Pascal's Triangle Explorer

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

Tranche

tranche-4

Evidence ID

t4-105

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

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