First Synthesis

First Synthesis engineers absolute mathematical boundaries for experimental logic and deterministic execution. This repository acts as the central hub and technical portal for our two flagship sibling projects: The Monist Engine and the NF-Sketches Formal Lab.

Acyclic by Design

While the mainstream computing industry spends massive development budgets fighting cycles and forcing safety through immutable tree structures, Monist accepts unstratified, cyclic, and infinite structures as native computational inputs. The engine translates these networks into a flat spatial matrix where contradictions manifest as quantifiable geometric friction, neutralizing infinite loops before they can consume physical hardware resources.

The Projects

• ⚙️ Monist: A high-performance Rust and WebGPU engine that compiles and executes experimental logic at hardware speed.
• 📐 NF-Sketches: A Lean 4 formal lab that mathematically guarantees the structural boundaries for NF Set Theory.

By abandoning traditional hierarchical type-checking in favor of geometric shortest-path routing, the ecosystem compiles structurally dense paradoxes into native, lock-free Interaction Nets on the GPU, while simultaneously guaranteeing their theoretical soundness in Lean 4.

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The 5-Layer Hybrid Synthetic Pipeline

Computation does not remain confined to a single paradigm; it transitions dynamically across optimization domains:

1. Natural Deduction (The Human Interface)

Users declare high-level logical constraints and manage goals using interactive tactics within the FormulaArena. This layer captures mathematical intent and strips away logical scaffolding.

2. The Geometry Layer (CPU Core)

The engine flattens text syntax into a topological matrix. The CPU executes Kosaraju's algorithm to contract zero-weight equality rings and runs Bellman-Ford shortest-path evaluation to intercept negative-weight paradox loops.

3. Graph Reduction (The Compiler)

The compiler destroys alphanumeric variables completely, replacing them with nameless de Bruijn levels and converting the structure into pure, untyped combinators.

4. The Physics Engine (GPU VRAM)

The hardware executor ships these combinator graphs to WGSL compute shaders. Lock-free atomic nodes physically collide and annihilate in parallel without central synchronization or garbage collection pauses.

5. The Holographic Co-processor

For high-density relational data, the system maps discrete graphs into a 10,000-dimensional continuous wave function using Vector Symbolic Architectures (HDC). It exploits destructive interference to cancel noise in $O(1)$ time before snapping results back to discrete boundaries.

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License & Contact

First Synthesis LLC employs a dual-licensing structure for the core engines:

1. Open Source: Committed to open mathematical research. Core components available for academic researchers and open-source developers.
2. Commercial License: Enterprise proprietary licensing available for organizations integrating First Synth technology into closed-source AI architectures or commercial verifiers.

This website and its associated documentation are licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0) - see the LICENSE file for details.

For enterprise licensing inquiries or dedicated NPU/GPU architecture consultations, please contact firstsynthesis@gmail.com.