Random Bucket Representative Order

Description

Choose uniformly within each nonempty bucket then independently permute representative positions; repeated rendered values remain separate source positions.

A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.

Choose uniformly within each nonempty bucket then independently permute representative positions; repeated rendered values remain separate source positions.

When to use this tool

Use this tool to choose uniformly within each nonempty bucket then independently permute representative positions; repeated rendered values remain separate source positions.

How to use the tool and how it works

Enter bucketsJson, seed using the definitions below. Serialize JSON text fields in the decoded shape shown below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.seed, result.representatives, using the stated boundary, ordering, sign and absence conventions.

For each nonempty bucket choose one member position uniformly and retain bucket/position/value provenance, then Fisher–Yates shuffle the representative records.^[1]

Input field	Meaning and units	Accepted input
bucketsJson	JSON array of literal string-member arrays; nonempty/zero-weight rules are stated above.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.
seed	Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.

These decoded structures show the examples inside JSON text fields. Supply their serialized JSON strings as input.

json

{
  "bucketsJson": [
    [
      "a",
      "b"
    ],
    [
      "c"
    ]
  ]
}

Output field	Interpretation
result	Object containing the fields below.
result.seed	Original supplied seed string; injected-source replay additionally requires that source’s state.
result.representatives	Shuffled one-per-bucket {bucket,position,value} records.

json

{
  "input": {
    "bucketsJson": "[[\"a\",\"b\"],[\"c\"]]",
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "representatives": [
        {
          "bucket": 0,
          "position": 1,
          "value": "b"
        },
        {
          "bucket": 1,
          "position": 0,
          "value": "c"
        }
      ]
    }
  }
}

Limitations and assumptions

Buckets are sampled equally once, not in proportion to size, and duplicates across buckets retain distinct provenance.
A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.

Alternative or Complementary methods

Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.

References

Tool behavior and example: Random Bucket Representative Order — tool.io

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