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pnxt

Research Overview

Research Philosophy

pnxt follows a research-first approach: theoretical soundness before implementation speed. Each phase builds on the previous, creating a solid foundation before moving to prototyping.

The foundational vision is defined in the master research prompt, which specifies the role of a Principal AI Systems Architect designing a ground-up programming paradigm for LLMs.

Phase 1: Core Architecture, State Separation & FFI

Status: Complete

Defined the high-level system architecture, solving the “State vs. Logic” problem:

  • How the immutable codebase (stored as a non-Euclidean Tree-sitter DKB Knowledge Graph) is separated from ephemeral runtime state (memory, queues, actor states)
  • The Legacy Interoperability Layer (FFI) for safe interaction with Web2 APIs without breaking noninterference guarantees

Phase 2: Bridge Layer & Mathematical Spec

Status: Complete

Defined the Bridge Layer — the constrained-decoding grammar that forces LLMs to output valid VPIR nodes:

  • Exact Bridge JSON Schema specification
  • Mathematical translation pipeline: Bridge Grammar JSON → HoTT morphisms → SMT constraints
  • Formalized in LaTeX with copy-pasteable JSON schemas

Phase 3: Deep Analysis

Status: Complete

Phase 3 expanded the foundational research with six detailed analysis documents. While Phases 1-2 established what ANP is and why it matters, Phase 3 addresses how it works in detail and where it fits in the broader landscape.

Deliverables

#DocumentFocus
1Agent-Computer InterfaceProtocol architecture, message taxonomy, capability discovery
2Semantic MemoryThree-layer memory model, lifecycle management, cross-agent sharing
3Multi-Agent CoordinationTopology models, task decomposition, conflict resolution
4Trust, Safety & GovernanceGraduated trust, capability permissions, sandboxing
5Comparative AnalysisANP vs. OOP, Actor Model, Microservices, EDA, FP
6Reference ArchitectureConcrete system design, deployment topologies, migration strategy

Recurring Themes

  1. Incrementalism — Every component designed for phased adoption
  2. Structural safety over behavioral discipline — Make correct behavior easy, incorrect behavior difficult
  3. Explicit over implicit — Side effects declared, capabilities negotiated, trust measured
  4. Memory as foundation — Persistent memory transforms stateless interactions into coherent experiences
  5. Human partnership, not replacement — Agents as colleagues with graduated trust

Phase 4: Prototype Implementation

Status: Complete

Phase 4 transitioned from research to prototype implementation and empirical evaluation. All priorities have been delivered. See the Phase 4 details for the full breakdown.

Completed deliverables:

  1. Core Infrastructure — Memory Service (three-layer model with pluggable backends), ACI Gateway (trust-checked protocol layer with audit logging), project scaffolding (TypeScript, Jest, CI/CD)
  2. Agent Runtime — Lifecycle management, versioned capability negotiation with 3-phase handshake, graduated trust engine with multi-dimensional scoring
  3. Validation & Evaluation — Multi-agent coordination scenarios, benchmark suite, security test suite with adversarial tests across 5 categories

Phase 5: Paradigm Foundation

Status: Complete (5 Sprints)

Following the Advisory Review Panel’s alignment assessment (3/10 for Phase 4), Phase 5 built the core paradigm components that distinguish pnxt from conventional agent frameworks:

  1. Sprint 1 — Typed FIFO channels (DPN), IFC security labels, VPIR node types and structural validator
  2. Sprint 2 — Bridge Grammar JSON Schema for constrained LLM decoding, Z3 SMT integration (4 properties), causal trust scoring
  3. Sprint 3 — VPIR interpreter with full execution, NL protocol state machines (delegation, negotiation, resolution), VPIR visualization
  4. Sprint 4 — Protocol-channel integration, VPIR parallel wave execution, result caching
  5. Sprint 5 — HoTT type foundations (categories, morphisms, paths), Tree-sitter knowledge graph, VPIR-to-HoTT bridge, Z3 categorical verification (6 total properties), end-to-end pipeline scenarios

Phase 6: Integration & Deepening

Status: Complete (9 Sprints — Sprints 6–9 of the overall numbering)

Phase 6 connected and validated the paradigm pillars together with real-world inputs:

  1. Sprint 6 — Tree-sitter TypeScript parser, LLM-driven VPIR generation via Claude API, integrated Code→KG→VPIR→HoTT→Z3 pipeline
  2. Sprint 7 — HoTT higher paths and groupoid structure, structured JSON visualization, Z3 groupoid law verification (8 properties)
  3. Sprint 8 — HoTT n-paths generalization, pipeline LLM integration, LLMbda Calculus core (typed lambda with IFC), Z3 expansion (10 properties)
  4. Sprint 9 — Weather API benchmark MVP (full NL→VPIR→HoTT→Z3→DPN→Result), DPN-as-runtime elevation, benchmark harness
  5. Sprint 10 — Formal noninterference via Z3, covert channel analysis, DPN liveness/progress/fairness verification (14 properties)
  6. Sprint 11 — Univalence axiom encoding, transport along paths, LLMbda as semantic foundation, typed LLMbda ADR (15 properties)
  7. Sprint 12 — User-program property verification, CVC5 integration, DPN bisimulation, multi-agent delegation and secure data pipeline benchmarks (17 properties)
  8. Sprint 13 — Neurosymbolic bridge: P-ASP confidence scoring, Active Inference graph patching, refinement pipeline
  9. Sprint 14 — Categorical tokenization experiment (42-token vocabulary), self-hosting proof of concept (M1), paradigm transition roadmap, advisory review alignment package (score: 9.2/10)

Phase 7: Self-Hosting Paradigm

Status: In Progress (3 Sprints complete)

Phase 7 transitions pnxt from verified prototype to self-modifying, LLM-programmable system. See the Phase 7 roadmap for full details.

Completed sprints:

  1. Sprint 10 — Standard handler library (8 handlers), declarative tool registry, DPN supervisor, runtime integration
  2. Sprint 11 — VPIR graph builder, external task runner, task-aware bridge grammar (M2 complete)
  3. Sprint 12 — Bridge grammar error taxonomy, auto-repair engine, confidence scorer, Z3 graph pre-verification, reliable generation pipeline (M3 foundation complete)

Current stats: 21 formally verified Z3 properties, 68 test suites, 1220+ tests. Advisory panel score: 9.35/10.