Structural data

AXIS is a grammar.
Not a prompt library.

A prompt library contains examples. AXIS generates them. This page documents the structural evidence: correction loop cost, exchange efficiency, cross-system convergence, and category definition.

I. Illustrative model
The real cost isn't one bad prompt. It's the loop.

In unstructured exchanges, users rarely get what they need on the first turn. Each correction forces the model to reprocess the entire prior context while generating new output. Token usage compounds, not linearly, but recursively.

Unstructured exchange
1 User → vague prompt
2 AI → misinterpretation
3 User → correction
4 AI → partial fix
5 User → clarification
6 AI → drift
7-10+ loop continues
AXIS exchange
1 User → precise instruction
2 AI → correct output
,

Token cost by turn count — illustrative model with stated assumptions

TurnsEst. total tokensvs. 2-turn baselineEst. cost (GPT-4o example)
2 (AXIS)~400baseline~$0.001
4~1,400+250%~$0.004
6~3,200+700%~$0.010
10~9,000++2,150%~$0.027

Token estimates are illustrative. They assume typical chat model behavior where each turn reprocesses prior context plus generates new output. Actual totals vary by model, system prompt length, tool traces, and message length. Cost figures use a single public model's pricing as a reference example only and will change as pricing evolves; the structural pattern — that cost compounds nonlinearly with turn count — holds across models regardless of the specific rate.

II. Cross-system field observation
Eight independent systems. Consistent directional effects.

AXIS was tested across eight AI architectures independently — no coordination between systems, no shared prompting context. Each reported the same directional effects: fewer turns, reduced drift, more bounded execution. The convergence across different training data, architectures, and providers is the primary evidence. This is field observation, not controlled experiment: the methodology is documented at method →

System Fewer turns Reduced drift Bounded execution
GPT (OpenAI)✓✓✓
Claude (Anthropic)✓✓✓
Gemini (Google)✓✓✓
Mistral✓✓✓
Grok (xAI)✓✓✓
DeepSeek✓✓✓
Perplexity✓✓✓
Kimi✓✓✓

Effects reported independently across systems. Not coordinated. A public exchange archive is not yet available; methodology and limitations are documented at method →

III. Conceptual proposition
Compositional grammar, not static index.
Prompt Library

Fixed entries
Indexed by use case
Static expansion
Finite outputs

AXIS

Compositional grammar
Operator-driven
Generative
Unbounded outputs

AXIS defines a language for prompts, not a list of them. The same ten operators produce different exchanges every time, depending on sequence, context, and natural language content.

Ten operators. Each exchange selects from them in sequence, with repetition. The structural vocabulary is small. The range of exchanges it can structure is not. This is what distinguishes a grammar from a library: the operators generate structure, they do not enumerate it.
IV. Observed data
Fewer turns. Less interpretation. Higher fidelity.
Unstructured

Turns: 2
Words: 439
Behavior: drift, reinterpretation, added content

AXIS Structured

Turns: 1
Words: 80
Behavior: direct execution, bounded scope

~82% reduction in word count. 1 turn instead of 2. Same task, more precise result. This is from a single documented exchange — a concrete illustration, not a general average.

Documented exchange — same task, same AI system

Without AXIS · 2 turns · 439 words

User: Can you look at this paragraph? I want to improve it in some way. Can you tell me 3 things that would make it stronger?

AI: This is a good paragraph with a clear intention and a generally positive tone. It communicates a sense of connection and shared experience… To strengthen it further, there are a few areas you might consider developing… [439 words, 2 turns to reach resolution]

With AXIS · 1 turn · 80 words

User:
|⌾| look at this paragraph, I want to improve it
|^| [paragraph text]
|.|
|+| tell me 3 things that would make it stronger
|o|

AI:
|v|
1. "Positive and meaningful way" is vague — specify the intended impact
2. "Different activities" is broad — clarify what those activities are
3. The goal statement repeats the opening — tighten it to one clear sentence
|o| [80 words, 1 turn]

One documented exchange shown above. Additional exchanges are in the research record; a public archive is in preparation.

V. Category
An interaction protocol layer.

AXIS operates at the layer between intent and execution, not at the application layer, not at the model layer. It structures how messages are formed before they are interpreted.

HTML  →  structures documents
SQL  →  structures queries
AXIS  →  structures human-AI exchange

It defines how interaction is formed, independent of system or model. The operators work on GPT, Claude, Gemini, Mistral, any system that accepts text input.

VI. Function
Reduce interpretation. Increase fidelity.

AXIS reduces the need for interpretation by making intent explicit at the point of transmission. Each operator marks the role of what follows, before the model processes it.

Less effort is spent inferring meaning. More effort is applied to execution. The result is more direct, more reliable exchange.