Random Two-Level Run Trace

Description

Choose a fair initial level and independent uniform run lengths, then alternate two explicit distinct levels; support is level/run assignments, not uniform over all bounded traces.

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 a fair initial level and independent uniform run lengths, then alternate two explicit distinct levels; support is level/run assignments, not uniform over all bounded traces.

When to use this tool

Use this tool to choose a fair initial level and independent uniform run lengths, then alternate two explicit distinct levels; support is level/run assignments, not uniform over all bounded traces.

How to use the tool and how it works

Enter low, high, runs, minimum, maximum, seed using the definitions below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.seed, result.initialHigh, result.runs, result.values, using the stated boundary, ordering, sign and absence conventions.

Choose the initial low/high level with one fair binary draw, then draw every run length independently and uniformly in [minimum,maximum]. Alternate the two levels and return both run records and expanded values.^[1]

Input field	Meaning and units	Accepted input
low	First finite output level; it must differ from high.	Finite numeric value satisfying the stated comparisons.
high	Second finite output level; it must differ from low.	Finite numeric value satisfying the stated comparisons.
runs	Number of alternating runs, integer 1–128; runs×maximum must not exceed 128.	Finite safe integer satisfying the stated bounds.
minimum	Inclusive positive run/chunk-length lower bound, integer 1–128.	Finite safe integer satisfying the stated bounds.
maximum	Inclusive positive run/chunk-length upper bound, integer 1–128. It must be at least minimum; a reflecting walk requires it to be strictly greater.	Finite safe integer satisfying the stated bounds.
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.

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.initialHigh	Whether the first alternating run uses the supplied high level.
result.runs	Alternating numeric level/positive integer length records.
result.values	Generated/reordered literal values, preserving the stated positional support.

json

{
  "input": {
    "low": 0,
    "high": 1,
    "runs": 3,
    "minimum": 1,
    "maximum": 2,
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "initialHigh": true,
      "runs": [
        {
          "value": 1,
          "length": 2
        },
        {
          "value": 0,
          "length": 2
        },
        {
          "value": 1,
          "length": 2
        }
      ],
      "values": [
        1,
        1,
        0,
        0,
        1,
        1
      ]
    }
  }
}

Limitations and assumptions

Levels must differ. runs and lengths are 1–128 with runs×maximum≤128; the construction is not uniform over all arbitrary traces of a bounded total length.
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 Two-Level Run Trace — tool.io

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