Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
A perfectly retained bit gives zero conditional entropy reset bound
A calculated finite correlated-memory model illustrating the theorem's retained-register condition; no measurement or reset apparatus is described.
Example
Take memory and register bits M,R∈{0,1} with joint law p(0,0)=p(1,1)=1/2 and all other probabilities zero. Retain R and reset M to 0.
Facts & Assumptions
Given: The finite joint law and the physical assumptions of Conditional work bound for finite memory reset.
Conditional entropy of finite memory given side information: H(M,R)=H(R)+H(M∣R).
Conditional work bound for finite memory reset: the reset work bound uses H(M∣R), not H(M).
Verification
Given: The specified perfectly correlated two-bit distribution.
The memory marginal is uniform, so H(M)=log2. Given either value of R, the conditional law of M is a point mass; hence each conditional entropy is zero and H(M∣R)=0.
Therefore the theorem yields only W≥0 for this reset under its stated thermodynamic assumptions, while the unconditioned memory entropy is log2. It does not imply a kBTblog2 lower bound for this correlated preparation.