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Large-vertex merge (tau_u) and small source/sink reflection (sigma_u) from Domokos (doi:10.4171/JCA/97), with tau_sigma_reduce and is_taus_minimal. Formulas use QuiverTools' King sign, so the tau case split is mirrored.
Check tau/sigma against the paper's Section 9 pair and reductions to P^2 and the 3-Kronecker 6-fold, sigma involution, and tau-sigma minimality.
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Implements the two reduction operations from Domokos, Quiver moduli spaces of a given dimension (doi:10.4171/JCA/97):
tau_reduction(τ_u) merges and deletes a large vertex (Definition 2.1, Lemma 3.1);sigma_reduction(σ_u) reflects a small source or sink (Definition 2.2, Lemma 3.3).Both operations have pair-only
(Q, d)methods matching the paper and weight-aware(Q, d, theta)methods that transport a King-normalized stability parameter.QuiverModuliSpaceoverloads return an isomorphic moduli problem with the standard denominatorsum, rather than reusing a closure tied to the original vertex set.The PR also provides
is_large,is_small_source,is_small_sink, the terminating greedy drivertau_sigma_reduce, andis_taus_minimalfor Definition 2.3 in the class of all sincere quiver-dimension-vector pairs.Correctness and contracts
bocklandthead.is_taus_minimaldepends only on(Q, d), as the cited definition does.true;truenow means the reachable reduction graph was exhausted.OverflowErrorinstead of wrapping into a false witness.popfirst!calls.Paper example and search limits
The paper does not give a finite bound for deciding Definition 2.3 by graph search. In Section 9 it proves its infinite-orbit example minimal by a case split and inequalities that force every reflection sequence to keep increasing total dimension. The docstring now explains this and includes both that example and a four-vertex pair where a cap of one is indeterminate but a cap of 100 finds a delayed
taureduction.Tests
The full local suite passes, including doctests and 31 Domokos tests. The regressions cover:
tauandsigmareductions;sigmainvolutivity and the greedy fixpoint;