Description
Calculate expected=period*fullCycles+partialSlots and missing=expected-observed.
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.
Calculate expected=period*fullCycles+partialSlots and missing=expected-observed.
When to use this tool
Use Periodic Cycle Missing Slot Budget 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 period, observed, fullCycles, partialSlots. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read expected, missing. Use the output convention below.
Calculate expected=period*fullCycles+partialSlots and missing=expected-observed. Require positive integer period, feasible nonnegative counts, partial slots below period, and a safe-integer expected total.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| period | Period | Required. Safe integer; minimum 1. |
| observed | Observed | Required. Safe integer; minimum 0. |
| fullCycles | Full Cycles | Required. Safe integer; minimum 0. |
| partialSlots | Partial Slots | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| expected | Expected | Required. Safe integer. |
| missing | Missing | Required. Safe integer. |
{
"input": {
"period": 7,
"observed": 18,
"fullCycles": 3,
"partialSlots": 0
},
"output": {
"expected": 21,
"missing": 3
}
}Limitations and assumptions
- This is a count budget, not verification of which slots were recorded. Duplicate observations, actual periodicity, and missing-value positions are not determined.
- 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
- Sequence: Periodic Index Quotient Remainder
Decompose a signed sequence index into floor quotient and nonnegative within-period phase, retaining negative cycle numbers.
- Periodic Interleaving Phase Source Index
Return stream=globalIndex%streams and sourceIndex=floor(globalIndex/streams) for nonnegative integer global index and positive stream count.