ZODA Sizing & Proofs — Tensor vs Hadamard

https://chatgpt.com/canvas/shared/6932b87fc41481918c7d43a54f743278

https://chatgpt.com/canvas/shared/693bc241917c819192f5bae040e4a0db

Common notation

• d = blob size in bytes
• n = number of subnetworks (also matrix size in Tensor)
• ceil(x) = ceiling of x
• depth = ceil(log2(n)) (binary Merkle tree)
• Hash size = 32 bytes
• Security trigger: warn if 2^k / n < 2^50 ⇔ k − log2(n) < 50
  • Minimum k to meet target: k_min = ceil(50 + log2(n))

ZODA — Tensor (2D RS)

Idea: Extend data in two directions (rate 1/2 along rows and columns). Total encoded size is 4·d bytes, arranged in an n × n square matrix. Each matrix entry (“chunk/symbol”) is one field element in F_{2^k}.

Inputs

• Blob size: d bytes
• Matrix size: n × n (with n = number of subnetworks)
• Field: F_{2^k} where one entry = k bits = ceil(k/8) bytes

Expansion

• Total encoded size: 4·d bytes

Entry (chunk) size and field bits

• Total entries: n^2