Opaque Key Fixed Alphabet Inverse

Description

Decode an exact nonnegative ordinal into a caller fixed-width opaque alphabet key; rejects overflow rather than growing the key or truncating leading symbols.

An opaque key’s representation can affect equality and ordering even when its underlying value is unchanged. Delimiter joining can be ambiguous, fixed-width padding can preserve numeric order within agreed bounds, and typed length-prefix framing keeps scalar types distinct. Lengths in this family count UTF-16 code units unless a different unit is stated.

Decode an exact nonnegative ordinal into a caller fixed-width opaque alphabet key; rejects overflow rather than growing the key or truncating leading symbols.

When to use this tool

Use this tool to decode an exact nonnegative ordinal into a caller fixed-width opaque alphabet key; rejects overflow rather than growing the key or truncating leading symbols.

How to use the tool and how it works

Enter ordinal, alphabet, width using the field definitions below.
Run the operation. Correct input errors before interpreting an output.
Read result.key. Use the ordering, boundary rules and absence conditions described below.

Require a nonnegative exact ordinal below alphabetLength to the power width, then repeatedly divide by the alphabet size to construct exactly width code units.^[1]

Input field	Meaning and units	Accepted input
ordinal	Nonnegative exact integer ordinal as decimal text.	Text, at most 8,192 UTF-16 code units; the operation’s grammar also applies.
alphabet	Ordered distinct UTF-16 code units used as allowed symbols or base digits.	Text, at most 8,192 UTF-16 code units; the operation’s grammar also applies.
width	Required UTF-16 width or decimal padding width under the stated operation.	A finite safe integer within the operation’s stated bounds.

Output field	Interpretation
result	Object containing the named fields below.
result.key	Encoded, normalized-affix or padded key under the stated framing/ordering convention.

json

{
  "input": {
    "ordinal": "3",
    "alphabet": "abc",
    "width": 2
  },
  "output": {
    "result": {
      "key": "ba"
    }
  }
}

Limitations and assumptions

Width restores leading zero-symbols and must be 0–128; the alphabet convention must match the encoder.
String framing and alphabet digits use UTF-16 code units, not bytes or grapheme clusters. Exact integer text accepts a signed decimal spelling of at most 256 digits before operation-specific range checks.
Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.

Alternative or Complementary methods

Use typed framing when distinct scalar types or tuple boundaries must remain distinguishable. Keep alphabet, width, normalization and numeric bounds consistent between producers and consumers.

References

Tool behavior and example: Opaque Key Fixed Alphabet Inverse — tool.io

Similar or alternative tools

Opaque Key Fixed Alphabet Ordinal
Encode a fixed-width opaque key as a zero-based positional integer in an explicitly ordered unique UTF-16 alphabet; leading alphabet-zero symbols remain width evidence.
Opaque Key Alphabet Audit
Audit opaque key UTF-16 code units against an explicit caller alphabet with positions; not Unicode grapheme, entropy or checksum validation.