Sort Key Tie Stability Audit

Audit only tie-order stability of an explicit numeric sort permutation, independently of whether the keys themselves are sorted.

Description

Audit only tie-order stability of an explicit numeric sort permutation, independently of whether the keys themselves are sorted.

A reordering can preserve sorted values while reversing equal-key items. Tie stability is a separate property from sortedness.

When to use this tool

Audit only tie-order stability of an explicit numeric sort permutation, independently of whether the keys themselves are sorted.

Prepare the supplied values, permutation fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter values, permutation. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.stable, result.reversedTiePairs. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Validate a same-length permutation of source indexes. For each pair in output order, report original indexes that have equal values but occur in descending source-index order. stable means no such pair exists.^[1]

Input field	Meaning and representation	Accepted input
values	values.	List of finite numbers; at most 128 entries
permutation	permutation.	List of finite numbers; at most 128 entries

Output field	Interpretation
result	Object containing the named outputs below.
result.stable	Flag for stable under the exact condition described above.
result.reversedTiePairs	The reversed tie pairs list in the ordering and representation described above.

json

{
  "input": {
    "values": [
      30,
      10,
      10,
      20
    ],
    "permutation": [
      2,
      1,
      3,
      0
    ]
  },
  "output": {
    "result": {
      "stable": false,
      "reversedTiePairs": [
        [
          2,
          1
        ]
      ]
    }
  }
}

Limitations and assumptions

The tool checks tie stability only and does not establish that all keys are sorted. Use a sort verifier when both properties are required.
All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.

Alternative or Complementary methods

Choose the tie policy and whether you need values, original indexes, sorted positions or one-based ranks. Use a complete sort verifier when a local stability or adjacent-comparison check is insufficient.

References

Tool behavior and example: Sort Key Tie Stability Audit — tool.io

Similar or alternative tools

Bottom K Cutoff Tie Partitioner
Partition a numeric bottom-K cutoff into strict selections and all tied candidates, reporting how many ties are needed without arbitrarily breaking them.
Competition Rank Tie Table
Assign one-based ascending competition numeric ranks; exact numeric ties are preserved according to the stated policy.