This document explores the mathematical foundations, cognitive models, and formal safety mechanisms that define the T81 Ecosystem. It is intended for researchers in computer science, mathematics, and AI safety.
The T81 stack is built fundamentally on balanced ternary arithmetic. Unlike binary (base-2) or standard ternary (base-3 with digits 0, 1, 2), balanced ternary uses the digits (trits) -1, 0, and 1 (often represented as -, 0, +).
T81 implements 90 canonical data types (the “TISC-90” set) that ensure every value—from a single trit to a high-rank tensor—has a unique, deterministic binary representation.
T81 organizes computation into five distinct Cognitive Tiers, defined in include/t81/cog/tier.hpp. This model allows the Axion safety layer to scale its scrutiny based on the complexity and “agency” of the code.
| Tier | Name | Description | Axion Enforcement |
|---|---|---|---|
| 1 | Deterministic | Pure arithmetic and fixed control flow. | Basic instruction counting. |
| 2 | Managed | Dynamic memory and bounded recursion. | Segment-trace validation (RFC-0020). |
| 3 | Reflective | Code that inspects its own state/trace. | Match-guard requirements (RFC-0019). |
| 4 | Self-Referential | High-tier cognitive loops (Tier4Loop). |
Alignment-clause verification. |
| 5 | Agentic | Full goal-directed agency and alignment. | Strict require-alignment policies. |
Axion is not just a monitor; it is a formal safety kernel that treats program execution as a sequence of provable transitions.
Every HanoiVM operation emits an AxionEvent. These events are collected into a deterministic trace that the Policy Engine evaluates against a set of S-expression predicates.
Policies are authored in a domain-specific language that allows researchers to specify exactly which events must occur before a privileged operation (like a Tier 4 loop) is allowed to proceed.
(policy
(tier 4)
(require-alignment (reason "self-referential loop verified")))
T81 enables Bit-Identical Reproducibility for large language models. By implementing transformer kernels (RMSNorm, RoPE, Softmax) directly in balanced ternary-native C++, we ensure that a model like Llama-3.2 produces the exact same output on every architecture, from x86_64 to ARM SVE.
Researchers can use the ` DistributedT81Tensor and HanoiVM` to explore how ternary numerics affect the convergence and safety characteristics of advanced AI models.
t81-verify harness (RFC-0008) to formally prove that TISC lowering is semantics-preserving.require-alignment clauses for autonomous agentic systems.