Трите бита за четност на Хеминг = адресът

Hamming(7,4) защитава 4 бита данни с точно 3 бита за четност; синдромът Е двоичен адрес на грешката. Квантовият код [[5,1,3]] насища 2⁴ = 16 = 3·5+1.

proof · Hamming's 3 parity bits = the address

Hamming(7,4) protects 4 data bits with EXACTLY 3 parity bits and corrects any single-bit error, because 3 check bits give 2³−1 = 7 syndromes covering all 7 positions — and the syndrome is literally a binary ADDRESS of the error location (Hamming 1950, BSTJ 29:147). The quantum analogue puts the same 3 (the 3 Pauli errors per qubit) inside the optimal-code bound 2^(n−k) ≥ 3n+1, saturated by the [[5,1,3]] perfect code (Laflamme et al. 1996, PRL 77:198).

checks — recomputed live in your browser

• ✓ Hamming Ok
• ✓ Quantum Bound Saturated
• ✓ Holds

evidence

Parity Bits

3

Positions

7

Data Bits

4

✓ all checks hold · recompute recipe — a pure function of the model seed, run client-side with zero tokens; the same seed always folds to the content-address 1e8363ef-f8ac-889d-8aa7-7e813d868fcd. Recompute and you get the same address — that determinism is the proof.

A genuine, non-numerological "3" linking error-correction to content-addressing: the syndrome IS an address. This is engineering arithmetic — explicitly distinct from the Rodin/Tesla 3-6-9 vortex narrative, which is base-10 numerology with no peer-reviewed standing and an unsourced Tesla quote.