Add shared vector linear-recurrence optimization for multi-array NaturalArray loops

[Copilot]

This change extends recurrence optimization from single-array linear recurrences to N interconnected recurrences in one loop. It detects multi-assignment recurrence systems, builds a shared vector recurrence model, and evaluates per-array terms via shared rolling state for sequential access.

• Vector recurrence model (new formula type)

  • Added VectorRecurrenceFormula to represent coupled recurrences across multiple arrays.
  • Supports:
    • dimension m (number of arrays/sequences)
    • order k (max lag)
    • constant vector
    • seed matrix
    • companion-matrix fallback for non-sequential/random access
  • Uses shared rolling state for sequential i -> i+1 evaluation.

• NaturalArray integration

  • Added vector recurrence bindings in NaturalArray (formula + sequenceIndex).
  • Added vector recurrence evaluation path before scalar recurrence formulas.
  • Multiple arrays can now share one recurrence model while each array resolves its own sequence slot.

• Loop optimizer: vector detection + extraction

  • Extended LoopOptimizationHandler to detect loop bodies with multiple assignments of form arr[i] = ....
  • Enforces linear structure over lagged indexed terms and extracts:
    • coefficient tensor (flattened to matrix form)
    • constant vector
    • recurrence start + seed window
  • Emits a new vector recurrence pattern for pattern application.

• Pattern application

  • Extended PatternHandler with VECTOR_LINEAR_RECURRENCE.
  • Builds one shared VectorRecurrenceFormula per detected system and attaches it to all target arrays with stable sequence indices.

• Coverage

  • Added VectorLinearRecurrenceOptimization.cod with coupled recurrence systems (including mixed lags and constant terms).

for i of [2 to N] {
    a[i] = a[i-1] + b[i-1]
    b[i] = a[i-1] - b[i-1]
}

This loop is now recognized as a single vector recurrence system and optimized as shared state instead of independent per-array fallback evaluation.