Pascal's Triangle Explorer mechanism

Model scope

The recurrence itself is standard and correct for interior Pascal entries, but the specification is not complete enough for an unambiguous implementation or verification. Define the row convention, base cases, input constraints, Fibonacci highlighting rule, and numeric-size limits before release.

• The recurrence C(n,k)=C(n-1,k-1)+C(n-1,k) is correct only for interior entries where 1 <= k <= n-1; boundary conditions C(n,0)=C(n,n)=1 and the initial row C(0,0)=1 are missing.
• The input description 'number of rows' is ambiguous: it could mean rows 0 through n, giving n+1 rows, or exactly n rows. The test vectors assume exactly R rows indexed 0 through R-1.
• The claimed Fibonacci diagonal pattern is not defined precisely. The vectors use the conventional shallow-diagonal sums 1, 1, 2, 3, 5, 8, ...; the specification should define which entries are highlighted.
• The powers-of-2 pattern is correctly implied by the row-sum identity sum(k=0..n) C(n,k)=2^n, but the row-index convention must be stated.

Units and conventions

• The row-count input is a dimensionless, finite, nonnegative integer.
• Rows are zero-indexed: row 0 is [1], and an input R requests exactly rows 0 through R-1.
• Binomial coefficients and row sums are exact integers. In JavaScript, sufficiently large rows will exceed Number's exact-integer range unless BigInt or another exact-arithmetic strategy is used.
• There are no physical units; all values are pure integers.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "number_of_rows": 0,
    "row_convention": "exactly R rows, zero-indexed"
  },
  "expected_outputs": {
    "triangle": [],
    "row_sums": [],
    "fibonacci_diagonal_sums": [],
    "powers_of_2_row_sums": []
  },
  "working": "R = 0, so there are no generated rows. No recurrence is evaluated, and all output sequences are empty."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The row-count convention is unspecified, so input 3 can validly be interpreted as either three rows or rows 0 through 3. Negative row counts also require explicit rejection to avoid undefined generation.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json