Local Carry Rules

Abstract

Four local Fibonacci carry rules preserve the value of finite raw W digits.

D5/S1/Digit/Carry defines the local, value-preserving carry rewrites on raw W-digit strings: adjacent ones merge upward, and doubled coefficients split by the Fibonacci identities for indices zero, one, and the general shifted case. Each rule carries its own value-preservation theorem against rawValue.

Termination and the normalization map are deliberately absent here; they live in D5/S1/Digit/Normalize with an explicit well-founded measure, so no rule in this file claims more than one local step.

References

• Dependency: D5/S1/Digit/Raw