Source: https://guthlabs.ai/docs/instruments/magic-square-latin-square-generator/

instrument / verified-clean

# Magic Square / Latin Square Generator

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

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/magic-square-latin-square-generator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/magic-square-latin-square-generator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/magic-square-latin-square-generator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/magic-square-latin-square-generator/qualification/>)

## 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**: t4-237

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## 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": {
    "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."
}
````

## 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`