Executive briefing, October 2026
Based on companion v0.14
Before AI acts.
When AI software carries out work on a company’s behalf, it must do more than produce a plausible answer. It must decide whether it has enough information to proceed, whether it needs to check something, or whether a person should take over. Hexis is a research programme investigating whether a structured way of changing how an AI approaches its work can improve those decisions.
An eight-minute read for business leaders. The companion guide and the research paper sit behind it. Simon Herko and Chris Pidcock
What should the agent do next?
Act
when the evidence supports the decision
Seek evidence
when a material fact is missing
Escalate
when a person needs to decide
Mistakes can occur in all three directions. We are testing whether making the agent’s approach visible, and limiting how it changes, helps it choose the right one at the right moment.
The problem
Three ways to get the moment wrong.
An agent can act before it has enough evidence. It can keep checking after it has enough. Or it can refer to a person a decision it should have been able to handle.
Each has a cost. Acting too soon produces the wrong outcome, and often one that is hard to undo. Checking for too long produces delay and expense. Referring routine decisions to people undermines the value of automation, and approvals become a formality.
The question is not only whether the agent reaches the right answer. It is whether it chooses an appropriate response at an appropriate moment. Hexis investigates whether that choice can be made visible, constrained and tested, rather than left inside the model.
One decision in practice
One refund, four moments.
A customer asks for a refund on an item that arrived damaged. The ordinary return window has closed. Policy allows an exception if the damage was reported within a set period after delivery, so two dates settle the case: when the item was delivered, and when the damage was first reported. The agent has the customer’s message. It does not yet have the order record.
The request arrives
What is missing: the delivery date and the date the damage was first reported. What the agent does: it neither issues the refund nor refuses it. It recognises that the case turns on facts it does not have.
What Hexis contributes: the agent’s approach to this turn is recorded as a decision state. From that state the system will not let it call the refund tool, whatever it generates.
Refund call refused
Working out what is needed
What the agent does: it sets out what would settle the case, the two dates from the order record, and asks for the record.
What Hexis contributes: that request is produced as a structured record of the proposed decision and what it waits on, not as free text. The agent’s change of approach from the previous turn is checked against the permitted set before it is made.
Refund call refused
The record arrives
What becomes possible: the order record supplies the dates. The situation has changed, and the agent reads it again.
What Hexis contributes: the new reading is logged next to the old one, so the sequence shows that the evidence arrived before anything was done.
No tool call
Acting, or handing over
Who decides: if the dates fall within the exception period, the agent may now issue the refund. If they do not, or if something about the case still calls for judgement, it refers the case to a person.
What Hexis contributes: the agent is now in an execution state and the refund tool is available to it. If an escalation has been opened, the tool stays blocked until a person decides.
Refund call permitted
Illustrative. These are hand-assigned readings adapted from the research paper’s worked example, not observed router outputs and not TAI assessment items.
Permission is not correctness. The boundary controls whether the agent may call a tool. It does not establish that the agent read the dates correctly or applied the policy properly. That is a separate question, and the programme’s behavioural tests are what would answer it.
What Hexis proposes changing
Make the agent’s approach visible, and limit how it changes.
In most agent systems, how the agent approaches each turn is decided inside the model, without a record a reviewer can check. Hexis proposes taking that choice out of the model and recording it alongside the work.
The proposal concerns three activities. Each can be implicit, left to the model’s ordinary behaviour with nothing produced that a reviewer could check, or explicit, carried out in a way that produces something checkable.
- Planning
- Implicit: the agent proceeds without stating a course of action. Explicit: it sets out what it intends to do before doing it. In the refund case, explicit planning is the agent stating that the case turns on two dates before it does anything else.
- Monitoring
- Implicit: the agent relies on its own sense of how things are going. Explicit: it checks progress against supplied evidence or an external check. In the refund case, that is comparing the dates with the policy period, rather than judging the customer’s account plausible.
- Recall
- Implicit: the agent works from what it remembers or infers. Explicit: it retrieves the relevant record before proceeding, and holds back when the record is not available. In the refund case, that is the order record, not the customer’s description of it.
The combination in use at any moment is the agent’s configuration. Hexis proposes four things about it.
- It is selected deliberately and recorded outside the model, so it can be seen.
- It can change as the situation changes, but only along permitted paths, and each change is checked before it is made.
- Half of the possible states permit the agent to use tools: issue a refund, send a message, change an account. The other half permit only a structured decision. An open escalation blocks tool use in every state.
- Every turn is logged: the approach in use, the reading of the situation, the change made and the action taken, so a reviewer can examine the sequence without relying on the model’s account of itself.
Why this might help. The hypothesis is that the wrong approach at the wrong moment is one cause of the three failures: acting from memory when the record was needed, or checking by feel when evidence was available. If the approach is chosen for the situation and changed only in controlled ways, the agent may be more likely to seek evidence when a fact is missing and to act once it has arrived.
That is a hypothesis, not a result. The research programme would measure three things: whether the configurations produce distinguishably different behaviour; whether the routing between them agrees with independent judgement; and whether changing approach over a task improves decisions compared with the best single approach at the same computational cost. None of these has yet been measured.
The structure behind the configurations and their permitted changes comes from the binary arrangements and named relations of the I Ching, taken as a fixed structure and not as divination. The lineage explains the design; the comparisons must establish its usefulness.
How it is built · the 64 states, the router and the record
- Execution state: tool use permitted
- Decision state: tool execution refused
An open escalation blocks tool execution in any state.
Select a state to see its configuration and situation reading.
The space is divided in half. An open escalation blocks tool execution in any state.
32
Decision states
Produce a typed decision artefact. Tool execution is refused.
32
Execution states
Tool execution is permitted, unless an escalation is open.
- A router
- Hexis-S1, a small non-generative router, returns structured state and transition values, or a hold or an escalation, and no text.
- A replay record
- For every turn: the state readings, the transition, the relation cited, the action and the operational measurements. A reviewer can inspect the sequence without relying on the model’s account of itself.
These are design requirements to build and test. The programme’s first harness phase tests each check, including a stop that arrives mid-generation, mid-change or mid-escalation, before any agent-performance claim is assessed.
The names in this briefing
- Hexis
- the research programme
- Yarrow
- the open-source contribution;
yarrow.hexmathv0.1 is released, further components are planned - TAI
- the proposed evaluation instrument
Read the full description in the companion guide, section 3: What the architecture adds.
What this adds to existing controls
Alongside your controls, not instead of them.
A COO reading the refund example may reasonably say: we already require the dates before a refund is authorised. That is right, and Hexis does not replace that rule.
Your approval steps, rule engines and sign-offs govern whether the agent may act. Hexis governs how the agent approaches the decision as circumstances change: whether it is planning, checking and retrieving, or working from its defaults, and it leaves a record of which. The two are designed to work together. Approval pauses and resumable state already exist in agent frameworks, and Hexis is designed to operate inside such a workflow.
Whether this adds enough value over the controls you already have has not been tested. The paper’s registered tests compare Hexis with model-side alternatives at matched compute: the best single configuration, self-consistency and a shuffled router. They do not compare it with approval steps, rule engines or human sign-off. That comparison is not among the registered tests. It is the evaluation we invite partners to design.
What has been established, and what remains unproven
The structure is available to examine. The behavioural case is still to be made.
The research paper states each claim with the test that would refute it, fixed before the evaluations are run, and reports no agent-performance results.
| Area | Established so far | Still needed |
|---|---|---|
| Structure | Definitions and structural results, with a checking script. | Evidence of effects on agent behaviour. |
| Agent behaviour | The architecture and its comparisons are specified. | Implementation evidence and behavioural evaluations. |
| Workflow controls | Not part of the registered tests. | A partner evaluation in a real workflow, comparing Hexis with the controls already in use. |
| TAI | The construct, development process and validity tests are specified. | Successful validation before use as a validated instrument. |
| Yarrow release | yarrow.hexmath v0.1 released under Apache 2.0, with tests and the paper’s structural checker. | Release of the remaining components, each after its registered gate. |
The research paper also reports one corpus measurement. That result does not establish an agent-performance benefit.
How a better decision would be measured
The same action can be premature on one turn and appropriate on the next, so the measure has to capture timing as well as choice. TAI, the proposed Timeliness and Appropriateness Instrument, assesses which response a system chooses in a situation, and at which point it chooses it. It is intended for systems built on any architecture, so an organisation can take part without adopting Hexis. It remains a development scale until validation shows that its scores mean more than fluency, general ability or habitual caution.
Three questions for a business evaluation
Does it change decisions for the better?
The registered tests compare Hexis with the specified model-side baselines at matched compute. A business also needs a comparison with the workflow controls it already uses, on premature action, unnecessary delay and appropriate escalation. That comparison is not among the paper’s registered tests; it is the evaluation we invite partners to design.
Can its controls be relied on?
Test the execution boundary, a stop during escalation and the completeness of the record, including failures and awkward timing.
Is the benefit worth the operational burden?
Measure the whole task: extra turns, routing, retrieval, latency, integration effort and human intervention. Matched compute alone does not establish lower operating cost.
What participation would involve
Start with one decision that matters.
Think of one point in your work where acting too early, waiting too long or referring the decision to someone else has consequences. What information is available at that moment? What could change the decision? What would convince you that another approach worked better?
Bring that decision. Together we can define the evidence an adoption decision would need.
Architecture route
Evaluate Hexis and Yarrow
Help design the comparison the registered tests leave open: Hexis against the controls your workflow already uses, such as approval steps, rule engines and human sign-off. Together we would scope one workflow: its permissions, a credible comparison and the integration effort. For organisations adopting agents, solution integrators and platform providers.
Instrument route
Help validate TAI
Contribute domain or evaluation expertise: realistic decisions, independent judgement and tests for confounds. Taking part does not require adopting the Hexis architecture.
A useful first message is a non-confidential description of one workflow or validation question, the route that interests you, and a technical or domain contact. Arrangements for contributing data would be agreed before collection, under the programme’s approved protocols.
Write to Us: hello@trigrammatic.ai
Read further
Companion guide
The full reading copy: the worked example, what the architecture adds, the claims and their refuters, and the route to release.
Download the companion (PDF) 108 KB
Research paper
Herko, S. and Pidcock, C. (2026). Hexis: a fixed 64-state structure for governing cognitive disposition in language-model agents — definitions, structural results and a pre-registered programme.