Magic Square / Latin Square Generator mechanism

Model scope

The specification is not sufficient to certify deterministic generation or complete verification semantics. The honest_label field is empty; it should disclose that generated-square orientation may vary and that supported orders and symbol conventions are explicitly constrained.

• The Siamese method is named but not specified precisely enough to verify its movement rules, wraparound behavior, starting cell, or tie-breaking behavior.
• The LUX method is named but no LUX pattern construction, block ordering, or symbol-permutation rules are provided, so its generated output cannot be independently verified.
• Doubly-even magic-square generation is claimed, but no construction method or formula for orders divisible by 4 is specified.
• The magic-constant formula is omitted; for a normal n×n magic square containing 1 through n², it should be M=n(n²+1)/2.
• Latin-square verification is underspecified: the required symbol set, whether symbols must be exactly 1 through n, and whether only rows and columns or also other properties are checked are not stated.

Units and conventions

• n is a positive integer order; there are no physical units.
• A normal magic square is assumed to contain each integer from 1 through n² exactly once.
• A normal magic square is assumed valid only when every row, every column, and both principal diagonals sum to n(n²+1)/2.
• Latin-square inputs are assumed to use exactly the symbols 1 through n, with each symbol occurring once in every row and column.
• Singly-even order means n is divisible by 2 but not by 4; doubly-even order means n is divisible by 4.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "operation": "generate_magic",
    "order": 1
  },
  "expected_outputs": {
    "square": [
      [
        1
      ]
    ],
    "magic_constant": 1,
    "valid": true
  },
  "working": "Magic constant: M=1(1²+1)/2=1(2)/2=1. The only row, column, and both diagonals contain 1, so each sums to 1. The square is valid."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The extreme-order vector exposes an unsafe acceptance path: n=1,000,000,000 requires 10^18 cells, exceeds JavaScript safe-integer precision, and cannot be practically allocated. The Latin-square vector also exposes an unresolved zero-based versus one-based symbol convention that can change the validity result.

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