AI that can prove every decision it makes. Exactly.
A deterministic substrate for sovereign, auditable AI -- deploy on your own hardware, keep proprietary knowledge inside the enterprise, and reproduce every result exactly.
18 modalities. One kernel. Zero stochastic drift.
A single deterministic primitive collapses into 18 production-grade AI modalities -- 6 that beat stochastic tools outright, 12 with no mainstream ML equivalent.
Find known and unknown anomalies in your data.
Any data expressed as a vector: sensor telemetry, transactions, network features, or embeddings from another system. Same measurement engine everywhere -- zero configuration between domains.
Six compete head-to-head with stochastic AI. Twelve more are kernel-native capabilities with no mainstream machine learning equivalent.
How this is different from the AI you already know
For most people, “AI” means a chatbot. Triaxis is something else entirely -- infrastructure for decisions that have to hold up under audit, not another app that writes text.
Chatbots and large language models
- --Tools like ChatGPT, Claude, and Copilot -- you type a question, the model writes an answer.
- --Impressive for conversation, drafting, and search -- but answers can vary, and the reasoning is not something you can replay or prove.
- --That is not what Triaxis builds. We are not another LLM company.
Decisions you can stand behind
- --Run the model again and get the same answer -- not "close enough," but identical.
- --See which inputs drove the outcome, not a black-box guess after the fact.
- --Produce evidence an auditor, regulator, or customer can verify independently.
Deterministic AI plus geometric monitoring
- --Triaxis Atum is decision-grade AI -- fraud scores, risk models, sensor analytics -- built from a deterministic kernel, not a chat interface.
- --Triaxis GDI measures vector data for anomalies -- including LLM embeddings -- without requiring you to adopt Atum first.
- --Use either product alone, or both together when you need provable models and geometric detection on the same streams.
The sections below go deeper into the Sheffer kernel, individual modalities, and measured benchmarks. Start here if Triaxis is new to you.
The gap in mainstream AI
Conventional AI -- the kind behind most chatbots, recommenders, and fraud scores -- is built on randomness and approximation. It can be very accurate, but it was not designed to give you the same answer every time or a proof you can hand to an auditor.
Teams in regulated industries often paper over that gap with shadow models, sampled audits, and manual logs. That works until someone asks: “Show me exactly how this decision was produced.”
What Atum changes
Atum starts from a deterministic mathematical kernel -- one shared primitive instead of millions of opaque parameters. The goal is not just good predictions, but predictions that are repeatable, traceable, and backed by evidence.
Reproducibility, audit trails, and cryptographic verification are properties of how the math works -- not features bolted on after training or checked only by sampling a fraction of decisions.
18 modalities. One kernel.
Six compete head-to-head with stochastic AI. Twelve more are kernel-native capabilities with no mainstream machine learning equivalent.
The 6 -- compete with stochastic AI
Direct successors to established stochastic approaches, benchmarked head-to-head.
The 12 -- only possible on the Sheffer kernel
Input-space, data-space, and representation capabilities with no mainstream machine learning equivalent.
Trained networks as math objects: add, subtract, SHA-256 commit, combine with Boolean logic. No stochastic equivalent.
Every decision ships with a 128-byte proof. Bit-exact Python/Rust forward pass with Groth16 verification.
35-parameter formulas for complex systems with a zero-knowledge audit package. Not a Neural ODE approximation.
Guaranteed output bounds over input boxes for committed Sheffer models -- theorems, not Monte Carlo samples.
Exact means, variances, and Sobol indices for shallow Sheffer models. Monte Carlo replaced by closed-form quadrature.
Canonical normal form where equal bytes mean equal functions -- court-grade model forensics and deduplication.
Run committed Sheffer kernels backwards: exact preimages, interval clamp regions, and provably minimal counterfactuals.
Deterministic drift detection on any tabular data via committed kernel mean embeddings -- not limited to Sheffer models.
Distribution-free prediction intervals around any deterministic Atum point predictor -- no posterior sampling.
Hash-committed spectral features for time-series and waveform data -- cyber, clinical, and industrial signal paths.
Sheffer-native tensor train with rank-cliff hardening and hash commitment -- mixed-alpha CompProg composition.
Distill any stochastic model into a committed CPU shadow with an empirical disagreement bound over a declared envelope.
Geometric anomaly detection. With or without Atum.
GDI stands for Geometric Deterministic Intelligence. It finds anomalies in data by measuring distances and angles in mathematical space -- known rare events and novel patterns alike -- not by training another opaque model.
Geometric Deterministic Intelligence finds anomalies in data through deterministic geometric measurement -- known rare events and novel patterns alike. No labeled training data, no domain-specific models, and no GPU required.
GDI is a standalone product. Most teams can deploy it on existing data streams without adopting Atum. The two products are siblings -- built to run together when you want provable models and continuous geometric measurement in one stack.
GDI computes distances and angles in the space your data already occupies. No millions of fitted parameters, no stochastic training runs.
Every flag reports which features drove the score and by how much -- verifiable facts about the data, not a separate interpretability layer.
Raw telemetry, tabular features, or embeddings from any model. Same deterministic engine routes to the right geometric measurement automatically.
Three ways teams deploy GDI
Detect anomalies in telemetry, transactions, sensors, or embeddings -- standalone, without Atum.
Find where deterministic, auditable inference matters most, then bring in the Sheffer kernel for those workloads.
Deploy deterministic models and keep geometric measurement on the same streams for drift and novel deviations.
Built for regulated industries
Technical properties teams in these sectors often need -- reproducibility, explainability, and geometric anomaly detection.
Framework names below are context only. We do not claim certification, clearance, or formal validation against any regulatory standard.
Teams often need reproducible model runs and audit trails. Atum targets byte-exact inference and algebraic accountability -- we have not validated against SR 11-7 or similar rules.
Regulated health AI teams care about traceable decisions and evidence packages. Our verifiable inference path is built for that class of need -- not a cleared or certified medical device.
Mission systems favor deterministic, explainable behavior. The kernel is designed for traceability and proof -- formal accreditation against DoD frameworks is the customer's process, not ours.
Safety-critical software teams reference assurance levels like DO-178C. GDI and Atum provide measurement and reproducibility properties those programs often ask for -- without claiming compliance.
The numbers, exactly as measured
Two products, two evidence bases. Atum metrics come from the Sheffer kernel portfolio; GDI metrics come from the public multi-domain benchmark program.
Triaxis Atum
Deterministic AI suite -- Sheffer kernelTriaxis GDI
Geometric Deterministic IntelligenceStart with the pilot. One model risk portfolio. 90 days.
Measured against your own baseline costs.