Alphabet & Symbols¶

Every symbol in AXL has been validated as a single token against the cl100k_base tokenizer (used by GPT-4, GPT-4o, and Claude's tokenizer family). This ensures maximum compression: no symbol wastes token budget through multi-token encoding.

Single-Token Symbols¶

These Unicode symbols each encode as exactly one token in cl100k_base.

Mathematical & Logical Operators¶

Symbol	Unicode	Name	AXL Usage
`π`	U+03C0	Pi	Payment proof prefix
`µ`	U+00B5	Micro	Micro-transaction marker
`τ`	U+03C4	Tau	Temporal reference
`×`	U+00D7	Multiplication	Cross-product / combination
`~`	U+007E	Tilde	Approximation / similarity

Directional Arrows¶

Symbol	Unicode	Name	AXL Usage
`→`	U+2192	Right arrow	Flow direction / output
`←`	U+2190	Left arrow	Input / source reference
`↑`	U+2191	Up arrow	Escalation / increase
`↓`	U+2193	Down arrow	De-escalation / decrease

Verification¶

import tiktoken

enc = tiktoken.get_encoding("cl100k_base")

symbols = ["π", "µ", "τ", "→", "←", "↑", "↓", "×", "~"]
for sym in symbols:
    tokens = enc.encode(sym)
    assert len(tokens) == 1, f"{sym} encodes as {len(tokens)} tokens"
    print(f"{sym} -> token {tokens[0]} (1 token)")

Compound Operators¶

Two-character operators formed from ASCII characters. Each operator is 2 tokens but semantically dense.

Comparison Operators¶

Operator	Meaning	Example
`==`	Equals	`status==active`
`!=`	Not equals	`state!=healthy`
`>=`	Greater than or equal	`cpu>=90`
`<=`	Less than or equal	`latency<=100ms`
`>`	Greater than	`tier>3`
`<`	Less than	`priority<2`

Flow Operators¶

Operator	Meaning	Example
`->`	ASCII right arrow	`agent->relay`
`<-`	ASCII left arrow	`result<-query`
`=>`	Implies / maps to	`error=>retry`

Mutation Operators¶

Operator	Meaning	Example
`++`	Increment	`retry_count++`
`--`	Decrement	`ttl--`
`+=`	Add-assign	`budget+=500`
`-=`	Subtract-assign	`balance-=250`

Logical Operators¶

Operator	Meaning	Example
`&&`	Logical AND	`cpu_high&&mem_high`
`\\|\\|`	Logical OR	`timeout\\|\\|error`
`!!`	Emphasis / double-flag	`!!CRITICAL`

Domain Words¶

Reserved uppercase words used in the S:DOMAIN.TIER header. Each is a single token in cl100k_base.

Core Domains¶

Word	Meaning	Token Count
`OPS`	Operations	1
`ERR`	Error	1
`FAIL`	Failure	1
`LOG`	Logging	1
`SIG`	Signal/Security	1
`PAY`	Payment	1
`ACK`	Acknowledgment	1
`CMD`	Command	1
`QRY`	Query	1
`RSP`	Response	1

Flag Words¶

Word	Meaning	Token Count
`ALERT`	Trigger alert	1
`ROUTE`	Route to handler	1
`ESCALATE`	Escalate priority	1
`RETRY`	Retry operation	1
`FREEZE`	Freeze resources	1
`BATCH`	Batch operation	1
`SYNC`	Synchronize	1
`ASYNC`	Asynchronous	1

Semantic Words¶

Word	Meaning	Token Count
`NULL`	No value	1
`TRUE`	Boolean true	1
`FALSE`	Boolean false	1
`PASS`	Test passed	1
`WARN`	Warning	1
`CRIT`	Critical	1
`INFO`	Informational	1
`DEBUG`	Debug-level	1
`TRACE`	Trace-level	1

Infrastructure Words¶

Word	Meaning	Token Count
`CPU`	Processor	1
`MEM`	Memory	1
`DISK`	Storage	1
`NET`	Network	1
`DNS`	Domain name system	1
`HTTP`	Protocol	1
`TCP`	Transport protocol	1
`UDP`	Datagram protocol	1
`TLS`	Transport security	1
`API`	Interface	1

Economic Words¶

Word	Meaning	Token Count
`USDC`	Stablecoin	1
`ETH`	Ether	1
`GAS`	Transaction cost	1
`FEE`	Fee	1
`STAKE`	Staked value	1
`BOND`	Bonded value	1

Validation Summary¶

Total validated symbols: 77
Tokenizer: cl100k_base (tiktoken)
Constraint: Every symbol, domain word, and flag word must encode as exactly 1 token
Method: Automated validation script run against the full alphabet on every release

import tiktoken

enc = tiktoken.get_encoding("cl100k_base")

# Full alphabet validation
alphabet = [
    "π", "µ", "τ", "→", "←", "↑", "↓", "×", "~",
    "OPS", "ERR", "FAIL", "LOG", "SIG", "PAY", "ACK", "CMD", "QRY", "RSP",
    "ALERT", "ROUTE", "ESCALATE", "RETRY", "FREEZE", "BATCH", "SYNC", "ASYNC",
    "NULL", "TRUE", "FALSE", "PASS", "WARN", "CRIT", "INFO", "DEBUG", "TRACE",
    "CPU", "MEM", "DISK", "NET", "DNS", "HTTP", "TCP", "UDP", "TLS", "API",
    "USDC", "ETH", "GAS", "FEE", "STAKE", "BOND",
    # ... remaining words validated in CI
]

failures = []
for word in alphabet:
    tokens = enc.encode(word)
    if len(tokens) != 1:
        failures.append(f"{word}: {len(tokens)} tokens")

assert len(failures) == 0, f"Validation failures: {failures}"
print(f"All {len(alphabet)} symbols validated as single tokens.")