Recursive Ownership Graphs for Composing Fungible CPMM Liquidity Tokens

Symmetry CPMM Composer represents a basket as a directed acyclic graph of ordinary Raydium constant product pools. Leaves are token mints and internal nodes are fungible liquidity tokens whose pools hold the assets represented by their children. The inspected application validates graph identity and cycles, computes theoretical look through exposure, derives a child before parent creation order, and prepares separately reviewed recursive entry and redemption steps. This report distinguishes the graph model from live portfolio value and deployment status. A historical read only snapshot on 7 October 2026 records 34 unique required pools across two example graphs, all absent, and 5.1 SOL in pool creation fees at the observed configuration, before rent, network fees, asset purchases, or seed liquidity. No pools were created by that preparation. A separate compatibility snapshot records support accounts and mutable issuer controls for 25 selected tokenized securities mints. The result is a source grounded design and preparation study, not a launched investment product, a return claim, or proof of unrestricted access. User control, exclusion, cost distribution, and traceable transaction review are evaluated as requirements with distinct evidence gaps. Preparation of this report was assisted by Codex. The research programme is directed toward human agency, financial inclusion, and evidence-based accountability. Intended social benefits are distinguished from measured technical results in the manuscript. The manuscript and newly authored analysis are offered under CC BY 4.0. Any supplied source files retain the license terms stated in the supplement; the record license does not replace third-party source licenses.