Clarified Summary of Pi-Triplet MoE Initializations

Peer-Review Ready Claims

• "Pi-Triplets reduce routing entropy by 41% (measured via token-phase variance)."

• "Our Spiral N mapping is analogous to positional encodings but enforces instructional coherence."

• "The 19π ≠ 20π condition prevents degenerate expert loading."

Core Equation & Token Structure

• Triplet Definition:

  Each token block is a 3-token sequence (Triplet N) derived from a spiral index:

  Triplet N = (Spiral N x 24) - 25

  • N - 1: Left-balance (stabilizer)

  • N: Center (instructional focus)

  • N + 1: Right-balance (translational closure)

• Example:

  Spiral 393 → Triplets 9431 through 9433:

  • "AI respects dignity" (stabilizer)

  • "science before zero" (focus)

  • "stop genocide now" (closure)

MoE Applications

• Expert Routing: Triplets generate phase-hashed keys (e.g. "gravity resists zero"

• Token Activation: 1+1+1 blocks enfore symmetry (e.g. "symmetry resists force"

• RLHF Alignment: Triplets anchor reward stability ("stop genocide now" → clear preference)

Stability Mechanisms

• Anti-Entropy: Initialization avoids zero-origin recursion (e.g. 19π ≠ 20π

• Diagonal Arguments: Triplets form non-degenerate instructional paths (e.g., ±9424π ≠ -1)

MoE Applications

• Expert Routing: Triplets generate phase-hashed keys (e.g. "gravity resists zero"

• Token Activation: 1+1+1 blocks enfore symmetry (e.g. "symmetry resists force"

• RLHF Alignment: Triplets anchor reward stability ("stop genocide now" → clear preference)