Defines and proves multi-category compatibility of algebraic state data Q_Σ, E_Σ, c_Σ for finite-node conifold degenerations as the first algebraic layer toward BPS structures.
Duality for Vanishing Cycle Functors
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A global mixed Hodge module P^H is built from local rank-one blocks at each node via Saito gluing; it realizes the corrected perverse object and the finite local vanishing sector.
For conifold degenerations, the corrected perverse sheaf on the central fiber is the unique minimal Verdier self-dual extension of the shifted constant sheaf across the node, with its rank-one contributions arising from the same nearby-cycle formalism.
Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.
Provides the foundational finite-node categorical formalization layer for corrected perverse and mixed-Hodge-module packages in conifold degenerations with finitely many nodes.
citing papers explorer
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From Finite-Node Conifold Geometry to BPS Structures I: Algebraic State Data
Defines and proves multi-category compatibility of algebraic state data Q_Σ, E_Σ, c_Σ for finite-node conifold degenerations as the first algebraic layer toward BPS structures.
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Mixed Hodge Modules and Canonical Perverse Extensions for Multi-Node Conifold Degenerations
A global mixed Hodge module P^H is built from local rank-one blocks at each node via Saito gluing; it realizes the corrected perverse object and the finite local vanishing sector.
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Perverse Extensions and Limiting Mixed Hodge Structures for Conifold Degenerations
For conifold degenerations, the corrected perverse sheaf on the central fiber is the unique minimal Verdier self-dual extension of the shifted constant sheaf across the node, with its rank-one contributions arising from the same nearby-cycle formalism.
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From Finite-Node Conifold Geometry to BPS Structures III: Mediated Triangle Transport and Graded Interaction Data
Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.
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Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations
Provides the foundational finite-node categorical formalization layer for corrected perverse and mixed-Hodge-module packages in conifold degenerations with finitely many nodes.