Research index
The papers are the foundation.
The Cnidarian Foundation publishes the Gradient Papers, a series of nine papers on cooperative governance, biomimetic systems thinking, paraconsistent consensus, and the design of AI compute infrastructure. The canonical versions live at cnidarian.org. The index below is the Mozi-side citation reference.
The Gradient Papers
Nine papers, in order of publication. Each paper has a Mozi-side citation context page (linked from the card) and a canonical version on cnidarian.org.
PAPER IPUBLISHED · 2026.04 The Medusa Paradigm — A biomimetic foundation for distributed AI infrastructure
Larry Klosowski
Cnidarians have coordinated complex behavior through decentralized nerve nets for over five hundred million years. The Medusa Paradigm reads that coordination as a biomimetic foundation for distributed AI compute: nodes that share state without a central controller, that route work without a router, that reach decisions without a vote. The paper develops the analogy carefully — where the biology maps cleanly to distributed-systems primitives, where it doesn't, and what we owe the metaphor when it strains. The result is a design vocabulary the rest of the Gradient Papers build on.
PAPER IIPUBLISHED · 2026.04 The Reef Paradigm — Cooperative governance through coral biology
Larry Klosowski · Lauren Mendenhall
Coral reefs scale through localized growth that responds to seven-streams pressures — light, current, salinity, predation, sediment, temperature, neighbor-density. The Reef Paradigm reads that growth pattern as a model for cooperative governance: how a federation expands without losing the structural integrity of its constituent cooperatives. The paper develops the parallel against Mondragon's seventy-year history, against the failed federations of the post-war Basque Country, and against the recent literature on commons governance. It closes with a set of governance principles encoded in the Mozi bylaws.
PAPER IIIPUBLISHED · 2026.04 Paraconsensus — Paraconsistent four-valued logic for federated meta-learning on BlockDAG
Larry Klosowski · Kurt McKelvey
Standard consensus protocols treat disagreement as failure: when nodes produce contradictory outputs, the protocol picks one and discards the others. Paraconsensus extends consensus to a paraconsistent four-valued logic — true, false, both, neither — that preserves disagreement as information. The paper develops the formal model, proves liveness and safety in the BFT setting, and demonstrates the protocol's performance on a federated meta-learning workload where contradictory model outputs carry epistemic content. The Citrate Network's inference verification layer is the production implementation.
PAPER IVIN PROGRESS · 2026.05 Agentile
Saul Loveman · Larry Klosowski
Agentile is the institutional methodology developed during the Citrate Network build: a set of operating rules for human-agent software engineering that produced a Layer-1 blockchain with one engineer plus an AI in four months. The paper extracts the methodology from the codebase that proved it: the four ratchets (test count, formal specs, CI tripwires, frontmatter coverage), the named failure modes catalog, the audit-immutability discipline, the mock-budget gate. The methodology travels — this monorepo is the second project to adopt it, with planned per-project case studies.
PAPER VFORTHCOMING · 2026 Paper V — title to be confirmed
(Authors to be confirmed)
The fifth Gradient Paper is in preparation. Title and abstract publish once the cooperative team confirms the working title for public attribution.
PAPER VIFORTHCOMING · 2026 Paper VI — title to be confirmed
(Authors to be confirmed)
The sixth Gradient Paper is in preparation. Title and abstract publish once the cooperative team confirms the working title.
PAPER VIIFORTHCOMING · 2026 Paper VII — title to be confirmed
(Authors to be confirmed)
The seventh Gradient Paper is in preparation. Title and abstract publish once the cooperative team confirms the working title.
PAPER VIIIFORTHCOMING · 2027 Paper VIII — title to be confirmed
(Authors to be confirmed)
The eighth Gradient Paper is in preparation. Title and abstract publish once the cooperative team confirms the working title.
PAPER IXFORTHCOMING · 2027 Paper IX — title to be confirmed
(Authors to be confirmed)
The ninth Gradient Paper is in preparation. The paper closes the initial Gradient Papers cycle; subsequent papers continue the series under cooperative editorial review.
The Cnidarian Foundation site launches in Sprint 4 of the family build. Until then, deep-links to cnidarian.org route back to the Mozi-side per-paper landings to avoid 404s. The placeholder rolls off when the canonical surface goes live.