Description
Sample validated practice cases for Beat Error Milliseconds from an explicit candidate bank, returning separate prompts and calculator answers with repeat policy and replay metadata.
A worked-example generator selects educational cases from a finite bank supplied by the user. It validates those cases with an existing calculator and returns prompts separately from calculated answers. Sampling changes which eligible cases appear; it does not create a new scientific model or invent measurements.
Watch measurements depend on conventions such as beats versus full oscillations, gauge pressure versus physical depth, and the units used for periods or dimensions. A chosen arithmetic model does not measure a movement or establish its condition.
Calculator model: Timegrapher beat error as half the absolute difference between alternating long and short beat intervals.1
When to use this tool
Use this generator when you already have candidate Beat Error Milliseconds inputs and want reproducible practice prompts with separately available calculator answers.
How to use the tool and how it works
- Prepare candidatesJson as distinct {id,input} records using the calculator fields and units below. Choose a replay seed, exercise count and repeat policy.
- Run the generator and read result.status and result.rejected before using the exercise list. Correct or deliberately exclude rejected candidates.
- Read each exercise’s prompt and separate answer. Keep result.model and result.replay with exported examples so units, source calculator and repeat policy remain explicit.
Validate each explicit candidate {id,input} through horology/beat-error-milliseconds before sampling. Keep successful prompt/answer pairs and structured rejection records. Sample eligible IDs uniformly with the explicit replacement policy using one advancing source, then return separate prompt and actual calculator answer data with original indexes and model ports. Equal answers do not merge distinct candidate IDs.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| 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. |
| count | Requested exercise count, integer 1–32. | Finite safe integer satisfying the stated bounds. |
| withoutReplacement | True selects distinct eligible candidate IDs; false allows an eligible ID to recur. | Boolean true or false. |
| candidatesJson | JSON text for at most 128 exact {id,input} records. id is a nonempty distinct string; input is an object for the linked calculator using the candidate fields below. Equal inputs/answers may have different IDs. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
Every candidate is evaluated before selection. count is 1–32; candidatesJson contains at most 128 records with exactly id and input keys. Duplicate or empty IDs, malformed bank records and invalid outer fields cause an input error. A base-calculator failure is retained in rejected rather than silently discarded.
If no candidate succeeds, status is empty-eligible-bank. If distinct selection requests more cases than succeed, status is insufficient-eligible-bank. Both return no exercises. Otherwise status is ok. Every selected answer is the actual output object of the linked calculator, not a fabricated answer inferred from a prompt.
| Candidate input field | Meaning | Required / type and units |
|---|---|---|
| longIntervalMilliseconds | Long Interval Milliseconds | Required. number; unit: ms |
| shortIntervalMilliseconds | Short Interval Milliseconds | Required. number; unit: ms |
| Answer field | Meaning | Declared type and units |
|---|---|---|
| beatErrorMilliseconds | Beat Error Milliseconds | number; unit: ms |
These decoded structures show the examples inside JSON text fields. Supply their serialized JSON strings as input.
{
"candidatesJson": [
{
"id": "canonical",
"input": {
"longIntervalMilliseconds": 125.5,
"shortIntervalMilliseconds": 124.5
}
}
]
}| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.status | ok, empty-eligible-bank or insufficient-eligible-bank. Non-ok banks return no exercises. |
| result.baseToolId | Canonical calculator ID used to validate and answer every candidate. |
| result.model | Underlying calculator description and actual input/output port definitions, including declared units. |
| result.replay | Seed, source kind, requested count/replacement policy and actual selection-source call count. |
| result.eligibleCandidateIds | All successfully validated candidate IDs in original candidate-bank order. |
| result.rejected | Original candidate ID/index and structured calculator or evidence-budget error. |
| result.exercises | Selected {candidateId,sourceIndex,prompt,answer} records in draw order; answers are actual calculator output objects. |
{
"input": {
"seed": "batch56-example",
"count": 1,
"withoutReplacement": true,
"candidatesJson": "[{\"id\":\"canonical\",\"input\":{\"longIntervalMilliseconds\":125.5,\"shortIntervalMilliseconds\":124.5}}]"
},
"output": {
"result": {
"status": "ok",
"baseToolId": "horology/beat-error-milliseconds",
"model": {
"description": "Timegrapher beat error as half the absolute difference between alternating long and short beat intervals.",
"inputs": [
{
"id": "longIntervalMilliseconds",
"label": "Long Interval Milliseconds",
"required": true,
"valueType": {
"unit": "ms",
"type": "number"
}
},
{
"id": "shortIntervalMilliseconds",
"label": "Short Interval Milliseconds",
"required": true,
"valueType": {
"unit": "ms",
"type": "number"
}
}
],
"outputs": [
{
"id": "beatErrorMilliseconds",
"label": "Beat Error Milliseconds",
"valueType": {
"unit": "ms",
"type": "number"
}
}
]
},
"replay": {
"seed": "batch56-example",
"source": "seeded",
"count": 1,
"withoutReplacement": true,
"draws": 1
},
"eligibleCandidateIds": [
"canonical"
],
"rejected": [],
"exercises": [
{
"candidateId": "canonical",
"sourceIndex": 0,
"prompt": {
"longIntervalMilliseconds": 125.5,
"shortIntervalMilliseconds": 124.5
},
"answer": {
"beatErrorMilliseconds": 0.5
}
}
]
}
}
}Limitations and assumptions
- This is practice selection over a supplied finite bank, not a new model or automatic scenario generator. The underlying calculator’s input constraints, units, approximations and limitations apply. Empty or too-small eligible banks are returned as explicit status values without invented exercises.
- 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.
- Candidate inputs and answers remain subject to the linked calculator’s model assumptions. The sampler tests its executable contract, not real-world truth, calibration, fitness for a decision or scientific validity.
- Candidates whose prompt/answer exceed portable evidence bounds are rejected with a structured evidence-budget error. The complete selected output also has a bounded size and can fail if the combined evidence exceeds it.
- 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
Use the linked calculator to inspect an individual candidate directly. Use this generator to select and package already supplied cases; build or review the exercise bank separately so topic coverage and difficulty reflect the teaching objective.
References
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