setting remains independent, and unchecked Higgs calculations retain their formal-series interpretation. Separate retained-state and coefficient limits bound intermediate storage. It does not make every gauge group or matter representation supported, or make a divergent UV monopole grading convergent. Select a time allowance from 3 seconds to 30 minutes per engine; 10 seconds remains the default. Selecting Patient increases a 3- or 10-second allowance to 5 minutes, while preserving an already longer choice. Both Coulomb and Higgs expansions can be requested through t⁸⁰. High orders may need substantially more time and memory. Compute Higgs only and Compute Coulomb only run their respective branch in the selected mode.

Each calculation runs in a separate interruptible worker. Time and state limits are enforced. A stopped branch calculation retains its last completed prefix, with the completed order and stop reason. Coulomb and checked Higgs prefixes retain their certification; unchecked Higgs prefixes retain exact formal coefficients without a certified Hilbert-series interpretation. An unfinished sum is never returned as a complete expansion. Save quivers as JSON, export the drawing as SVG, and export results with inputs, parameters, methods, and diagnostics. Large ranks and orders can exceed the browser’s practical limits.

References

Cremonesi–Hanany–Zaffaroni, arXiv:1309.2657
Cremonesi–Ferlito–Hanany–Mekareeya, arXiv:1408.6835
Folding Orthosymplectic Quivers, arXiv:2107.00754
Monopole-fan reference, arXiv:1611.07030
Trifundamental benchmark, arXiv:1403.2384, Eq. (5.7)
Bourget–Sperling–Zhong, arXiv:2401.08757
Crawley-Boevey, Geometry of the moment map for representations of quivers

Research software · version 1.7.4 · standalone offline edition. Check the method and scope of each computation before using it in a proof or publication.

Draw a theory. Explore its geometry.

Geometry & invariants

Conventions & methods