Description
Emit state[0] and return the nonempty state's remaining entries followed by supplied next.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Emit state[0] and return the nonempty state's remaining entries followed by supplied next.
When to use this tool
Use Recurrence Initial State Shift Step when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter state, next. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read state, emitted. Use the output convention below.
Emit state[0] and return the nonempty state's remaining entries followed by supplied next.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| state | Oldest-first queue: first value emitted, next appended. | Required. Array of finite number; maximum items 256. |
| next | Next | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| state | Oldest-first queue: first value emitted, next appended. | Required. Array of finite number; maximum items 256. |
| emitted | Emitted | Required. Finite number. |
{
"input": {
"state": [
1,
2,
3
],
"next": 5
},
"output": {
"state": [
2,
3,
5
],
"emitted": 1
}
}Limitations and assumptions
- This uses an oldest-first queue convention and does not calculate next from a recurrence. State values, recurrence coefficients, and consistency with other state-order conventions are not verified.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Recurrence Delay State Shift Index
Return nextIndex=index+1 for a bounded state index except the final position, which returns minus one and dropped true.
- Sequence: Linear Recurrence First Difference Step
Advance one short real linear recurrence with oldest-to-newest state and matching coefficient order, returning next state and its first difference; no symbolic recurrence solving.