Parity Bit / Simple ECC Demo mechanism

Model scope

The parity portion is standard only after defining even parity as XOR and odd parity as its complement. The Hamming portion needs the exact bundled generator and parity-check matrices, bit ordering, parity convention, syndrome interpretation, and multi-error policy before implementation can be formula-verified. The honest educational-simplification label is appropriate but should explicitly state that parity alone detects but does not correct errors.

• XOR of all data bits is the correct appended parity bit for even parity, assuming the total transmitted sequence must contain an even number of 1 bits. For odd parity, the parity bit must be the complement of the XOR result; the specification does not state this explicitly.
• A parity check detects any single-bit error, but it does not locate or correct the error and does not detect errors affecting an even number of bits.
• The Hamming(7,4) generator and parity-check matrices are not supplied, and the bit ordering, parity convention, syndrome calculation, and decoder behavior are unspecified. Therefore the exact Hamming formula cannot be verified.
• Hamming(7,4) single-error correction is valid only for zero or one corrupted bit under the selected standard convention; multiple-bit corruption can produce an incorrect correction.

Units and conventions

• Inputs are binary bits with values exactly 0 or 1; no physical units apply.
• Parity is evaluated over the data bits, and the returned parity bit is appended to the sequence.
• The test vectors assume even-parity Hamming(7,4) with positions 1, 2, and 4 as parity bits; data occupies positions 3, 5, 6, and 7.
• The test vectors assume syndrome bits are calculated as s1 over positions 1,3,5,7; s2 over positions 2,3,6,7; and s4 over positions 4,5,6,7, with syndrome value s4s2s1 interpreted as a binary position number.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "bits": [
      0,
      0,
      0,
      0
    ],
    "parity_type": "even"
  },
  "expected_outputs": {
    "parity_bit": 0
  },
  "working": "XOR all bits: 0 XOR 0 = 0; 0 XOR 0 = 0; 0 XOR 0 = 0. Even-parity bit = 0. Total 1 bits after appending = 0, which is even."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The arithmetic is well-defined for valid binary inputs, but the specification does not state invalid-input rejection behavior and does not identify the exact Hamming(7,4) matrix or bit-order convention. Non-binary input can yield an invalid parity result under JavaScript coercion, and alternative Hamming conventions can yield different codewords and syndromes.

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