Systems Formalisms · Formal Invariants

Computational Methods & Mathematical Specifications

Formal physical formulations, algorithmic complexity bounds, and machine-checked proofs underlying our open-source software architectures.

SPECIFICATION SUITE:LEAN 4 · COQ VERIFIED·DETERMINISTIC RUNTIMES

Interactive System Verification

Distributed Consensus & Neural Kernel Engine

Interactive simulation of DAG block commits, sparse mixture-of-experts routing, and JIT compiler passes.

3D ARCHITECTURE RUNTIME SIMULATION[GPU WEBGL · ACTIVE]
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THROUGHPUT
142,000 tx/s
COMMIT LATENCY
240 ms (99.9%)
FAULT TOLERANCE
f < n/3 Byzantine
VERIFICATION
Formally Verified Coq
[TH-AI-02]Compiler Optimization

Polyhedral Memory Bound Kernel Fusion

Mathematical formalization of polyhedral loop transformations for sparse tensor operators running on heterogeneous accelerator clusters.

Governing Mathematical Formulations:
Affine Transformation Invariant
T(\vec{i}) = A\vec{i} + \vec{b}
Preserves causality and memory dependencies across parallel SIMD warp dispatches.
SAFETY & CONSTRAINTS: N/A
[TH-SYS-01]Distributed Algorithms

Leaderless DAG Consensus Virtual Voting

Algorithmic specification of virtual voting over asynchronous Directed Acyclic Graphs, guaranteeing safety under up to f < n/3 Byzantine faults.

Governing Mathematical Formulations:
Quorum Intersection Lemma
|Q_1 \cap Q_2| \ge f + 1
Guarantees that any two quorums share at least one honest validator.
SAFETY & CONSTRAINTS: N/A