Description
Generate fair independent unit-step proposals and reflect outward steps inward at either endpoint in an explicit bounded integer interval; every step consumes a proposal, including steps taken from a boundary.
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.
Generate fair independent unit-step proposals and reflect outward steps inward at either endpoint in an explicit bounded integer interval; every step consumes a proposal, including steps taken from a boundary.
When to use this tool
Use this tool to generate fair independent unit-step proposals and reflect outward steps inward at either endpoint in an explicit bounded integer interval; every step consumes a proposal, including steps taken from a boundary.
How to use the tool and how it works
- Enter initial, minimum, maximum, steps, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.states, result.proposals, using the stated boundary, ordering, sign and absence conventions.
Draw independent ±1 proposals. An outward proposal below minimum reflects to minimum+1 and one above maximum reflects to maximum−1; other proposals advance normally. Return proposals and initial-plus-step states.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| initial | Initial integer state within the explicitly supplied counter/walk bounds. | Finite safe integer satisfying the stated bounds. |
| minimum | Inclusive integer state lower bound within ±1,000,000. | Finite safe integer satisfying the stated bounds. |
| maximum | Inclusive integer state upper bound within ±1,000,000. It must be at least minimum; a reflecting walk requires it to be strictly greater. | Finite safe integer satisfying the stated bounds. |
| steps | Number of transitions, integer 1–127; the states output includes the initial state as well. | 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.states | State sequence including the initial coordinate followed by every transition. |
| result.proposals | Independent signed ±1 proposals before reflection. |
{
"input": {
"initial": 1,
"minimum": 0,
"maximum": 2,
"steps": 3,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"states": [
1,
2,
1,
2
],
"proposals": [
1,
1,
1
]
}
}
}Limitations and assumptions
- Integer bounds lie within ±1,000,000 with maximum>minimum and steps 1–127. The support is proposal sequences, not uniform state paths.
- 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
Similar or alternative tools
- Random Fixed-Endpoint Unit Walk
Uniformly sample all unit-step walks with specified start/end and step count by choosing exactly the required up-step subset; impossible endpoint/parity requests reject.
- Random Specified Bit-Length Integer
Generate an exact unsigned integer with a specified positive bit length, setting the top bit and drawing remaining bits independently; integer text avoids unsafe numbers.