Description
Return nextIndex=index+1 for a bounded state index except the final position, which returns minus one and dropped true.
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.
Return nextIndex=index+1 for a bounded state index except the final position, which returns minus one and dropped true.
When to use this tool
Use Recurrence Delay State Shift Index 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 stateLength, index. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read nextIndex, dropped. Inspect dropped before interpreting the associated values.
Return nextIndex=index+1 for a bounded state index except the final position, which returns minus one and dropped true. Require positive integer stateLength.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| stateLength | State Length | Required. Safe integer; minimum 1. |
| index | Zero-based index unless the mechanics explicitly state otherwise. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| nextIndex | Index shifted higher, or minus one for the dropped final position. | Required. Safe integer. |
| dropped | Dropped | Required. Boolean. |
{
"input": {
"stateLength": 4,
"index": 2
},
"output": {
"nextIndex": 3,
"dropped": false
}
}Limitations and assumptions
- This models a shift toward higher indices, not the oldest-first array shift used by every recurrence helper. No state data are transformed or recurrence values computed.
- 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 Companion State Index Map
Return shiftEntry one only for row>0 and column=row-1, and coefficientRow for row zero.
- Recurrence Initial State Shift Step
Emit state[0] and return the nonempty state's remaining entries followed by supplied next.